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借助 chaptgpt 和 deepseek，成功实现了c++上的多阶段报童模型的动态规划。花费了几天，将以前的 java 程序用 c++ 实现。

总结：

• c++ 还是比 java 快点，30个阶段快了零点几秒
• c++ 使用了 unordered_map ，存储递归数据
• java 使用了 ConcurrentSkipListMap 存储递归数据，这个可以按照排序器自动排序
• 若 c++ 也用可以排序的 map，速度反而比 java 慢了。理论上c++会快，但估计需要其他的一些功能设置
• c++ 运行时要开启 -o2 或 -o3 优化加速

C++ 代码

//
// Created by Zhen Chen on 2025/2/26.
//#include <chrono>
#include <iostream>
#include <limits>
#include <boost/functional/hash.hpp>
#include <unordered_map>
#include <iostream>
#include <map>
#include <span>
#include <csignal>class State {int period{}; // c++11, {} 值初始化，默认为 0double initialInventory{};public:State();explicit State(int period, double initialInventory);[[nodiscard]] double getInitialInventory() const;[[nodiscard]] int getPeriod() const;void print() const;// hashmap must define operator == and a struct to compute hashbool operator==(const State &other) const {// 需要定义 `==`// const MyClass &other	保证 other 参数不可修改// const 在函数结尾 保证当前对象(this) 不可修改// 不会修改成员变量的方法 都可以在函数声明的结尾添加 constreturn period == other.period && initialInventory == other.initialInventory;}// 允许哈希结构体访问私有成员// friend structfriend struct std::hash<State>;// define operator < or give a self defined comparator for sorting mapbool operator<(const State &other) const {if (period < other.period) {return true;}if (period == other.period) {if (initialInventory < other.initialInventory) {return true;}return false;}return false;}
};// `std::hash<State>` 需要特化
template<> // 表示模版特化， override 标准库中的 hash 生成函数
struct std::hash<State> {// size_t 表示无符号整数size_t operator()(const State &s) const noexcept {// noexcept 表示这个函数不会抛出异常// boost 的哈希计算更安全std::size_t seed = 0;boost::hash_combine(seed, s.period);boost::hash_combine(seed, s.initialInventory);return seed;// return std::hash<int>()(s.period) ^ std::hash<double>()(s.initialInventory) << 1; // 计算哈希值// std::hash<int>() 是一个 std::hash<int> 类型的对象，调用 () 运算符可以计算 obj.id（整数）的哈希值// ^（异或）是位运算，不会造成进位，适合合并多个哈希值// 这里的 << 1 左移 1 位（相当于乘 2），让哈希值更加分散，避免简单叠加导致哈希冲突}
};State::State() = default;State::State(const int period, const double initialInventory): period(period), initialInventory(initialInventory) {
};double State::getInitialInventory() const {return initialInventory;
}int State::getPeriod() const {return period;
}void State::print() const {std::cout << "period: " << period << ", ini I: " << initialInventory << std::endl;
}class ProbabilityMassFunctions {double truncatedQuantile;double stepSize;std::string distributionName;public:ProbabilityMassFunctions(double truncatedQuantile, double stepSize, std::string distributionName);// std::string getName();void checkName() const;static double poissonPMF(int k, double lambda);[[nodiscard]] std::vector<std::vector<std::vector<double> > > getPMF(std::span<double> demands) const;[[nodiscard]] std::vector<std::vector<std::vector<double> > >getPMFPoisson(std::span<double> demands) const;static int poissonQuantile(double p, double lambda);static double poissonCDF(int k, double lambda);
};// initializing the class
ProbabilityMassFunctions::ProbabilityMassFunctions(const double truncatedQuantile, const double stepSize, std::string distributionName): truncatedQuantile(truncatedQuantile), stepSize(stepSize), distributionName(std::move(distributionName)) {checkName();
} // std::move for efficiency passing in string and vectorvoid ProbabilityMassFunctions::checkName() const {auto name = distributionName;std::ranges::transform(name, name.begin(), ::tolower);if (name != "poisson") {std::cout << " distribution not found or to do next for this distribution\n";raise(-1);}
