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Математическое программирование vs RL: может ли ИИ догнать классику в оптимизации?

С определенным успехом методы математического программирования захватили множество задач автоматизации и оптимизации бизнес процессов (маршрутизация доставки, планирование производства или графиков работы сотрудников, планирование сетей и т.д.). Используемые методы решения и классические постановки задач десятилетиями остаются без серьезных изменений. Когда ждать революцию? Кто имеет потенциал для ее организации?

Проведем эксперимент на предмет того, есть ли у RL способности решать оптимизационные задачи. Для исследования возьмем не сложную практическую оптимизационную задачу и оценим как обучение с подкреплением справится.

Материал будет полезен как заядлым специалистам по мат.оптимизации, так и ml-инженерам или data scientist’ам. Рассматриваемая задача может быть интересна специалистам из области логистики/транспортных перевозок.

RL в комбинаторной оптимизации

Прогресс в области обучения с подкреплением строится на последовательном тестировании подходов: каждая новая задача становится испытанием, где успех закрепляется, а неудачи служат источником данных для доработки модели. Этот механизм проб и ошибок позволил адаптировать RL и к задачам комбинаторной оптимизации (CO).

В рамках CO методы RL используются двумя основными путями:

встраиваются в уже существующие алгоритмы, усиливая их возможности;
выступают как самодостаточная технология для поиска решений.

Интеграция RL с другими методами оптимизации.

Комбинаторные задачи часто имеют огромное пространство решений, что затрудняет поиск оптимального варианта. Интеграция обучения с подкреплением (RL) с традиционными методами оптимизации позволяет использовать сильные стороны каждого подхода: RL даёт адаптивность и способность обучаться на опыте, а классические алгоритмы — гарантированную сходимость и эффективные эвристики.

Основные стратегии интеграции:

RL как генератор начальных решений. RL-агент обучается генерировать «хорошие» начальные решения, которые затем уточняются с помощью точных методов (например, метода ветвей и границ или линейного программирования). Это сокращает время поиска глобального оптимума. Пример, в задаче коммивояжёра (TSP) RL может быстро построить маршрут, близкий к оптимальному, который затем дорабатывается локальным поиском или 2‑opt алгоритмом.
Гибридные алгоритмы с локальным поиском. RL выбирает направление улучшения (например, какие рёбра заменить в маршруте), а локальные эвристики (2‑opt, 3‑opt) выполняют конкретные изменения. Агент учится, какие операции наиболее перспективны в текущем состоянии. Преимущества: снижение вычислительной сложности и ускорение сходимости за счёт фокусировки на перспективных областях.
RL для настройки параметров метаэвристик. Метаэвристики (генетический алгоритм, имитация отжига, муравьиные алгоритмы) имеют множество параметров (вероятности мутации, температура охлаждения и т.д.). RL-агент может динамически адаптировать эти параметры в процессе решения. Например, в генетическом алгоритме RL управляет вероятностью кроссовера и мутации на основе прогресса популяции.
Иерархическое RL для декомпозиции задач. Сложная задача разбивается на подзадачи, каждая из которых решается отдельным RL‑агентом или классическим алгоритмом: на верхнем уровне RL-агент определяет стратегию (например, кластеризует города в TSP); на нижнем уровне точные методы оптимизируют маршруты внутри каждого кластера.
RL в рамках метода ветвей и границ. В методе ветвей и границ RL может выбирать, какую ветвь дерева решений исследовать следующей, оценивать перспективность узла (вместо эвристических функций) или сокращать пространство поиска за счёт предсказания границ.

Neural Combinatorial Optimization (NCO)

Перспективное направление, сочетающее мощь нейросетей с требованиями комбинаторной оптимизации. Они особенно полезны для динамических задач, где нужна быстрая генерация решений, и для сценариев, где традиционные методы слишком медленны. Спектр успешно решаемых задач весьма ограничен. И нет, это не универсальный солвер на все случаи жизни.

Ниже приведу примеры задач с условием, что NCO теоретически решает эту задачу. Это предполагает что текущее развитие NCO позволяет решать задачу малого размера, с определенными ограничениями, при определенных условиях или классическую (академическую) постановку.

Задача коммивояжёра (TSP). Найти кратчайший маршрут, проходящий через заданный набор городов ровно один раз и возвращающийся в исходный пункт. NCO используют Pointer Networks или GNN для генерации перестановок городов. По сути, задача сводится к сортировке. Пример NCO (решение задачи с применением cp-sat солвера разбирал здесь и ).
Задача маршрутизации транспортных средств (VRP). Оптимизация маршрутов для парка транспортных средств с учётом ограничений по вместимости (CVRP), по временным окнам (VRPTW) и т.д. Пример NCO.
Задача о рюкзаке (Knapsack Problem). Выбор предметов с максимальной суммарной ценностью при ограничении на вес/объём рюкзака. Пример для многомерной задачи о рюкзаке.
Задача покрытия множества (Set Cover). Выбор минимального набора множеств, покрывающих все элементы.
Планирование работы цеха (Job‑Shop Scheduling). Распределение операций между станками с минимизацией времени выполнения всех заказов. Пример одна из свежих научных работ.
Раскраска графа. Минимизация количества цветов так, чтобы смежные вершины имели разные цвета (применяется в составлении расписаний, распределении частот). Одно из ключевых исследований по задаче.
Задача размещения объектов (Facility Location). Оптимальное размещение складов, станций зарядки, вышек связи с учётом спроса и затрат на обслуживание. Вариацию решения задачи рассматривал в статье (Mixed Integer Programming).
Оптимизация цепочек поставок. Планирование закупок, производства, хранения и доставки с учётом неопределённостей.
Задача назначения (Assignment Problem). Оптимальное сопоставление агентов и задач (например, такси и пассажиров) с минимизацией суммарных затрат. Вариацию постановки задачи рассматривал в статье.
SAT‑задача (выполнимость булевых формул). Определение, существует ли набор значений переменных, удовлетворяющий заданной формуле. Пример: NeuroSAT.

Выше привел уже существующее реализацию RL в решение комбинаторных задач. Классические постановки имеют ограничение в практическом применении. Преодоление этого гэпа может быть непосильным для RL.

Отойдем от классических стандартизированных задач и попробуем решить небольшую вполне практическую комбинаторную задачу полностью силами RL (from scratch).

