有两个集合,一个是容器集合,一个是放置位集合,一个放置位放的容器是有限的,怎么让容器平均分配到各个放置位,用Java代码实现

可以使用模拟退火算法来解决这个问题，具体步骤如下：

1. 随机生成一个初始解，即容器的随机分配情况。
2. 计算当前解的适应度函数值，即容器分配到各个放置位的标准差。
3. 对当前解进行变异操作，即将一个容器从一个放置位移动到另一个放置位。
4. 计算变异后的解的适应度函数值。
5. 如果变异后的解比当前解更优，则接受变异后的解作为新的当前解。
6. 如果变异后的解比当前解差，则以一定概率接受变异后的解作为新的当前解，概率的计算可以使用Boltzmann函数。
7. 重复步骤3-6直到达到一定的停止条件。

下面是Java代码实现：

public class ContainerPlacement {
    private int[][] placement; // 放置位集合，每行表示一个放置位，每列表示一个容器
    private int[] containerCount; // 容器集合，每个元素表示一个容器的数量
    private int maxIteration; // 最大迭代次数
    private double temperature; // 初始温度
    private double coolingRate; // 温度降低率

    public ContainerPlacement(int[][] placement, int[] containerCount, int maxIteration, double temperature, double coolingRate) {
        this.placement = placement;
        this.containerCount = containerCount;
        this.maxIteration = maxIteration;
        this.temperature = temperature;
        this.coolingRate = coolingRate;
    }

    public void optimize() {
        int n = placement.length; // 放置位数量
        int m = containerCount.length; // 容器数量

        double currentFitness = fitnessFunction(); // 当前解的适应度函数值
        double bestFitness = currentFitness; // 最优解的适应度函数值
        int[][] bestPlacement = copyPlacement(placement); // 最优解的放置位集合

        Random random = new Random();

        for (int i = 0; i < maxIteration; i++) {
            int x = random.nextInt(n);
            int y = random.nextInt(n);
            int j = random.nextInt(m);

            int delta = containerCount[j] / n; // 每个放置位应该分配的数量
            int oldXi = placement[x][j];
            int oldYi = placement[y][j];
            int newXi = Math.min(containerCount[j] - delta * (n - 1), oldXi + delta); // 容器移动后x放置位的容器数量
            int newYi = Math.min(containerCount[j] - delta * (n - 1), oldYi - delta); // 容器移动后y放置位的容器数量

            if (newXi == oldXi && newYi == oldYi) {
                continue; // 容器没有移动，不进行计算
            }

            double newFitness = fitnessFunction(newXi, newYi);

            if (newFitness < currentFitness) {
                placement[x][j] = newXi;
                placement[y][j] = newYi;
                currentFitness = newFitness;
            } else {
                double deltaFitness = newFitness - currentFitness;
                double acceptProbability = Math.exp(-deltaFitness / temperature);

                if (random.nextDouble() < acceptProbability) {
                    placement[x][j] = newXi;
                    placement[y][j] = newYi;
                    currentFitness = newFitness;
                }
            }

            if (currentFitness < bestFitness) {
                bestFitness = currentFitness;
                bestPlacement = copyPlacement(placement);
            }

            temperature *= coolingRate; // 降低温度
        }

        placement = bestPlacement; // 更新最优解
    }

    private double fitnessFunction() {
        int n = placement.length; // 放置位数量
        int m = containerCount.length; // 容器数量
        double[] mean = new double[n]; // 各个放置位的容器数量均值
        double sum = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                mean[i] += placement[i][j];
            }
            mean[i] /= m;
        }

        for (int i = 0; i < n; i++) {
            double diff = 0;
            for (int j = 0; j < m; j++) {
                diff += Math.pow(placement[i][j] - mean[i], 2);
            }
            sum += diff / m;
        }

        return Math.sqrt(sum / n);
    }

    private double fitnessFunction(int newXi, int newYi) {
        int n = placement.length; // 放置位数量
        int m = containerCount.length; // 容器数量
        double[] mean = new double[n]; // 各个放置位的容器数量均值
        double sum = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (i == x) {
                    mean[i] += newXi;
                } else if (i == y) {
                    mean[i] += newYi;
                } else {
                    mean[i] += placement[i][j];
                }
            }
            mean[i] /= m;
        }

        for (int i = 0; i < n; i++) {
            double diff = 0;
            for (int j = 0; j < m; j++) {
                if (i == x) {
                    diff += Math.pow(newXi - mean[i], 2);
                } else if (i == y) {
                    diff += Math.pow(newYi - mean[i], 2);
                } else {
                    diff += Math.pow(placement[i][j] - mean[i], 2);
                }
            }
            sum += diff / m;
        }

        return Math.sqrt(sum / n);
    }

    private int[][] copyPlacement(int[][] placement) {
        int n = placement.length;
        int m = placement[0].length;
        int[][] copy = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                copy[i][j] = placement[i][j];
            }
        }
        return copy;
    }

    public int[][] getPlacement() {
        return placement;
    }
}

使用方法：

int[][] placement = new int[][] {
    {10, 10, 10},
    {10, 10, 10},
    {10, 10, 10},
    {10, 10, 10},
    {10, 10, 10},
};
int[] containerCount = new int[] {50, 50, 50};
int maxIteration = 10000;
double temperature = 100;
double coolingRate = 0.99;

ContainerPlacement cp = new ContainerPlacement(placement, containerCount, maxIteration, temperature, coolingRate);
cp.optimize();
int[][] optimizedPlacement = cp.getPlacement();