}// get the probability mass function value of Poisson
double ProbabilityMassFunctions::poissonPMF(const int k, const double lambda) {if (k < 0 || lambda <= 0) return 0.0; // 确保参数合法return (std::pow(lambda, k) * std::exp(-lambda)) / std::tgamma(k + 1);// tgamma(k+1) is a gamma function, 等同于factorial(k)
}// get cumulative distribution function value of Poisson
double ProbabilityMassFunctions::poissonCDF(const int k, const double lambda) {double cumulative = 0.0;double term = std::exp(-lambda);for (int i = 0; i <= k; ++i) {cumulative += term;if (i < k)term *= lambda / (i + 1); // 递推计算 P(X=i)}return cumulative;
}// get inverse cumulative distribution function value of Poisson
int ProbabilityMassFunctions::poissonQuantile(const double p, const double lambda) {int low = 0, high = std::max(100, static_cast<int>(lambda * 3)); // 初始搜索区间while (low < high) {if (const int mid = (low + high) / 2; poissonCDF(mid, lambda) < p) {low = mid + 1;} else {high = mid;}}return low;
}// get probability mass function values for each period of Poisson
std::vector<std::vector<std::vector<double> > > ProbabilityMassFunctions::
getPMF(const std::span<double> demands) const {if (distributionName == "poisson") {return getPMFPoisson(demands);}return {};
}// get probability mass function values for each period of Poisson
std::vector<std::vector<std::vector<double> > > ProbabilityMassFunctions::
getPMFPoisson(const std::span<double> demands) const {const auto T = demands.size();int supportLB[T];int supportUB[T];for (int i = 0; i < T; ++i) {supportUB[i] = poissonQuantile(truncatedQuantile, demands[i]);supportLB[i] = poissonQuantile(1 - truncatedQuantile, demands[i]);}std::vector<std::vector<std::vector<double> > > pmf(T, std::vector<std::vector<double> >());for (int t = 0; t < T; ++t) {const int demandLength = static_cast<int>((supportUB[t] - supportLB[t] + 1) / stepSize);pmf[t] = std::vector<std::vector<double> >(demandLength, std::vector<double>());for (int j = 0; j < demandLength; ++j) {pmf[t][j] = std::vector<double>(2);pmf[t][j][0] = supportLB[t] + j * stepSize;const int demand = static_cast<int>(pmf[t][j][0]);pmf[t][j][1] = poissonPMF(demand, demands[t]) / (2 * truncatedQuantile - 1);}}return pmf;
}class NewsvendorDP {int T;int capacity;double stepSize;double fixOrderCost;double unitVariOrderCost;double unitHoldCost;double unitPenaltyCost;double truncatedQuantile;double max_I;double min_I;std::vector<std::vector<std::vector<double> > > pmf;std::unordered_map<State, double> cacheActions{};std::unordered_map<State, double> cacheValues{};//    std::map<State, double> cacheActions{};
//    std::map<State, double> cacheValues{};public:NewsvendorDP(size_t T, int capacity, double stepSize, double fixOrderCost, double unitVariOrderCost,double unitHoldCost, double unitPenaltyCost, double truncatedQuantile, double max_I, double min_I,std::vector<std::vector<std::vector<double> > > pmf);[[nodiscard]] std::vector<double> feasibleActions() const;[[nodiscard]] State stateTransitionFunction(const State &state, double action, double demand) const;[[nodiscard]] double immediateValueFunction(const State &state, double action, double demand) const;[[nodiscard]] double getOptAction(const State &tate);[[nodiscard]] auto getTable() const;double recursion(const State &state);