Бизнес задача

Расходы на топливо одна из главных статей затрат в автотранспортных перевозках грузов. По разным оценкам, они могут составлять около трети всех расходов грузоперевозчиков. Точное соотношение зависит от множества факторов: типа транспорта, условий эксплуатации, маршрута, стиля вождения, технического состояния автомобиля и других параметров.

Стратегическое планирование заправок в пути — эффективный способ снизить топливные затраты. Разброс цен на АЗС (обусловленный различиями в операторах, корпоративных контрактах и региональной ценовой политике) даёт возможность выбирать наиболее экономичные точки заправки. Особенно это актуально для дальних маршрутов, где число доступных АЗС может превышать сотню.

Процесс заправки транспортных средств зачастую не получает должного управленческого контроля и делегируется непосредственно водителям, которые самостоятельно определяют объём заправки и выбирают АЗС. Поскольку водители не всегда заинтересованы в минимизации топливных затрат, их выбор может определяться личными предпочтениями (комфортом, привычными маршрутами и т. д.). Это создаёт потенциал для оптимизации: грамотное планирование точек заправки и объёмов топлива способно обеспечить экономию до 1–1,5 %.

Визуализация задачи

Задача состоит в определении оптимальных точек заправки (АЗС) на маршруте и соответствующих объёмов топлива с соблюдением следующих ограничений:

Минимальный остаток топлива. На любом участке маршрута остаток в баке должен быть не ниже минимально допустимого уровня.
Вместимость бака. Объём топлива в баке не может превышать его максимальную вместимость.
Финальный остаток. В конце маршрута в баке должно оставаться не менее порогового количества топлива.
Минимальный объём заправки. Заезд на АЗС должен быть экономически оправдан: объём заправки не может быть ниже установленного минимума (исключаются случаи дозаправки незначительных объёмов, например, 1 л).

Задача нелинейного программирования

Сформулируем задачу оптимизации выбора АЗС и объёмов заправки в терминах нелинейного программирования. Но, для начала скорректируем ограничения задачи под RL. Ограничение коснется объема заправки. Предлагаю рассмотреть пять вариантов заправки: 0%, 25%, 50%, 75% и 100% от пустого места в баке. Это позволит перейти от непрерывного пространства к дискретному пространству решений. Управление таким решением в RL проще, на исследовательской составляющей материала сильных искажений результата не предвидится.

Индексы

$i \in I$ - индексы АЗС

Постоянные

c_i - объем потребления с i-1 до АЗС

p_i - стоимость заправки на АЗС

$v_\text{min}$ - минимальный объем заправки на АЗС

$s_0, s_{n}$ - объем топлива в баке в начале и конце маршрута

$s_{lb}, s_{ub}$ - минимальный и максимальный объем топлива в баке

- размер штрафа за нарушение минимального остатка в баке

Переменные

s_i - вещественная переменная, объем топлива в баке на -ой АЗС после заправки на этой АЗС

v_i - вещественная переменная, объем заправки на -ой АЗС

q_i - целочисленная переменная, процент заправки на -ой АЗС

b_i - бинарная переменная, индикатор наличия заправки на -ой АЗС

z_i - вещественная переменная, размер нарушения минимального остатка в баке

Целевая функция

Минимизация стоимости заправок и нарушений минимального остатка:

$\min \sum_{i \in I} (p_iv_i + wz_i)$

Ограничения

Баланс топлива в баке: $s_i = s_{i-1} - c_i + v_i, \quad \forall i\in I$
Кратность заправки доли от пустого места в баке: $v_i = 0.25q_i(s_{ub} -s_{i-1} + c_i), \quad \forall i \in I$
Минимальный остаток в баке: $s_{i-1} - c_i + z_i \ge s_{lb}, \quad \forall i \in I$
Остаток в конце маршрута: $s_{|I|} - c_{|I| + 1}\ge s_{n}, \quad \forall i\in I$
Минимальная заправка: $v_i \ge v_{\text{min}}b_i, \quad \forall i\in I$
Индикатор заправки: $q_i \le 4b_i, \quad \forall i\in I$

В постановке задачи сформулировано мягкое ограничение на минимальный объем топлива в баке. Это обусловлено реальной практикой, когда невозможно выполнить данное условие на реальных данных. Будем считать, что добавили эксплуатационной надежности в модель.

Реализацию оптимизационной модели нелинейного программирования с использованием солвера SCIP (pyscipopt) закинул на git.

Reinforcement learning для решения задачи

Обучение с подкреплением это метод машинного обучения, при котором агент учится оптимальным действиям через взаимодействие со средой и получение наград.

Ключевые компоненты:

среда — мир, в котором действует агент;
агент — обучающаяся сущность, принимающая решения;
состояние (s) — текущая ситуация в среде;
действие (a) — шаг, который агент может выполнить;
награда ( r ) — сигнал от среды, оценивающий действие (положительный или отрицательный).

Схема RL

Агент стремится максимизировать суммарную награду, постепенно улучшая стратегию выбора действий. Портал в более глубокое погружение - здесь!

Перейдем к практическим аспектам реализации агента, способного решать задачу планирования заправок ТС.

Environment

Агент взаимодействует со средой (Environment) через петлю обратной связи: наблюдает состояние → выбирает действие → получает награду и новое состояние. Среда - вероятно, самое важное в RL, поэтому начинаем именно с нее.

Для типовых задач есть готовые «песочницы» — среды с понятными правилами:

начать путь в RL помогут Gymnasium и Stable Baselines3;
для многоагентных игр:PettingZoo и SMAC;
для роботов и физики: PyBullet, MuJoCo, DeepMind Control Suite;
для навигации и беспилотников: Habitat и CARLA;
масштабирование и распределённое обучение: Ray RLlib;
поиграть и потренировать стратегию можно в ViZDoom, NetHack или Google Football.

Мы рассматриваем нестандартную задачу RL. Готовой средой невоспользоваться. Более того, как эффективно организовать эту среду - отдельная задача. Ниже презентую свой вариант реализации.

Под средой будем понимать набор маршрутов. Каждый маршрут характеризуется набором параметров: потребление топлива при движении между АЗС, цена топлива на АЗС и ограничений задачи (максимальный, минимальный, текущий, конечный остаток и минимальная заправка).

Пример вектора состояния

Предлагаю этот вектор использовать в качестве вектора состояния. Поработаем над его недостатками:

Длина динамическая. В зависимости от маршрута (задачи) кол-во АЗС может отличаться, а агент хотел бы получить на вход вектор фиксированной длины.

