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：[8.0001386745, 6.000077817430381]最优解为：8.000000014494901

搜索过程可视化

Java代码

import java.util.Arrays;import java.util.Random;/*** @Author：WSKH* @ClassName：FA_Solve* @ClassType：* @Description：* @Date：/6/8/18:26* @Email：1187560563@* @Blog：/weixin_51545953?type=blog*/public class FA_Solve {// 萤火虫对象class Firefly {// 当前萤火虫的坐标（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 Firefly(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 = 500;// 萤火虫群中萤火虫的个数int fireflyNum = 200;// 光吸收系数double gamma = 0.3;// 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();// 萤火虫群Firefly[] fireflies;// 最佳的萤火虫Firefly bestFirefly;// 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() {// 初始化萤火虫群initFireflyes();// 开始迭代for (int t = 0; t < maxGen; t++) {for (int i = 0; i < fireflyNum; i++) {for (int j = 0; j < fireflyNum; j++) {double light = getLight(getDistance(fireflies[i], fireflies[j]), fireflies[j].fit);if (i != j && fireflies[i].fit < fireflies[j].fit) {Firefly tempFirefly = copyFirefly(fireflies[i]);for (int m = 0; m < varNum; m++) {double move = light * (fireflies[j].curVars[m] - fireflies[i].curVars[m]) + stepArr[m] * (random.nextDouble()-0.5);moveFirefly(tempFirefly, m,move);}updateFireFly(tempFirefly);if(tempFirefly.fit > fireflies[i].fit){fireflies[i] = tempFirefly;if(bestFirefly.fit < tempFirefly.fit){bestFirefly = copyFirefly(tempFirefly);}}}}}report();}// 输出最好的结果System.out.println("变量取值为：" + Arrays.toString(bestFirefly.curVars));System.out.println("最优解为：" + bestFirefly.curObjValue);}// 记录void report() {for (int i = 0; i < fireflies.length; i++) {for (int j = 0; j < varNum; j++) {positionArr[r][i][j] = fireflies[i].curVars[j];}}r++;}// 获取光强double getLight(double r, double fit) {return fit * Math.exp(-gamma * Math.pow(r, 2));}// 求两个萤火虫之间的距离double getDistance(Firefly f1, Firefly 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);}// 初始化萤火虫群private void initFireflyes() {positionArr = new double[maxGen][fireflyNum][varNum];fireflies = new Firefly[fireflyNum];for (int i = 0; i < fireflyNum; i++) {fireflies[i] = getRandomFirefly();if (i == 0 || bestFirefly.fit < fireflies[i].fit) {bestFirefly = copyFirefly(fireflies[i]);}}}// 控制萤火虫在第m个维度上移动n个距离public void moveFirefly(Firefly firefly, int m, double n) {// 移动firefly.curVars[m] += n;// 超出定义域的判断if (firefly.curVars[m] < lb[m]) {firefly.curVars[m] = lb[m];}if (firefly.curVars[m] > ub[m]) {firefly.curVars[m] = ub[m];}}// 更新萤火虫信息void updateFireFly(Firefly firefly) {double objValue = getObjValue(firefly.curVars);firefly.curObjValue = objValue;firefly.fit = 1 / objValue;}// 获取一个随机生成的萤火虫Firefly getRandomFirefly() {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 Firefly(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;}// 复制萤火虫Firefly copyFirefly(Firefly old) {return new Firefly(old.curVars.clone(), old.curObjValue, old.fit);}}

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FA_Solve solver = new FA_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);}}}