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一、前言

本文以求解二元函数最小值为例，如果需要求解多元函数，只需要修改以下变量即可：

• varNum：变量维度数
• ub和lb：变量的上下界
• vMaxArr：每个维度的搜索速度限制

二、优化目标

目标：在变量区间范围最小化 Z = x^2 + y^2 - xy - 10x - 4y +60

三、求解结果

变量取值为：[8.00000005186109, 5.999999963566031]
最优解为：7.999999999999986

四、迭代结果可视化

这收敛速度也太快了，已经和SMO相当了！

五、算法流程图

六、Java代码实现

本项目的所有代码均上传至 GitHub 仓库：https://github.com/WSKH0929/SwarmIntelligenceAlgorithm（如果对你有帮助的话可以点个Star❤️哟~）

6.1 算法部分代码

import java.util.Arrays;
import java.util.Random;/*** @Author：WSKH* @ClassName：CSO_Solve* @ClassType：* @Description：* @Date：2022/6/8/18:26* @Email：1187560563@qq.com* @Blog：https://blog.csdn.net/weixin_51545953?type=blog*/
public class CSO_Solve {// 蟑螂对象class Cockroach {// 当前蟑螂的坐标（自变量数组）double[] curVars;// 当前自变量对应的目标函数值double curObjValue;// 适应度（解决最小化问题，所以适应度为目标函数值的倒数）double fit;// 全参构造public Cockroach(double[] curVars, double curObjValue, double fit) {this.curVars = curVars;this.curObjValue = curObjValue;this.fit = fit;}}// 算法参数// 变量个数int varNum = 2;// 最大迭代次数int maxGen = 1000;// 蟑螂群中蟑螂的个数int cockroachNum = 500;// 视野double visual = 50;// 残忍行为次数int ruthlessBehaviorCnt = 1;// 分散行为次数int dispersingBehaviorCnt = 30;// 步长数组（各个维度的步长）double[] stepArr = new double[]{1.2, 1.2};// 变量的上下界double[] ub = new double[]{1000, 1000};double[] lb = new double[]{-1000, -1000};// 随机数对象Random random = new Random();// 蟑螂群Cockroach[] cockroaches;// 最佳的蟑螂Cockroach bestCockroach;// 记录迭代过程public double[][][] positionArr;// 当前记录的行数int r;// 求解主函数public void solve() {// 初始化蟑螂群initCockroaches();// 开始迭代for (int t = 0; t < maxGen; t++) {// 聚集行为ChaseSwarmingBehavior();report();// 分散行为DispersingBehavior();report();// 残忍行为RuthlessBehavior();report();}// 输出最好的结果System.out.println("变量取值为：" + Arrays.toString(bestCockroach.curVars));System.out.println("最优解为：" + bestCockroach.curObjValue);}// 聚集行为void ChaseSwarmingBehavior() {// 找到个体最优Cockroach[] localBestCockroaches = new Cockroach[cockroachNum];for (int i = 0; i < cockroaches.length; i++) {localBestCockroaches[i] = findLocalBestCockroach(i);if(bestCockroach.fit < cockroaches[i].fit){bestCockroach = copyCockroach(cockroaches[i]);}}for (int i = 0; i < cockroaches.length; i++) {// 说明当前蟑螂就是个体最优（或接近个体最优）if(Math.abs(localBestCockroaches[i].curObjValue-cockroaches[i].curObjValue) <= 0.00001){// 那就朝着全局最优靠近Cockroach tempCockroach = copyCockroach(cockroaches[i]);for (int m = 0; m < varNum; m++) {moveCockroach(tempCockroach,m,stepArr[m]*(bestCockroach.curVars[m]-tempCockroach.curVars[m]));}tempCockroach.curObjValue = getObjValue(tempCockroach.curVars);tempCockroach.fit = 1/tempCockroach.curObjValue;if(tempCockroach.fit > cockroaches[i].fit){cockroaches[i] = tempCockroach;}}else{// 朝着个体最优移动Cockroach tempCockroach = copyCockroach(cockroaches[i]);for (int m = 0; m < varNum; m++) {moveCockroach(tempCockroach,m,stepArr[m]*(localBestCockroaches[i].curVars[m]-tempCockroach.curVars[m]));}tempCockroach.curObjValue = getObjValue(tempCockroach.curVars);tempCockroach.fit = 1/tempCockroach.curObjValue;if(tempCockroach.fit > cockroaches[i].fit){cockroaches[i] = tempCockroach;}}}}// 分散行为void DispersingBehavior() {for (int i = 0; i < cockroaches.length; i++) {for (int j = 0; j < dispersingBehaviorCnt; j++) {Cockroach tempCockroach = copyCockroach(cockroaches[i]);for (int m = 0; m < varNum; m++) {double move = stepArr[m] * (random.nextDouble()-0.5)*2;moveCockroach(tempCockroach,m,move);}if(tempCockroach.fit > cockroaches[i].fit){cockroaches[i] = tempCockroach;if(tempCockroach.fit > bestCockroach.fit){bestCockroach = copyCockroach(tempCockroach);}}}}}// 残忍行为void RuthlessBehavior() {for (int i = 0; i < ruthlessBehaviorCnt; i++) {cockroaches[random.nextInt(cockroachNum)] = copyCockroach(bestCockroach);}}// 寻找个体最优蟑螂Cockroach findLocalBestCockroach(int j) {Cockroach localBest = copyCockroach(cockroaches[j]);for (int i = 0; i < cockroaches.length; i++) {if (i != j) {if (localBest.fit < cockroaches[i].fit && getDistance(cockroaches[j], cockroaches[i]) <= visual) {localBest = copyCockroach(cockroaches[i]);}}}return localBest;}// 记录void report() {for (int i = 0; i < cockroaches.length; i++) {for (int j = 0; j < varNum; j++) {positionArr[r][i][j] = cockroaches[i].curVars[j];}}r++;}// 求两个蟑螂之间的距离double getDistance(Cockroach f1, Cockroach f2) {double dis = 0d;for (int i = 0; i < varNum; i++) {dis += Math.pow(f1.curVars[i] - f2.curVars[i], 2);}return Math.sqrt(dis);}// 初始化蟑螂群private void initCockroaches() {positionArr = new double[3 * maxGen][cockroachNum][varNum];cockroaches = new Cockroach[cockroachNum];for (int i = 0; i < cockroachNum; i++) {cockroaches[i] = getRandomCockroach();if (i == 0 || bestCockroach.fit < cockroaches[i].fit) {bestCockroach = copyCockroach(cockroaches[i]);}}}// 控制蟑螂在第m个维度上移动n个距离public void moveCockroach(Cockroach cockroach, int m, double n) {// 移动cockroach.curVars[m] += n;// 超出定义域的判断if (cockroach.curVars[m] < lb[m]) {cockroach.curVars[m] = lb[m];}if (cockroach.curVars[m] > ub[m]) {cockroach.curVars[m] = ub[m];}}// 获取一个随机生成的蟑螂Cockroach getRandomCockroach() {double[] vars = new double[varNum];for (int j = 0; j < vars.length; j++) {vars[j] = lb[j] + random.nextDouble() * (ub[j] - lb[j]);}double objValue = getObjValue(vars);return new Cockroach(vars.clone(), objValue, 1 / objValue);}/*** @param vars 自变量数组* @return 返回目标函数值*/public double getObjValue(double[] vars) {//目标：在变量区间范围最小化 Z = x^2 + y^2 - xy - 10x - 4y +60return Math.pow(vars[0], 2) + Math.pow(vars[1], 2) - vars[0] * vars[1] - 10 * vars[0] - 4 * vars[1] + 60;}// 复制蟑螂Cockroach copyCockroach(Cockroach old) {return new Cockroach(old.curVars.clone(), old.curObjValue, old.fit);}}