Решение: увеличиваем размер части потребления и части с ценами до фиксированного размера. Отсутствующие значения заполняем нулями. Например, пусть это будет 100, тогда размерность вектора состояния будет 100+100+5=205.

Масштаб значений. АЗС вдоль маршрута могут распологаться достаточно плотно (например, для маршрутов центральной части РФ) или быть сильно удалены (Забайкальский край или дальний восток). Это влияет на порядок значений в потреблении. Кроме того, максимальный, минимальный, текущий, конечный остаток и минимальная заправка могут разниться в зависимости от характеристик ТС. Значения такого вектора могут излишьне забирать внимание агента.

Решение: нормировать значения потребления и ограничений задачи поделив на максимальный остаток (все значения лягут в интервал от 0 до 1). Цены предлагаю преобразовать в относительную разность к минимальной цене.

После предложенных модификаций исходный вектор состояния преобразуется в это:

Пример отнормированного вектора состояния

Разберем динамику взаимодействия. Сбросили среду (reset), получили вектор состояния полной оптимизационной задачи (например, как на предыдущей картинке). Агент на основе вектора состояния выбирает одно из пяти возможных дейсткий: закупить топлива на 0%, 25%, 50%, 75% и 100% от пустого места в баке. Совершаем действие и формируем новый вектор состояния: корректируем вектор потребления, вектор цен (слева убираем значение, справа дописываем 0) и значение остатка в баке (+ объем закупки - объем потребления). Эпизод заканчивается когда совершили действие на каждой АЗС маршрута.

Исходя из вектора состояния агент всегда видит:

сколько топлива в настоящий момент в баке;
сколько топлива еще потребится;
когда и по какой цене можно закупить топливо;
сколько топлива должно остаться в конце маршрута.

Вектор состояния предоставляет достаточно информации для оптимального принятия решения на каждом шаге (в каждой точке маршрута). Дело за агентом, научиться распознавать паттерны этих оптимальных действий.

Награда (reward). Каждое действие агента оценивается средой. Основная составляющая награды - стоимость заправки. Этот показатель можно оценивать на каждом шаге взаимодействия со средой. Кроме затрат на топливо, есть ограничения на минимальный объем топлива в баке и остаток топлива в конце маршрута. Эти ограничения в исходной постановке - жесткие, но в процессе обучения дадим послабление и сделаем их мягкими. Т.е. нарушение этих ограничений будем штрафовать. Остаток в конце маршрута возможно оценить в конце эпизода.

Формула награды

Среда получилась достаточно детерминированной, последующее состояние зависит от совершенного действия. Пример реализации среды можно посмотреть здесь.

Итог: создана специализированная RL‑среда для оптимизации заправок на маршруте. Она предоставляет агенту структурированную информацию, чёткие правила взаимодействия и осмысленную функцию награды. Это позволяет обучать политику, минимизирующую затраты на топливо с учётом всех ограничений задачи.

Агент

В обучении с подкреплением агент принимает решения на основе оценки качества возможных действий в текущем состоянии среды. Ключевым инструментом такой оценки выступает Q‑функция Q(s,a) , которая прогнозирует суммарную будущую награду при выполнении действия в состоянии .

Когда для аппроксимации Q‑функции применяется нейронная сеть, соответствующий подход называют Deep Q‑Network (DQN). Обучение DQN происходит через последовательное взаимодействие агента со средой, на каждом шаге агент:

наблюдает текущее состояние ;
выбирает действие (с учётом текущей оценки );
получает награду $r_{t}$ и переходит в новое состояние $s_{t+1}$ ;
обновляет параметры сети, минимизируя ошибку предсказания будущей награды.

Такой цикл позволяет агенту постепенно улучшать стратегию выбора действий и максимизировать накопленную награду.

Dueling Deep Q‑Network (Dueling DQN) — модификация алгоритма DQN, предложенная в 2016 году. Её ключевая идея — разделение нейронной сети на две независимые части для более точной оценки Q‑функции. Это позволяет эффективнее обучаться в средах с большим числом действий и улучшает обобщающую способность агента.

Отличия от классического DQN

В DQN одна нейронная сеть напрямую аппроксимирует функцию $Q(s,a;\theta)$ , то есть оценивает суммарную будущую награду для каждой пары «состояние‑действие».

В Dueling DQN Q‑функция разбивается на два компонента:

$Q(s,a;\theta,\alpha,\beta)=V(s;\theta,\beta)+A(s,a;\theta,\alpha),$

где:

— ценность состояния (value): ожидаемая суммарная награда из состояния , независимо от выбранного действия. Отражает «хорошесть» самого состояния.
— преимущество действия (advantage): насколько конкретное действие лучше среднего действия в состоянии . Показывает относительную выгоду выбора.

Параметры $\theta$ — общие, $\alpha$ и $\beta$ — параметры отдельных полносвязных слоёв.

Архитектура сети

Типичная архитектура Dueling DQN состоит из трёх частей:

Общая часть (бэкбон):

обрабатывает входные данные;
извлекает признаки.

Ветвь ценности состояния :

один полносвязный слой;
выход — одно число, оценивающее состояние.

Ветвь преимущества действий :

один полносвязный слой;
выход — вектор размером (число действий), где каждый элемент — преимущество соответствующего действия.

На финальном слое происходит объединение:

$Q(s,a)=V(s)+(A(s,a) − \frac{1}{∣A∣} \sum_{a′} A(s,a′)).$

Вычитание среднего преимущества необходимо для устранения неоднозначности: и не определяются однозначно, а их сумма — да. Альтернатива — вычесть максимум преимуществ.

Dueling Q-network

Ключевые улучшения по сравнению с DQN

Более точная оценка состояний. Разделение позволяет агенту лучше понять, какие состояния принципиально выгодны или невыгодны, даже если конкретные действия пока не изучены.
Ускорение обучения. Информация о ценности состояния распространяется на все действия, что ускоряет обобщение.
Эффективность в средах с множеством действий. Когда большинство действий мало влияют на ценность состояния, преимущество будет близко к нулю, а обучение сфокусируется на .
Стабильность. Раздельная оценка снижает шум в градиентах и делает обучение более устойчивым.

Для решения задачи рассмотрел две нейронных сети: полносвязную и одномерную сверточную сеть. Со структурами сетей, которые использовал для решения задачи можно ознакомиться здесь. В скрипте представлены структуры трех сетей. В одну из полносвязных сетей добавил нормализацию линейных слоев.

Схема обучения

Среди разнообразных схем обучения DQN‑агентов был выбран подход Double DQN.

