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：[7.996330803705318, 6.022624753356061]最优解为：8.000608357127064

迭代结果可视化

算法流程

Java代码

import java.util.Arrays;import java.util.Random;/*** @Author：WSKH* @ClassName：AFSA_Solve* @ClassType：* @Description：* @Date：/6/8/18:26* @Email：1187560563@* @Blog：/weixin_51545953?type=blog*/public class AFSA_Solve {// 鱼对象class Fish {// 当前鱼的坐标（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 Fish(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;// 鱼群中鱼的个数int fishNum = 300;// 每次的最大觅食次数int preyCnt = 20;// 鱼的最大感知距离double visual = 50;// 可接受的拥挤程度double crowdedRate = 0.6;// 步长数组（各个维度的步长）double[] stepArr = new double[]{6, 6};// 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();// 鱼群Fish[] fishes;// 最佳的鱼Fish bestFish;// 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() {// 初始化鱼群initFishes();// 开始迭代for (int t = 0; t < maxGen; t++) {// 聚群行为AFSwarm();report();// 追尾AFFollow();report();// 觅食AFPrey();report();}for (Fish fish : fishes) {if (fish.fit > bestFish.fit) {bestFish = fish;}}// 输出最好的结果System.out.println("变量取值为：" + Arrays.toString(bestFish.curVars));System.out.println("最优解为：" + bestFish.curObjValue);}// 移动行为(在鱼群的移动过程中，当一条鱼或几条鱼找到食物时，附近的伙伴会迅速移动并到达食物)void AFFollow() {for (int i = 0; i < fishes.length; i++) {// 探索视野内的鱼有多少条，并找到最大适应值的鱼int friendCount = 0;Fish maxFish = copyFish(fishes[i]);for (int j = 0; j < fishes.length; j++) {if (i != j && getDistance(fishes[i], fishes[j]) <= visual) {friendCount++;if (fishes[j].fit > maxFish.fit) {maxFish = copyFish(fishes[j]);}}}// 如果周围不拥挤，且两个鱼的目标函数不相等if ((double) friendCount / fishNum <= crowdedRate && Math.abs(maxFish.curObjValue - fishes[i].curObjValue) > 0.0000001) {// 尝试往最大适应值位置游Fish tempFish = copyFish(fishes[i]);double distance = getDistance(maxFish, tempFish);for (int m = 0; m < varNum; m++) {double move = (maxFish.curVars[m] - tempFish.curVars[m]) / (distance) * stepArr[m] * random.nextDouble();moveFish(tempFish, m, move);}tempFish.curObjValue = getObjValue(tempFish.curVars);tempFish.fit = 1 / tempFish.curObjValue;if (tempFish.fit > fishes[i].fit) {fishes[i] = tempFish;} else {// 否则，进行觅食AFPrey(i);}} else {// 否则，进行觅食AFPrey(i);}}}// 聚群行为(鱼群在移动的过程中会自然地成群聚集，这是一种生活习惯，可以保证群体的存在，避免危险)void AFSwarm() {for (int i = 0; i < fishes.length; i++) {// 探索视野内的鱼有多少条，并计算周围鱼群的中心double[] midPoint = new double[varNum];int friendCount = 0;for (int j = 0; j < fishes.length; j++) {if (i != j && getDistance(fishes[i], fishes[j]) <= visual) {friendCount++;for (int m = 0; m < varNum; m++) {midPoint[m] += fishes[j].curVars[m];}}}// 计算中心for (int m = 0; m < midPoint.length; m++) {midPoint[m] /= friendCount;}double objValue = getObjValue(midPoint);// 获取中心的鱼Fish midFish = new Fish(midPoint, objValue, 1 / objValue);// 如果中心不拥挤if ((double) friendCount / fishNum <= crowdedRate) {// 尝试往中心位置游Fish tempFish = copyFish(fishes[i]);double distance = getDistance(midFish, tempFish);for (int m = 0; m < varNum; m++) {double move = (midPoint[m] - tempFish.curVars[m]) / (distance) * stepArr[m] * random.nextDouble();moveFish(tempFish, m, move);}tempFish.curObjValue = getObjValue(tempFish.curVars);tempFish.fit = 1 / tempFish.curObjValue;if (tempFish.fit > fishes[i].fit) {fishes[i] = tempFish;} else {// 否则，进行觅食AFPrey(i);}} else {// 否则，进行觅食AFPrey(i);}}}// 觅食行为(这是鱼类对食物的基本生物学行为。一般来说，鱼通过视觉感知水中食物的浓度来决定向哪移动，然后选择移动的方向)void AFPrey(int i) {// 尝试觅食preyCnt次for (int j = 0; j < preyCnt; j++) {Fish tempFish = copyFish(fishes[i]);for (int m = 0; m < varNum; m++) {moveFish(tempFish, m, visual * (random.nextDouble() - 0.5) * 2);}tempFish.curObjValue = getObjValue(tempFish.curVars);tempFish.fit = 1 / tempFish.curObjValue;if (tempFish.fit > fishes[i].fit) {double distance = getDistance(tempFish, fishes[i]);// 觅食成功，向成功方向移动for (int m = 0; m < varNum; m++) {double move = (tempFish.curVars[m] - fishes[i].curVars[m]) / (distance) * stepArr[m] * random.nextDouble();moveFish(fishes[i], m, move);}fishes[i].curObjValue = getObjValue(fishes[i].curVars);fishes[i].fit = 1 / fishes[i].curObjValue;} else {// 觅食失败，随机移动for (int m = 0; m < varNum; m++) {double move = stepArr[m] * (random.nextDouble() - 0.5) * 2;moveFish(tempFish, m, move);}tempFish.curObjValue = getObjValue(tempFish.curVars);tempFish.fit = 1 / tempFish.curObjValue;if(tempFish.fit > fishes[i].fit){fishes[i] = tempFish;}}}}void AFPrey(){for (int i = 0; i < fishes.length; i++) {AFPrey(i);}}// 记录void report(){for (int i = 0; i < fishes.length; i++) {for (int j = 0; j < varNum; j++) {positionArr[r][i][j] = fishes[i].curVars[j];}}r++;}// 初始化鱼群private void initFishes() {positionArr = new double[3*maxGen][fishNum][varNum];fishes = new Fish[fishNum];for (int i = 0; i < fishNum; i++) {fishes[i] = getRandomFish();if (i == 0 || bestFish.fit < fishes[i].fit) {bestFish = copyFish(fishes[i]);}}}// 控制鱼在第m个维度上移动n个距离public void moveFish(Fish fish, int m, double n) {// 移动fish.curVars[m] += n;// 超出定义域的判断if (fish.curVars[m] < lb[m]) {fish.curVars[m] = lb[m];}if (fish.curVars[m] > ub[m]) {fish.curVars[m] = ub[m];}}// 求两条鱼之间的距离double getDistance(Fish f1, Fish 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);}// 求两点之间的距离double getDistance(double p1, double p2) {return Math.sqrt(Math.pow(p1 - p2, 2));}// 获取一个随机生成的鱼Fish getRandomFish() {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 Fish(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;}// 复制鱼Fish copyFish(Fish old) {return new Fish(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AFSA_Solve solver = new AFSA_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);}}}