文章目录

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

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

求解结果

变量取值为：[8.000000075136509, 6.000000056246476]最优解为：7.999999999999979

搜索过程可视化

Java算法代码

import java.util.Arrays;import parator;import java.util.Random;/*** @Author：WSKH* @ClassName：MFO_Solve* @ClassType：* @Description：* @Date：/6/8/18:26* @Email：1187560563@* @Blog：/weixin_51545953?type=blog*/public class MFO_Solve {// 飞蛾对象class Moth {// 当前飞蛾的坐标（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;// 火焰（飞蛾目前到过的最佳位置）double[] bestVars;double bestObjValue;double bestFit;// 全参构造public Moth(double[] curVars, double curObjValue, double fit, double[] bestVars, double bestObjValue, double bestFit) {this.curVars = curVars;this.curObjValue = curObjValue;this.fit = fit;this.bestVars = bestVars;this.bestObjValue = bestObjValue;this.bestFit = bestFit;}}// 算法参数// 变量个数int varNum = 2;// 最大迭代次数int maxGen = 500;// 飞蛾群中飞蛾的个数int mothNum = 500;// 螺旋常量double b = 2;// 每一次搜索的火焰数int flyToFireCnt = 20;// 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();// 飞蛾群Moth[] moths;// 最佳的飞蛾Moth bestMoth;// 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() {// 初始化飞蛾群initMoths();// 开始迭代for (int i = 0; i < maxGen; i++) {flyToFire();report();}// 输出最好的结果System.out.println("变量取值为：" + Arrays.toString(bestMoth.curVars));System.out.println("最优解为：" + bestMoth.curObjValue);}// 扑火void flyToFire() {// 先按照火焰热度排序，热度高的排前面Arrays.sort(moths, new Comparator<Moth>() {@Overridepublic int compare(Moth o1, Moth o2) {return pare(o2.bestFit,o1.bestFit);}});// 开始扑火for (int i = 0; i < mothNum; i++) {int c = 0;for (int j = 0; j < mothNum; j++) {if (i != j && c <= flyToFireCnt) {Moth tempMoth = copyMoth(moths[i]);for (int m = 0; m < varNum; m++) {double t = (random.nextDouble() - 0.5) * 2;double move = Math.abs(tempMoth.curVars[m] - moths[j].bestVars[m]) * Math.exp(b * t) * Math.cos(2 * Math.PI * t) + moths[j].bestVars[m] - tempMoth.curVars[m];moveMoth(tempMoth, m, move);}updateMoth(tempMoth);moths[i] = tempMoth;if (tempMoth.fit > bestMoth.fit) {bestMoth = copyMoth(tempMoth);}c++;}}}}// 记录void report() {for (int i = 0; i < moths.length; i++) {for (int j = 0; j < varNum; j++) {positionArr[r][i][j] = moths[i].curVars[j];}}r++;}// 初始化飞蛾群private void initMoths() {positionArr = new double[2 * maxGen][mothNum][varNum];moths = new Moth[mothNum];for (int i = 0; i < mothNum; i++) {moths[i] = getRandomMoth();if (i == 0 || bestMoth.fit < moths[i].fit) {bestMoth = copyMoth(moths[i]);}}}// 控制飞蛾在第m个维度上移动n个距离public void moveMoth(Moth moth, int m, double n) {// 移动moth.curVars[m] += n;// 超出定义域的判断if (moth.curVars[m] < lb[m]) {moth.curVars[m] = lb[m];}if (moth.curVars[m] > ub[m]) {moth.curVars[m] = ub[m];}}// 更新飞蛾信息void updateMoth(Moth moth) {double objValue = getObjValue(moth.curVars);moth.curObjValue = objValue;moth.fit = 1 / objValue;if (moth.fit > moth.bestFit) {moth.bestFit = moth.fit;moth.bestObjValue = moth.curObjValue;moth.bestVars = moth.curVars.clone();}}// 获取一个随机生成的飞蛾Moth getRandomMoth() {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 Moth(vars.clone(), objValue, 1 / objValue, 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;}// 复制飞蛾Moth copyMoth(Moth old) {return new Moth(old.curVars.clone(), old.curObjValue, old.fit, old.bestVars.clone(), old.bestObjValue, old.bestFit);}}

可视化代码

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：/6/6/18:31* @Email：1187560563@* @Blog：/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MFO_Solve solver = new MFO_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);}}}