Double DQN — это модификация алгоритма DQN, направленная на устранение проблемы переоценки Q-значений, которая часто возникает в стандартном Q-обучении и DQN. Основная идея Double DQN заключается в разделении процессов выбора действия и оценки его ценности, что позволяет снизить оптимизм в оценках и улучшить стабильность обучения.

Принцип работы Double DQN

Double DQN использует две нейронные сети:

Основная сеть (online network) — используется для выбора действия в следующем состоянии. То есть с её помощью определяется, какое действие является наилучшим в новом состоянии.
Целевая сеть (target network) — используется для оценки Q-значения выбранного действия. То есть она вычисляет целевое Q-значение для обновления параметров основной сети.

Таким образом, выбор действия и оценка его ценности выполняются разными сетями, что снижает корреляцию между этими процессами и уменьшает переоценку.

Математически это можно записать так:

$Q(s_t,a_t)=r_t+\gamma Q(s_{t+1},\text{arg}\max_{a′}Q(s_{t+1},a′;\theta_t); \theta^*_t)$

где:

— текущее состояние;
— текущее действие;
— полученная награда;
$\gamma$ — коэффициент дисконтирования;
$Q(s, a; \theta)$ — основная сеть;
$Q(s, a; \theta^*)$ — целевая сеть (target).

Схема обучения

Как работает обучение

Инициализация сетей. Создаются две нейронные сети: основная $Q(s, a; \theta)$ и целевая $Q(s, a; \theta^*)$ . Изначально параметры целевой сети копируются из основной ( $\theta = \theta^*$ );
Пронаблюдать из среды;
Для каждого $t= 0, 1, 2, \dots$ :

с вероятностью $\epsilon$ выбрать действие случайно (exploration), иначе жадно: $a_t=\text{arg} \max_{a_t} Q(s_t, a_t; \theta)$ ;
отправить действие в среду, получить награду за шаг и следующее состояние $s_{t+1}$ ;
добавление перехода $(s_t, a_t, r_t, s_{t+1})$ в буфер (replay buffer);
если в буфере скопилось достаточное число переходов, провести шаг обучения. Для этого сэмплируем мини-батч переходов из буфера.
для каждого перехода считаем целевую переменную: $y=r+\gamma Q(s',\text{arg}\max_{a'}Q(s',a';\theta); \theta^*)$ ;
сделать шаг градиентного спуска для обновления $\theta$ , минимизируя $\sum (y - Q(s, a; \theta))^2$ ;
если пришло время ( кратно - шаг синхронизации весов), тогда $\theta^* \leftarrow \theta$ .

Нюансы обучения

Реплей‑буфер, хранящий переходы, имеет ограниченный объём для предотвращения избыточного потребления памяти. При достижении установленного лимита старые записи удаляются по принципу FIFO.

В процессе обучения коэффициент исследования (вероятность случайного действия) постепенно снижается. Это приводит к тому, что агент всё чаще опирается на выученную политику, а его решения становятся более взвешенными и эффективными.

Для ускорения обучения внедрён подход curriculum learning с привлечением экспертных решений. С заданной вероятностью выбор действия осуществляется на основе оптимального решения, рассчитанного заранее с помощью оптимизационной модели. Такой подход позволяет наполнять буфер высококачественными переходами, что способствует более быстрой сходимости алгоритма. Триггер активации экспертной стратегии срабатывает в начале маршрута: после его срабатывания весь эпизод разыгрывается с использованием оптимального решения.

Реализацию процесса обучения можно посмотреть здесь.

Что получилось

Всю описанную выше систему нужно напитать данными. Была возможность взять данные работающей оптимизационной модели. Но эти данные оказались не очень подходящими для обучения.

Не настроен сбор данных. Требуется собирать результаты из архивов.
Дублирование записей. Для одного рейса фиксируется несколько записей на разных этапах маршрута (например, отдельные запросы для первой и третьей АЗС одного маршрута).
Короткая история хранения данных. Ограниченный временной охват доступных данных.

Поэтому для обучения использовал искусственные данные. Генератор представлен здесь. Случайные распределения настроены под разброс из реальных данных.

Обучение

Распределение усредненной за последние 100 шагов награды в эпизодах в зависимости от шага обучения представлено ниже. Левый график соответствуют обучению полносвязной линейной нейронной сети, а правый - одномерной сверточной сети. Отличий практически нет, в обоих случаях обучение быстро сходится к средней награде -7 единиц.

Прогресс в обучении

Улучшения не удалось получить ни при увеличении исследовательских циклов, ни при добавлении эксперта, ни при ребалансировке весов в reward. Поведение повторяется и улучшений не происходит. Значит ли это, что обучили вполне качественного агента? Об этом в следующем разделе.

Сравнение

Модель RL будем сравнивать с оптимальным решением от оптимизационной модели. Построить небольшой сравнительный отчета можно с помощью скрипта. В основе сравнительного анализа лежат реальные 86 маршрутов (маршруты разной длины и разными параметрами). Отмечу, что для искусственного набора данных получались аналогичные результаты.

Обучены несколько вариантов Q-функций + рассмотрены различные подходу к обучению:

Linear: полносвязная нейронная сеть с линейными слоями;
Conv1d: одномерная сверточная сеть;
Overload: корректировка среды. В конце маршрута есть требование минимального конечного остатка. В исходном варианте среды установлено штраф за нарушение ограничения снизу. Эта модификация штрафует остаток в конце маршрут в том числе сверху.
Explore: увеличенный размер цикла исследования в процессе обучения.
Expert: в процессе обучения некоторые действия формируются экспертом (оптимизационной моделью).
Opt: решение задачи с помощью математического программирования.

Сравнения будем проводить по суммарным значениям 86 сценариям. Напомню, что задача заключается в минимизации затрат на заправку топлива. Этот параметр будем исследовать.

Общие затраты и объемы заправок

Исходя из графиков видим, что RL тратит и заправляет больше. Это обусловлено тем, что rl агенты не мотивированы в конце маршрута оставлять остаток близкий к требуемому остатку в конце маршрута (кроме overload). На протяжении маршрута объем заправок не очень оптимальный с точки зрения полного маршрута. Исключение Overload, который оказался достаточно близок к оптимальному решению.

Разброс по затратам от оптимального решения 8-54%. Если брать во внимание только эти показатели, то есть куда расти. Посмотрим на среднюю стоимость закупок.