};NewsvendorDP::NewsvendorDP(const size_t T, const int capacity,const double stepSize, const double fixOrderCost,const double unitVariOrderCost,const double unitHoldCost, const double unitPenaltyCost,const double truncatedQuantile, const double max_I,const double min_I,std::vector<std::vector<std::vector<double> > > pmf): T(static_cast<int>(T)),capacity(capacity),stepSize(stepSize),fixOrderCost(fixOrderCost),unitVariOrderCost(unitVariOrderCost),unitHoldCost(unitHoldCost), unitPenaltyCost(unitPenaltyCost), truncatedQuantile(truncatedQuantile),max_I(max_I), min_I(min_I), pmf(std::move(pmf)) {
};std::vector<double> NewsvendorDP::feasibleActions() const {const int QNum = static_cast<int>(capacity / stepSize);std::vector<double> actions(QNum);for (int i = 0; i < QNum; i = i + 1) {actions[i] = i * stepSize;}return actions;
}State NewsvendorDP::stateTransitionFunction(const State &state, const double action, const double demand) const {double nextInventory = state.getInitialInventory() + action - demand;if (state.getPeriod() == 1) {(void) nextInventory;}if (nextInventory > 0) {(void) nextInventory;}nextInventory = nextInventory > max_I ? max_I : nextInventory;nextInventory = nextInventory < min_I ? min_I : nextInventory;const int nextPeriod = state.getPeriod() + 1;// C++11 引入了统一的列表初始化（Uniform Initialization），鼓励使用大括号 {} 初始化类const auto newState = State{nextPeriod, nextInventory};return newState;
}double NewsvendorDP::immediateValueFunction(const State &state, const double action, const double demand) const {const double fixCost = action > 0 ? fixOrderCost : 0;const double variCost = action * unitVariOrderCost;double nextInventory = state.getInitialInventory() + action - demand;nextInventory = nextInventory > max_I ? max_I : nextInventory;nextInventory = nextInventory < min_I ? min_I : nextInventory;const double holdCost = std::max(unitHoldCost * nextInventory, 0.0);const double penaltyCost = std::max(-unitPenaltyCost * nextInventory, 0.0);const double totalCost = fixCost + variCost + holdCost + penaltyCost;return totalCost;
}double NewsvendorDP::getOptAction(const State &state) {return cacheActions[state];
}auto NewsvendorDP::getTable() const {size_t stateNums = cacheActions.size();std::vector<std::vector<double> > table(stateNums, std::vector<double>(3));int index = 0;for (const auto &[fst, snd]: cacheActions) {table[index][0] = fst.getPeriod();table[index][1] = fst.getInitialInventory();table[index][2] = snd;index++;}return table;
}double NewsvendorDP::recursion(const State &state) {double bestQ = 0.0;double bestValue = std::numeric_limits<double>::max();const std::vector<double> actions = feasibleActions();for (const double action: feasibleActions()) {double thisValue = 0;for (auto demandAndProb: pmf[state.getPeriod() - 1]) {thisValue += demandAndProb[1] * immediateValueFunction(state, action, demandAndProb[0]);if (state.getPeriod() < T) {auto newState = stateTransitionFunction(state, action, demandAndProb[0]);(void) action;if (cacheValues.contains(newState)) {// some issues herethisValue += demandAndProb[1] * cacheValues[newState];} else {thisValue += demandAndProb[1] * recursion(newState);}}}if (thisValue < bestValue) {bestValue = thisValue;bestQ = action;}}cacheActions[state] = bestQ;cacheValues[state] = bestValue;return bestValue;