6.2 可视化部分代码

import javafx.animation.KeyFrame;
import javafx.animation.Timeline;
import javafx.application.Application;
import javafx.geometry.Pos;
import javafx.scene.Scene;
import javafx.scene.canvas.Canvas;
import javafx.scene.canvas.GraphicsContext;
import javafx.scene.control.Button;
import javafx.scene.input.MouseEvent;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.HBox;
import javafx.scene.paint.Color;
import javafx.stage.Stage;
import javafx.util.Duration;/*** @Author：WSKH* @ClassName：PlotUtil* @ClassType：* @Description：* @Date：2022/6/6/18:31* @Email：1187560563@qq.com* @Blog：https://blog.csdn.net/weixin_51545953?type=blog*/
public class PlotUtil extends Application {//当前的时间轴private Timeline nowTimeline;//绘图位置坐标private double[][][] positionArr;public static void main(String[] args) {launch(args);}@Overridepublic void start(Stage primaryStage) throws Exception {// 调用算法获取绘图数据CSO_Solve solver = new CSO_Solve();solver.solve();positionArr = solver.positionArr;// 画图try {BorderPane root = new BorderPane();root.setStyle("-fx-padding: 20;");Scene scene = new Scene(root, 1600, 900);double canvasWid = 800;double canvasHei = 800;//根据画布大小缩放坐标值this.fixPosition(canvasWid - 100, canvasHei - 100);//画布和画笔HBox canvasHbox = new HBox();Canvas canvas = new Canvas();canvas.setWidth(canvasWid);canvas.setHeight(canvasHei);canvasHbox.setPrefWidth(canvasWid);canvasHbox.getChildren().add(canvas);canvasHbox.setAlignment(Pos.CENTER);canvasHbox.setStyle("-fx-spacing: 20;" +"-fx-background-color: #87e775;");root.setTop(canvasHbox);GraphicsContext paintBrush = canvas.getGraphicsContext2D();//启动HBox hBox2 = new HBox();Button beginButton = new Button("播放迭代过程");hBox2.getChildren().add(beginButton);root.setBottom(hBox2);hBox2.setAlignment(Pos.CENTER);//启动仿真以及暂停仿真beginButton.addEventHandler(MouseEvent.MOUSE_CLICKED, event -> {nowTimeline.play();});//创建扫描线连接动画nowTimeline = new Timeline();createAnimation(paintBrush);primaryStage.setScene(scene);primaryStage.show();} catch (Exception e) {e.printStackTrace();}}/*** 修正cityPositionArr的坐标，让画出来的点在画布内** @param width* @param height*/private void fixPosition(double width, double height) {double minX = Double.MAX_VALUE;double maxX = -Double.MAX_VALUE;double minY = Double.MAX_VALUE;double maxY = -Double.MAX_VALUE;for (int i = 0; i < this.positionArr.length; i++) {for (int j = 0; j < this.positionArr[0].length; j++) {minX = Math.min(minX, this.positionArr[i][j][0]);maxX = Math.max(maxX, this.positionArr[i][j][0]);minY = Math.min(minY, this.positionArr[i][j][1]);maxY = Math.max(maxY, this.positionArr[i][j][1]);}}double multiple = Math.max((maxX - minX) / width, (maxY - minY) / height);//转化为正数数for (int i = 0; i < this.positionArr.length; i++) {for (int j = 0; j < this.positionArr[0].length; j++) {if (minX < 0) {this.positionArr[i][j][0] = this.positionArr[i][j][0] - minX;}if (minY < 0) {this.positionArr[i][j][1] = this.positionArr[i][j][1] - minY;}}}for (int i = 0; i < this.positionArr.length; i++) {for (int j = 0; j < this.positionArr[0].length; j++) {this.positionArr[i][j][0] = this.positionArr[i][j][0] / multiple;this.positionArr[i][j][1] = this.positionArr[i][j][1] / multiple;}}}/*** 用画笔在画布上画出所有的孔* 画第i代的所有粒子*/private void drawAllCircle(GraphicsContext paintBrush, int i) {paintBrush.clearRect(0, 0, 2000, 2000);paintBrush.setFill(Color.RED);for (int j = 0; j < this.positionArr[i].length; j++) {drawCircle(paintBrush, i, j);}}/*** 用画笔在画布上画出一个孔* 画第i代的第j个粒子*/private void drawCircle(GraphicsContext paintBrush, int i, int j) {double x = this.positionArr[i][j][0];double y = this.positionArr[i][j][1];double radius = 2;// 圆的直径double diameter = radius * 2;paintBrush.fillOval(x, y, diameter, diameter);}/*** 创建动画*/private void createAnimation(GraphicsContext paintBrush) {for (int i = 0; i < this.positionArr[0].length; i++) {int finalI = i;KeyFrame keyFrame = new KeyFrame(Duration.seconds(i * 0.05), event -> drawAllCircle(paintBrush, finalI));nowTimeline.getKeyFrames().add(keyFrame);}}}