Средняя цена закупки

Получили обратную ситуацию: rl модели закупают топливо в среднем по более низкой цене. Значение этого показателя уже выходит за рамки задачи. Потому что необходимо учитывать дальнейшие связанные маршруты для оценки экономии покупки большего объема на текущем маршруте. Если сейчас закупаем больше, но дешевле, будет ли это дешевле чем заправки в начале следующего маршрута.

Такой эффект с моделью Opt возник из-за корректировки условия задачи: кратность заправки от пустого места в баке. Если рассматривать непрерывную область решений для объема заправки, то таких проблем у оптимизационной модели не должно возникнуть.

Этот момент выходит за рамки задачи, мы останемся в рамках задачи.

Нарушение минимального остатка в баке - еще один важный показатель. Посмотрим что у нас с нарушением этого параметра.

Объем нарушений минимального остатка

Среди 86 сценариев был один с несовсем консистентными условиями, поэтому минимальное значение: нарушений минимального остатка 57л. В силу большого штрафа за нарушение минимального остатка, rl модели научились достаточно хорошо следовать этому правилу. В модели Overload возможно требуется более качественная настройка весов между штрафами.

Нарушение остатка в конце маршрута незначительные, не более 10л. Этот показатель не будет удостоен своего графика.

Последнее, на что хочу обратить внимание - производительность. Для решения оптимизационной задачи использовался коммерческий солвер.

Объем нарушений минимального остатка

Суммарная длительность расчетов (inference) у rl моделей ниже, чем у солвера. Но это не такое большое преимущество, учитывая порядок и нефункциональные требования к решению. Если учесть время обучения модели (около 1ч), то ситуация кардинально меняется в пользу Opt.

Послесловие

Что касается RL у меня академические познания. Постарался учесть “хорошие” практики организации среды, распределения награды и организовать хороший процесс обучения. Но этого оказалось недостаточно. В планах попробовать:

Распределение награды после завершения эпизода. Это должно уменьшить объем закупок топлива;
Рассмотреть непрерывную область решений по объему заправок. Это приблизит к реальной задаче;
Усложнить структуру нейронной сети для Q-функции;
Скорректировать среду. Изменение нормировок и системы штрафов. Это позволит точнее формировать цель для агента.

Что касается RL как инструмента для решения комбинаторных задач. Вместо постановки задачи в виде правил и ограничений в RL дополнительно возникают работы по:

Разработке среды и системы наград. Как в оптимизационной задаче напрямую передавать данные задачи уже не получится. Много зависит от представления данных и размера награды.
Данные. Требуются большие объемы разных данных/ситуаций для качественного обучения (проблема обобщения). В оптимизационных задачах эти данные в очень скудном объеме. Генераторы данных как компромисс, но не универсальный.
Подбор нейронной сети для обучения. Здесь как минимум нужно разбираться и иметь опыт.

RL требует много исследований, мало общедоступных примеров решения комбинаторных задач (в основном TSP/VRP). Как дополнительные требования к задаче будут встраиваться в уже решаемые задачи с помощью RL, тоже большая неопределенность. В сравнении с математическим программированием - бОльшие инвестиции в трудозатраты.

Исследование не претендует на исчерпывающую оценку применимости RL к задачам математической оптимизации: речь идёт о базовой проверке гипотезы. Тем не менее, если вера в возможности RL сохранится, это может стать отправной точкой для более глубоких изысканий.

Заключение

Разработанный алгоритм решения оптимизационной задачи демонстрирует работоспособность даже в академическом варианте исполнения. Текущая реализация подтверждает перспективность RL, хотя ряд аспектов требует углублённого исследования.

В статье рассмотрел бизнес задачу планирования заправок ТС на маршруте, сформулировал задачу в виде задачи нелинейного программирования, выстроил с нуля весь процесс обучения нейронной сети для принятия решения по заправкам. С реализацией в python можно ознакомиться здесь.

Ссылки

Git репозиторий решения задачи заправки ТС с помощью RL и NLP;
NoML семинар по материалу статьи;
Neural Combinatorial Optimization для задач TSP и VRP (CVRP).

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31 мар. 2026 г.

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CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.06.26 01:58 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.06.26 14:16 Universina da Mota

Becoming a victim of an investment scam is never anyone's intention it often happens because fraudsters exploit trust and a lack of awareness. I would like to express my sincere gratitude to the dedicated team at ResQpro for their professionalism and commitment to helping victims of online investment fraud. Their efforts in assisting individuals with the recovery of stolen assets and holding scammers accountable are truly commendable. If you need assistance or would like to learn more, you can contact them through: Email: [email protected] Alternative Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 (985) 296-9146
24.06.26 14:21 Elizabeth Thompson

If you believe you have been the victim of an investment scam, it is important to act promptly and gather all relevant information. Keep records of transaction receipts, wallet addresses, communication logs, account details, and any other evidence related to the incident. Providing accurate documentation can help investigators, financial institutions, legal professionals, or recovery specialists review your case and determine what options may be available. Be cautious of anyone who guarantees the recovery of lost funds or requests large upfront payments. For additional information, you may contact: Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 (985) 296-9146
24.06.26 15:33 Júlia Castro

If you have fallen victim to an investment scam, it is important to act quickly and gather all available evidence related to the incident. This may include transaction records, wallet addresses, screenshots of conversations, emails, account details, and any information connected to the individuals or entities involved. Having complete documentation can help professionals assess your situation and explore possible recovery options. Always exercise caution when seeking assistance and carefully verify the credentials of any service provider before proceeding. For further information, you may contact: Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 (985) 296-9146
24.06.26 22:01 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.06.26 22:01 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.06.26 21:13 Emilie Safi

A fraudulent investment scheme operated by BTCMining.limited functions as a fake return scam. In this setup, scammers lure victims with false promises of high returns. Through manipulative tactics, they gain individuals' trust and convince them to invest, ultimately leading to financial loss. If you have ever faced a cyber threat or fallen victim to an online crypto scam and need to reach the authorities, I recommend contacting [email protected], [email protected], WhatsApp +19852969146, telegram @resqprofirm. They are a legitimate team that helps victims of online crypto scams using advanced tools.
25.06.26 21:25 Emilie Safi

So I ended up losing $38,000 to this platform. At first, they kept asking me to put in more money so I could get into my portfolio. I did that, but then they wouldn’t let me withdraw anything—just kept asking for more deposits. It got way too suspicious, so I stopped. I found this company called ResQProfirm on Google and told them what happened. They got in touch, asked me to walk them through everything, and I gave them all the proof I had. They did an amazing job tracking down my money and getting it back. Big thanks to them at [email protected] and on WhatsApp at +19852969146. Please be careful out there and always research before investing.
26.06.26 01:04 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.06.26 01:04 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.06.26 02:48 Miriam Rocha