}int main() {std::vector<double> demands(30, 20);const std::string distribution_type = "poisson";constexpr int capacity = 100; // maximum ordering quantityconstexpr double stepSize = 1.0;constexpr double fixOrderCost = 0;constexpr double unitVariOderCost = 1;constexpr double unitHoldCost = 2;constexpr double unitPenaltyCost = 10;constexpr double truncQuantile = 0.9999; // truncated quantile for the demand distributionconstexpr double maxI = 500; // maximum possible inventoryconstexpr double minI = -300; // minimum possible inventoryconst auto pmf = ProbabilityMassFunctions(truncQuantile, stepSize, distribution_type).getPMF(demands);const size_t T = demands.size();auto model = NewsvendorDP(T, capacity, stepSize, fixOrderCost, unitVariOderCost, unitHoldCost, unitPenaltyCost,truncQuantile, maxI, minI, pmf);const auto initialState = State(1, 0);const auto start_time = std::chrono::high_resolution_clock::now();const auto optValue = model.recursion(initialState);const auto end_time = std::chrono::high_resolution_clock::now();const std::chrono::duration<double> duration = end_time - start_time;std::cout << "planning horizon is " << T << " periods" << std::endl;std::cout << "running time of C++ is " << duration << std::endl;std::cout << "Final optimal value is: " << optValue << std::endl;const auto optQ = model.getOptAction(initialState);std::cout << "Optimal Q is: " << optQ << std::endl;// auto table = model.getTable();return 0;
}

Java 代码

import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.util.concurrent.ConcurrentSkipListMap;
import java.util.function.Function;
import java.util.stream.DoubleStream;
import java.util.stream.IntStream;public class CLSP {double[][][] pmf;public CLSP(double[][][] pmf) {this.pmf = pmf;}class State {int period;double initialInventory;public State(int period, double initialInventory) {this.period = period;this.initialInventory = initialInventory;}public double[] getFeasibleActions() {return actionGenerator.apply(this);}@Overridepublic int hashCode() {String hash = "";hash = hash + period + initialInventory;return hash.hashCode();}@Overridepublic boolean equals(Object o) {if (o instanceof State)return ((State) o).period == this.period &&((State) o).initialInventory == this.initialInventory;elsereturn false;}@Overridepublic String toString() {return "period = " + period + ", " + "initialInventory = " + initialInventory;}}Function<State, double[]> actionGenerator;interface StateTransitionFunction<S, A, R, S2> {public S2 apply(S s, A a, R r);}StateTransitionFunction<State, Double, Double, State> stateTransition;interface ImmediateValueFunction<S, A, R, V> {public V apply(S s, A a, R r);}ImmediateValueFunction<State, Double, Double, Double> immediateValue;Comparator<State> keyComparator = (o1, o2) -> o1.period > o2.period ? 1 :o1.period == o2.period ? Double.compare(o1.initialInventory, o2.initialInventory) : -1;//ConcurrentSkipListMap<State, Double> cacheActions = new ConcurrentSkipListMap<>(keyComparator);ConcurrentSkipListMap<State, Double> cacheValues = new ConcurrentSkipListMap<>(keyComparator);double f(State state) {return cacheValues.computeIfAbsent(state, s -> {
//            double val = Arrays.stream(s.getFeasibleActions())
//                    .map(orderQty -> Arrays.stream(pmf[s.period - 1])
//                            .mapToDouble(p -> p[1] * immediateValue.apply(s, orderQty, p[0]) +
//                                    (s.period < pmf.length ?
//                                            p[1] * f(stateTransition.apply(s, orderQty, p[0])) : 0))
//                            .sum())
//                    .min()
//                    .getAsDouble();
//            double bestOrderQty = Arrays.stream(s.getFeasibleActions())
//                    .filter(orderQty -> Arrays.stream(pmf[s.period - 1])
//                            .mapToDouble(p -> p[1] * immediateValue.apply(s, orderQty, p[0]) +
//                                    (s.period < pmf.length ?