I trusted this platform with $120,000 of my hard-earned money. Then they started asking for more deposits just so I could access my own portfolio. I paid, but every withdrawal request was denied. They kept pushing for more money. I finally stopped it just felt wrong. Desperate, I found ResQProfirm on Google. They didn't just hear me out; they truly listened. I shared all my proof, and they launched an investigation. Thanks to their hard work, they tracked and returned my funds. From the bottom of my heart, thank you to [email protected] and their WhatsApp +19852969146. Please stay safe and always verify a platform before investing
26.06.26 02:52 Miško Bakić

I got my $232,000 refund thanks to [email protected] and WhatsApp +19852969146. Highly recommended for anyone in a similar situation.
26.06.26 02:56 Asunción Herrera

A recovery of $48,330 was facilitated by [email protected]. Individuals who have experienced financial fraud may consider contacting this service.
26.06.26 15:05 Riley Stephens

If withdrawals keep getting denied, stay calm. I went through the same, and this firm helped me recover everything. Their assistance was outstanding. Contact: [ResQProFirm @Gmail|•|com], Telegram: ResQprofirm, WhatsApp: <+198> <5296> <9146>.
26.06.26 15:09 Antonio Riley

Withdrawal troubles shouldn’t stress you out. I faced a similar problem, and this firm stepped in and recovered my funds. Their support truly mattered. Contact them: [[email protected], ResQprofirm @aol.com], Telegram: ResQprofirm, WhatsApp: +19852969146.
28.06.26 00:37 kimberlyhebertt673

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text Number: +1 (336) 390-6684
28.06.26 00:37 kimberlyhebertt673

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text Number: +1 (336) 390-6684
29.06.26 11:57 Lisadonato0726

For 43 years, I struggled with bad credit due to my own poor decisions, and my credit score was around 490. When my girlfriend and I decided to buy a house, a mortgage broker informed us that it would be impossible to secure a mortgage with my credit score. As a result, she referred me to a company called HACK MAVENS CREDIT SPECIALIST, assuring me of their professionalism and ability to assist with credit improvement. Upon contacting them, I was impressed by their professionalism and they assured me that they could help. In less than 6 days, my credit score skyrocketed to 785, and they also successfully resolved issues in my credit report, including the bankruptcy. I am incredibly satisfied with their service and would highly recommend HACK MAVENS CREDIT SPECIALIST for reliable credit repairs. You can reach them at H A C K M A V E N S 5 [AT] G M A I L [DOT] COM or at [+] [1] [2 0 9] [4 1 7] – [1 9 5 7]. Thanks to their help, my girlfriend and I are now proud homeowners.
29.06.26 22:37 riley777

Back in 2025, I watched my life savings vanish. A thief took every cent. I felt desperate and went looking for a way to get it back. I found a guy here who said he was an expert haha. He talked about special software that could find my missing cash. I trusted him. That was a big mistake. He was just another scammer. I paid him a software fee and then he just stopped answering my texts and ran off with my money too. I felt so ashamed that I kept quiet about it for months. It is hard to admit you got fooled twice. Later on, I found a real pro. she did not use a fancy sales pitch. she just looked at the trans screenshots and followed the path the money took. she worked fast and got my funds back into my account. Having that money back changed everything. I can sleep again. her info; [email protected]. Call/chatroom on Whtasapp/ +44 7476618364.
30.06.26 15:08 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.06.26 15:08 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
02.07.26 01:22 Lieneke Bonnema

I highly recommend ResQprofirm for their professional asset recovery services of my $120,000 scammed funds. Their expertise, professionalism, and commitment to achieving results make them a reliable choice for anyone seeking dependable recovery assistance. [email protected], WhatsApp +19852969146, telegram @resqprofirm
02.07.26 01:26 Clara Morin

I want to extend my deepest appreciation for showing that circumstances do not define one’s potential for greatness. Your support has been a major source of inspiration during my trading journey, and I am sincerely grateful for your insight and mentorship. Thank you so much. [email protected], WhatsApp +19852969146, telegram ResQprofirm
02.07.26 01:31 Robin Hale

I sincerely want to thank you for demonstrating that anyone can rise above their circumstances and achieve success. Your constant support has been incredibly inspiring during my trading journey, and your wisdom and advice mean so much to me. I appreciate you deeply. [email protected], WhatsApp +19852969146, telegram Resqprofirm
04.07.26 15:32 Fraddy Pual

There are few companies I trust as much as FUNDSRETRIEVER. When I lost $653,000 in Ethereum to a ruthless scam, I thought my life would never be the same. The betrayal cut deep, but I refused to give up. I searched tirelessly for a legitimate way to recover what was stolen, and finally found FUNDSRETRIEVER—the most competent and compassionate recovery team I could have imagined. They handled my case with precision and care, and in the end, my entire ETH wallet was restored. More than the money, they gave me back my hope and happiness. I'm sharing my story because I want others to know that recovery is possible. If a scam has taken from you, don't hesitate—contact FUNDSRETRIEVER today. Email: FUNDSRETRIEVER1@ Gmail.com | WhatsApp: +1 603-512-1448 | Telegram: @FUNDSRETRIEVER
05.07.26 14:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/Text: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
05.07.26 14:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/Text: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
06.07.26 16:20 Olga Ognjanović

Having trouble withdrawing funds from an investment platform? ResQprofirm provides fund recovery assistance for individuals seeking help with investment-related disputes. I reached out to them after experiencing problems with an investment platform, and I appreciated their professionalism and support throughout the process. If you're facing a similar situation, act promptly, keep records of your transactions and communications, and seek assistance from a qualified recovery service or the appropriate authorities. Contact: Email: [email protected] Telegram: @ResQprofirm WhatsApp: +1 985 296 9146
06.07.26 16:31 Joseph Weigl

Invest wisely and stay cautious. Don't be influenced by promises of unusually high returns or convincing sales pitches from brokers. I learned this the hard way after falling victim to an investment scam that promised huge profits. Fortunately, I acted quickly and reported the incident to a recovery firm for assistance. Contact: Email: [email protected] Telegram: @Resqprofirm WhatsApp: +1 985 296 9146
06.07.26 16:33 Jaran Løvlien