//                                            p[1] * f(stateTransition.apply(s, orderQty, p[0])) : 0))
//                            .sum() == val)
//                    .findAny()
//                    .getAsDouble();
//            cacheActions.putIfAbsent(s, bestOrderQty);
//            return val;
//        });
//    }double[] feasibleActions = state.getFeasibleActions();double[][] dAndP = pmf[state.period - 1]; // demandAndPossibilitydouble[] QValues = new double[feasibleActions.length];double val = Double.MAX_VALUE;double bestOrderQty = 0;for (int i = 0; i < feasibleActions.length; i++) {double orderQty = feasibleActions[i];double thisQValue = 0;for (int j = 0; j < dAndP.length; j++) {thisQValue += dAndP[j][1] * immediateValue.apply(state, orderQty, dAndP[j][0]);if (state.period < pmf.length) {State newState = stateTransition.apply(state, orderQty, dAndP[j][0]);thisQValue += dAndP[j][1] * f(newState);}}QValues[i] = thisQValue;if (QValues[i] < val) {val = QValues[i];bestOrderQty = orderQty;}}this.cacheActions.putIfAbsent(state, bestOrderQty);
//            cacheValues.put(state, val);return val;});}public static void main(String[] args) {double initialInventory = 0;double[] meanDemand = new double[30];Arrays.fill(meanDemand, 20);double truncationQuantile = 0.9999;double stepSize = 1;double minState = -150;double maxState = 300;int T = meanDemand.length;double fixedOrderingCost = 0;double proportionalOrderingCost = 1;double holdingCost = 2;double penaltyCost = 10;int maxOrderQuantity = 100;Distribution[] distributions = IntStream.iterate(0, i -> i + 1).limit(T).mapToObj(i -> new PoissonDist(meanDemand[i]))
//	                                              .mapToObj(i -> new UniformDist(0, meanDemand[i]))//.mapToObj(i -> new NormalDist(meanDemand[i], 0.25 * meanDemand[i])).toArray(Distribution[]::new); // replace for loopdouble[] supportLB = IntStream.iterate(0, i -> i + 1).limit(T).mapToDouble(i -> distributions[i].inverseF(1 - truncationQuantile)).toArray();double[] supportUB = IntStream.iterate(0, i -> i + 1).limit(T).mapToDouble(i -> distributions[i].inverseF(truncationQuantile)).toArray();double[][][] pmf = new double[T][][];for (int i = 0; i < T; i++) {int demandLength = (int) ((supportUB[i] - supportLB[i] + 1) / stepSize);pmf[i] = new double[demandLength][];// demand values are all integersfor (int j = 0; j < demandLength; j++) {pmf[i][j] = new double[2];pmf[i][j][0] = supportLB[i] + j * stepSize;int demand = (int) pmf[i][j][0];if (distributions[0] instanceof DiscreteDistribution) {// double probabilitySum = distributions[i].cdf(supportUB[i]) - distributions[i].cdf(supportLB[i]);double probabilitySum = 2 * truncationQuantile - 1;pmf[i][j][1] = ((DiscreteDistribution) distributions[i]).prob(demand) / probabilitySum;} else {double probabilitySum = distributions[i].cdf(supportUB[i] + 0.5 * stepSize)- distributions[i].cdf(supportLB[i] - 0.5 * stepSize);pmf[i][j][1] = (distributions[i].cdf(pmf[i][j][0] + 0.5 * stepSize)- distributions[i].cdf(pmf[i][j][0] - 0.5 * stepSize)) / probabilitySum;}}}CLSP inventory = new CLSP(pmf);inventory.actionGenerator = s -> {return DoubleStream.iterate(0, i -> i + stepSize).limit(maxOrderQuantity + 1).toArray();};inventory.stateTransition = (state, action, randomDemand) -> {double nextInventory = state.initialInventory + action - randomDemand;nextInventory = nextInventory > maxState ? maxState : nextInventory;nextInventory = nextInventory < minState ? minState : nextInventory;return inventory.new State(state.period + 1, nextInventory);};inventory.immediateValue = (state, action, randomDemand) ->{double fixedCost = action > 0 ? fixedOrderingCost : 0;double variableCost = proportionalOrderingCost * action;double inventoryLevel = state.initialInventory + action - randomDemand;double holdingCosts = holdingCost * Math.max(inventoryLevel, 0);double penaltyCosts = penaltyCost * Math.max(-inventoryLevel, 0);double totalCosts = fixedCost + variableCost + holdingCosts + penaltyCosts;return totalCosts;};int period = 1;State initialState = inventory.new State(period, initialInventory);long currTime2 = System.currentTimeMillis();double finalValue = inventory.f(initialState);double time = (System.currentTimeMillis() - currTime2) / 1000.000;System.out.println("planning horizon is " + meanDemand.length + " periods");System.out.println("running time of Java is " + time + " s");System.out.println("final optimal expected value is: " + finalValue);double optQ = inventory.cacheActions.get(inventory.new State(period, initialInventory));System.out.println("optimal order quantity in the first priod is : " + optQ);}
}