A heartfelt thank you to RESQPRO FIRM for their commitment and professionalism throughout the investigation of my case. Their team worked diligently and helped recover assets valued at $88,000, which were returned to my wallet. I truly appreciate their support, clear communication, and dedication, and I'm grateful for the assistance I received. Contact: Email: [email protected] Telegram: @Resqprofirm WhatsApp: +1 985 296 9146
07.07.26 18:00 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
07.07.26 18:01 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
09.07.26 19:06 Toivo Walli

I lost 8.56btc to a fake Bitcoin mining site, I tried withdrawing but couldn't approved my process, I reported to !R£SQPROFIRM! via °R£SQproFirm°àt°gmail•com° °tEL£°gram=R£SQprofirm °whaT°Zap+198°52°96°91°46
09.07.26 19:10 Misty Alexander

Ongoing messages demanding more money before approving withdrawals are a major red flag. Stop engaging and report the incident to a trusted recovery team. For professional support, you can contact R£sQprofirm using °ResQproFirm°àt°g,*ma'il(•)¢m°, TEL£gram ResQprofirm, or |whaTZap| +1-985-296-9146.
09.07.26 19:13 Clara Soto

Anyone receiving continued requests for additional deposits from a scam platform should immediately cut off communication and submit the case to a reputable recovery service for investigation. R£sQprofirm is a dependable firm you can reach at °ResQproFirm°àt°g,*ma'il(•)¢om°, TEL£gram ResQprofirm, or |whaTZap| +1-985-296-9146.
12.07.26 03:30 Kora Baltacha

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12.07.26 03:33 Pahal Mathew

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30.07.26 00:04 Ahmed

A really cool analysis, thank you. I was especially struck by how strictly the order is defined: data processing and formatting come first, with color only at the very end. This really saves you from the typical mistake of "first a pretty palette, then we figure out what the chart is for." And the palette validator with OKLCH + colorblindness check is absolutely fantastic; you almost never see that in regular tools. By the way, while reading about rank-trajectory and the logarithmic scale, I immediately remembered how convenient it is to analyze dynamics on charts in ExpertOption—I've been trading there for quite some time now. When the data is well visualized, decisions are noticeably easier and more relaxed. I also liked the point about "no more than eight colors" and the dual-axis ban. Strict restrictions sometimes actually produce better results than complete freedom. I'll try this approach myself.
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03.08.26 20:05 Philip

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03.08.26 20:06 Philip

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04.08.26 11:05 Kisnoles

Excellent analysis, thank you. I was particularly struck by how rigidly the skill sets the order: data processing and form come first, with color coming last. This really cures the habit of "first a pretty palette, then we'll figure it out." A palette validator using OKLCH + color blindness + WCAG is something most chart generators lack. And regarding the boundaries of competence, it's very clear. Where there's a self-checking loop (color), you delegate freely. Where there's a heuristic (form, data interpretation), you remain the final filter. This is a universal principle, not just for /dataviz. By the way, when you look at trading dashboards (including those of decent platforms like ExpertOption), it's immediately clear who thought about readability and who just threw in rainbow lines. Tools like this skill could greatly improve the quality of analytics. Thanks again for the detailed analysis – saved.
04.08.26 12:37 kimberlyhebertt6877

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I learned an important lesson after investing in what appeared to be a genuine opportunity. Unfortunately, I was unable to access my funds, which reinforced the importance of carrying out thorough due diligence, checking whether an investment is appropriately regulated, and seeking qualified professional advice rather than relying solely on online reviews or testimonials. During the process of addressing my case, I worked with Mrs. Tatiana Sorina , who communicated clearly, provided regular updates, and handled the matter in a professional manner. According to my experience, I have recovered $50,000 so far, while efforts to resolve the remaining balance are still in progress. If you wish to contact her, the details I used are: Mrs. Tatiana Sorina TEXT : (tatianasorina06 at G_Ma IL dot ..c 0 m)…. Before committing money to any investment, take time to verify the legitimacy of the platform, confirm any relevant regulatory authorisations, and avoid investing more than you can comfortably afford to lose.
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CapitalNode Analytics. They help to investigate and recover stolen digital assets from fake trading platforms. Great firm i must say.
18.08.26 04:59 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone WhatsApp/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
18.08.26 04:59 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone WhatsApp/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.08.26 14:50 BAYER7043

My account was locked, and I couldn’t access my own information until [email protected] +447476618364 whats?up? helped me recover it. This lady hacker was kind and professional, but this experience showed me how risky account lockouts can be. If you’re facing the same problem, do not panic consult her A. S. A. P. Be careful with recovery agents outchea, and research their name, business, and reviews before sharing any details. Never send passwords, security codes, banking information, or copies of your ID unless you’ve confirmed who you’re dealing with. Be wary of promises that sound too good to be true, especially claims that require little information or guarantee instant access with outrageous fees.
20.08.26 11:32 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
20.08.26 11:32 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR WhatsApp Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.08.26 20:02 leslieyee

Excellent analysis by /dataviz! I was particularly struck by how strictly the order is defined: "data meaning first, color last" and how the validator actually adjusts the palette according to OKLCH, color blindness, and WCAG standards. These rules greatly improve the quality of charts. By the way, a similar approach to clean and legible charts is highly valued in trading—for example, on the ExpertOption platform, the interface and price visualization are designed to ensure information is read instantly and without unnecessary noise.
25.08.26 13:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.08.26 13:44 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.08.26 15:37 [email protected]

Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.
30.08.26 15:37 [email protected]

Discovering I had been defrauded, I searched online for services claiming to recover stolen ETH. I contacted several companies, but none succeeded. Although some claimed they could trace assets or recover funds, I could not verify their success or recover my money. I later found SYLVESTER BRYANT Recovery through Google. After contacting him, he recovered 450,000,00. He can be reached at [email protected] or WhatsApp at +1 512 577 7957.
01.09.26 11:16 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
01.09.26 11:16 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
01.09.26 17:34 Garry42

Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.
01.09.26 17:34 Garry42

Really crazy world. These fraudsters go at any length to steal your hard earned funds. I have been a victim of a bitcoin scam about 7 months back. A Con artist gained access to my cashapp account through a phishing scam. They stole $409,000. I was really devastated. I did everything to get back my funds by contacting the FBI but they claimed there was nothing they could do. A friend told me about a recovery expert. He helps fight against various phishing and investment scams and they were able to help trace and recover my funds even though it took over 2 days. you can reach out to him through recoverydarek@gmail. com . I can guarantee his services are still active.
02.09.26 03:43 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
02.09.26 03:43 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
04.09.26 21:51 Kovengray

Recovering your lost investment funds as the case might be, is not what you can do alone, you’d require the service of a trained recovery specialist. A recovery specialist is a person or a group of people who are well equipped to work around the brokerage network. They have vast knowledge about the whole network and have the right software and private keys to follow any transaction. I was ripped off trading online to an investment broker, good thing I got every penny back through the help of Gavin ray he’s a genius Contact : Gavinray78 at gmail com or WhatsApp +1 352 322 2096 It is also important to be patient and really calm during the process.
05.09.26 21:38 [email protected]

I invested 45,000 Euro, and later aggreviated to 198,000 Euro. I requested to place ‎Withdrawal of my funds to be paid to my Bank account. But nothing happened I was subjected to pay more fee until I can get my funds on my account, i got in touch with Theodore ryan here on this platform who had helped a lot of people, I followed all instructions and he legally got back my withheld funds, I got threatened by the company that if I don’t pay they will get my account frozen, all thanks to Theodore ryan and I highly recommend him to anyone dealing with an unregulated broker company… contact him on his Gmail - theodoreryan318@ gmail . com
09.09.26 21:31 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
09.09.26 21:31 lisawerth897

My Experience With Cryptocurrency — CAPITAL CRYPTO RECOVER I lost over $82,000 in Bitcoin after falling victim to a fraudulent online investment scheme. After realizing I had been scammed, I spent considerable time researching possible ways to recover my funds. During my research, I came across CAPITAL CRYPTO RECOVER and decided to contact them after reading their reported success record and encouraging client positive reviews and testimonials. Their team guided me through the recovery process, and I was grateful to successfully recover my lost cryptocurrency. The experience was challenging, but I appreciated the assistance and support I received throughout the process. I’m sharing my experience in the hope that it may encourage other victims to carefully research their options and verify any recovery service before proceeding. I will forever be thankful to you CAPITAL CRYPTO RECOVER 📧 [email protected] 🌐 Website: recovercapital.wixsite.com/capital-crypto-rec-1 📧 [email protected] 📞 Call/WhatsApp: +1 (336) 390-6684
09.09.26 23:22 Fraddy Pual

Hearing that these individuals are focusing on other people makes me very sad. I had a similar situation with them and lost a lot of money, but after learning about (Cruxcipherteam @ proton DoT me), whataqq:+168160-15021, telegram: @Cruxcipherteam I was able to get my money back. It's critical that we all be watchful and keep reporting these occurrences.
11.09.26 03:23 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
11.09.26 03:23 kimberlyhebertt6877

I invested in bitcoin trading After losing $78.4 USDT) linked to a romance fraud scam worth of cryptocurrency through an online investment platform and later discovered it was a scam. After extensive research for recovery options, I contacted CAPITAL CRYPTO RECOVER based on positive client reviews and recommendations. Their professional security team guided me through the recovery process using advanced technology, and I was able to recover my lost cryptocurrency successfully. I am truly grateful for their support and assistance during such a difficult experience. I will advise you to contact CAPITAL CRYPTO RECOVER helped me recover my funds. For anyone facing similar issues, Website: https://recovercapital.wixsite.com/capital-crypto-rec-1 Email: [email protected] Telegram: @Capitalcryptorecover Contact: [email protected] WhatsApp/Text Number: +1 (336) 390-6684
15.09.26 03:35 elioduncan

I fell victim to a freelance web development contract scam that ultimately cost me CAD 4,000. It all started when I came across a job posting on Indeed Canada, a popular online job portal. The position seemed perfect: a freelance web developer role for an established company looking for someone to design and build a fully functional e-commerce website. The job promised a high payment of CAD 20,000 upon successful completion, which sounded like a great opportunity for me to gain experience and earn decent pay.The employer, who introduced himself as a project manager from a "well-known" tech company, was very persuasive and professional in our initial communication. He explained that the project involved developing a user-friendly, responsive online store for their client and that they had a strict timeline to meet. He assured me that the payment would be made promptly after completing the tasks. However, before starting the work, he told me that I would need to pay an upfront fee of CAD 4,000 to cover certain software tools and licensing fees required for the project. This was supposedly a part of their company policy for freelance contractors, ensuring access to their premium resources. The idea of working on a professional project, coupled with the promise of a substantial payout, convinced me to pay the upfront fee.As soon as I made the payment, the project manager became increasingly difficult to reach. He initially responded to my emails and provided some vague instructions on what the project would entail, but as time went on, communication slowed to a complete halt. I never received the required tools or any proper project details. My emails went unanswered, and any attempts to contact the company were met with silence. After waiting for weeks, I realized that I had been scammed.Desperate to recover my money, I turned to TechY Force Cyber Retrieval, a service that specializes in helping victims of online scams. They helped me track the payment and took legal steps to pursue the fraudsters. Through their guidance, I was able to recover the full CAD 4,000. TechY Force Cyber Retrieval worked with my bank to reverse the transaction and liaised with the authorities to trace the scammer's details.This was a hard lesson, and I now know to be highly cautious about online job offers that require upfront payments. It is crucial to research companies thoroughly and avoid any job that seems too good to be true, especially when it involves paying money upfront. WhatsApp https://wa.link/2x6ktp Mail. [email protected]
15.09.26 15:45 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.09.26 15:45 lydiassmith567

HIRE A HACKER YOUR STOLEN CRYPTO RECOVERY / BTC / USDT / ETH WITH THE HELP OF CAPITAL CRYPTO RECOVER. I want to share my experience publicly regarding cryptocurrency wallet recovery, I highly recommend you to contact CAPITAL CRYPTO RECOVER, a professional private investigator in the Bitcoin world. They have a certified expert security team specializing in Bitcoin Recovery Services and have helped many people worldwide recover their lost funds. My wife and I were defrauded by an online manipulator posing as an experienced crypto investment professional. We lost $9.2 Million Stolen BTC in cryptocurrency and were left feeling homeless. After spending hours searching for a reliable crypto recovery service, I discovered CAPITAL CRYPTO RECOVER online. By patiently explaining my situation to their team, I was able to recover all my funds. Remarkably, my money was returned to my wallet in less than 24 hours. I am extremely grateful to CAPITAL CRYPTO RECOVER for their excellent assistance—they truly were a godsend in my difficult situation. If you have fallen victim to a cryptocurrency scam, you can reach CAPITAL CRYPTO RECOVER through the following channels Email: [email protected] OR Call/WhatsApp: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1