文章目录

前言优化目标优化结果迭代过程可视化Java代码可视化代码优化流程（图太大了，所以放最后...）

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

优化结果

变量取值为：[8.000000025138169, 6.000000008671988]最优解为：7.999999999999986

迭代过程可视化

注意，下图可没有加速处理！SMO算法的收敛速度就是那么快！

在SMO中，局部领导者阶段和全局领导者阶段有助于利用搜索空间，而探索则通过局部领导者决策阶段和全局领导者决策阶段完成。SMO性能分析表明，SMO在可靠性、有效性和精度方面超过了ABC、DE和PSO。

Java代码

import java.util.*;/*** @Author：WSKH* @ClassName：SMO_Solver* @ClassType：* @Description：* @Date：/6/8/13:42* @Email：1187560563@* @Blog：/weixin_51545953?type=blog*/public class SMO_Solver {// 蜘蛛猴对象class SpiderMonkey {// 当前蜘蛛猴坐标（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;// 全参数构造public SpiderMonkey(double[] curVars, double curObjValue, double fit) {this.curVars = curVars;this.curObjValue = curObjValue;this.fit = fit;}}// 算法参数// 蜘蛛猴群List<SpiderMonkey[]> spiderMonkeyList = new ArrayList<>();// 局部领导者List<SpiderMonkey> localLeaderList = new ArrayList<>();// 最好的蜘蛛猴(全局领导者)SpiderMonkey bestSpiderMonkey;// 随机数对象Random random = new Random();// 最大迭代次数int maxGen = 500;// 蜘蛛猴数量int spiderMonkeyNum = 300;// 局部搜索次数(一般等于蜘蛛猴数量)int localSearchCount = spiderMonkeyNum;// 局部领导者决策阶段的更新几率double LLDP_PR = 0.1;// 局部领导者阶段的更新几率double LLP_PR = 0.8;// 变量维度数int varNum = 2;// 最大组数(一般要至少保证每组里有10个蜘蛛猴)int maxgroupNum = spiderMonkeyNum/10 ;// 变量的上下界double[] ub = new double[]{1000, 1000};double[] lb = new double[]{-1000, -1000};// 局部计数器int[] localLimitCount = new int[]{0};// 停止条件int limitCnt = 50;// 全局计数器int globalLimitCount;// 记录迭代过程public double[][][] positionArr;// 记录迭代器的行数int curC = 0;// 是否开启贪心机制（只接受比当前解好的解）boolean greedy = true;// 求解主函数public void solve() {// 初始化蜘蛛猴种群initSpiderMonkeys();// 开始迭代for (int t = 0; t < maxGen; t++) {// 局部领导者阶段（LLP：所有的蜘蛛猴都有机会更新自己）LLP();// 全局领导者阶段（GLP：轮盘赌，随机选取，偏向于对fit值大的蜘蛛猴进行更新）GLP();// 全局领导者学习阶段（如果全局领导者有更新，则globalLimitCount=0，否则globalLimitCount++）GLLP();// 局部领导者学习阶段（如果局部领导者有更新，则localLimitCount=0，否则localLimitCount++）LLLP();// 局部领导者决策阶段LLDP();// 全局领导者决策阶段GLDP();}// 输出最好的结果System.out.println("变量取值为：" + Arrays.toString(bestSpiderMonkey.curVars));System.out.println("最优解为：" + bestSpiderMonkey.curObjValue);}// 全局领导者决策阶段private void GLDP() {if (globalLimitCount >= limitCnt) {globalLimitCount = 0;if (spiderMonkeyList.size() < maxgroupNum) {// 分裂List<SpiderMonkey> tempList = new ArrayList<>();for (SpiderMonkey[] spiderMonkeys : spiderMonkeyList) {tempList.addAll(Arrays.asList(spiderMonkeys));}tempList.sort(new Comparator<SpiderMonkey>() {@Overridepublic int compare(SpiderMonkey o1, SpiderMonkey o2) {return pare(o2.fit,o1.fit);}});//int groupNum = spiderMonkeyList.size() + 1;spiderMonkeyList = new ArrayList<>();int avgNum = spiderMonkeyNum / groupNum;for (int i = 0; i < groupNum - 1; i++) {SpiderMonkey[] spiderMonkeys = new SpiderMonkey[avgNum];for (int j = 0; j < avgNum; j++) {spiderMonkeys[j] = copySpiderMonkey(tempList.remove(0));}spiderMonkeyList.add(spiderMonkeys);}spiderMonkeyList.add(tempList.toArray(new SpiderMonkey[0]));localLimitCount = new int[groupNum];} else {// 融合SpiderMonkey[] spiderMonkeys = new SpiderMonkey[spiderMonkeyNum];int i = 0;for (SpiderMonkey[] monkeys : spiderMonkeyList) {for (SpiderMonkey monkey : monkeys) {spiderMonkeys[i++] = copySpiderMonkey(monkey);}}spiderMonkeyList = new ArrayList<>();spiderMonkeyList.add(spiderMonkeys);localLimitCount = new int[]{0};}// 更新局部领导者localLeaderList = new ArrayList<>();for (SpiderMonkey[] spiderMonkeys : spiderMonkeyList) {localLeaderList.add(copySpiderMonkey(spiderMonkeys[0]));int index = localLeaderList.size() - 1;for (int i = 1; i < spiderMonkeys.length; i++) {if (localLeaderList.get(index).fit < spiderMonkeys[i].fit) {localLeaderList.set(index, copySpiderMonkey(spiderMonkeys[i]));}}}}}// 局部领导者决策阶段private void LLDP() {int c = 0;for (int i = 0; i < spiderMonkeyList.size(); i++) {SpiderMonkey[] spiderMonkeys = spiderMonkeyList.get(i);if (localLimitCount[i] < limitCnt) {for (int j = 0; j < spiderMonkeys.length; j++) {SpiderMonkey tempSpiderMonkey = copySpiderMonkey(spiderMonkeys[j]);for (int m = 0; m < varNum; m++) {if (random.nextDouble() <= LLDP_PR) {tempSpiderMonkey.curVars[m] = lb[m] + random.nextDouble() * (ub[m] - lb[m]);} else {double moveDist = random.nextDouble() * (bestSpiderMonkey.curVars[m] - tempSpiderMonkey.curVars[m])+ random.nextDouble() * (spiderMonkeys[random.nextInt(spiderMonkeys.length)].curVars[m] - tempSpiderMonkey.curVars[m]);moveSpiderMonkey(tempSpiderMonkey, m, moveDist);}}tempSpiderMonkey.curObjValue = getObjValue(tempSpiderMonkey.curVars);tempSpiderMonkey.fit = 1 / tempSpiderMonkey.curObjValue;if(greedy){if(tempSpiderMonkey.fit > spiderMonkeys[j].fit){spiderMonkeys[j] = tempSpiderMonkey;}}else{spiderMonkeys[j] = tempSpiderMonkey;}}}for (int j = 0; j < spiderMonkeys.length; j++) {for (int m = 0; m < spiderMonkeys[j].curVars.length; m++) {positionArr[curC][c][m] = spiderMonkeys[j].curVars[m];}c++;}}curC++;}// 局部领导者学习阶段（如果局部领导者有更新，则localLimitCount=0，否则localLimitCount++）private void LLLP() {for (int i = 0; i < spiderMonkeyList.size(); i++) {boolean isUpdate = false;for (SpiderMonkey spiderMonkey : spiderMonkeyList.get(i)) {if (localLeaderList.get(i).fit < spiderMonkey.fit) {localLeaderList.set(i, copySpiderMonkey(spiderMonkey));isUpdate = true;}}if (isUpdate) {localLimitCount[i] = 0;} else {localLimitCount[i]++;}}}// 全局领导者学习阶段（如果全局领导者有更新，则globalLimitCount=0，否则globalLimitCount++）private void GLLP() {boolean isUpdate = false;for (int i = 0; i < spiderMonkeyList.size(); i++) {for (SpiderMonkey spiderMonkey : spiderMonkeyList.get(i)) {if (spiderMonkey.fit > bestSpiderMonkey.fit) {bestSpiderMonkey = copySpiderMonkey(spiderMonkey);isUpdate = true;}}}if (isUpdate) {globalLimitCount = 0;} else {globalLimitCount++;}}// 全局领导者阶段（GLP：轮盘赌，随机选取，偏向于对fit值大的蜘蛛猴进行更新）private void GLP() {int c = 0;for (int i = 0; i < spiderMonkeyList.size(); i++) {SpiderMonkey[] spiderMonkeys = spiderMonkeyList.get(i);// 计算fit总和double totalFit = 0;for (SpiderMonkey spiderMonkey : spiderMonkeys) {totalFit += spiderMonkey.fit;}// 轮盘赌的累计概率数组double[] p = new double[spiderMonkeys.length];for (int j = 0; j < p.length; j++) {p[j] = (spiderMonkeys[j].fit / totalFit) + (j == 0 ? 0 : p[j - 1]);}// 局部搜索for (int j = 0; j < localSearchCount; j++) {double r = random.nextDouble();for (int k = 0; k < p.length; k++) {if (r <= p[k]) {for (int m = 0; m < varNum; m++) {double moveDist = random.nextDouble() * (bestSpiderMonkey.curVars[m] - spiderMonkeys[k].curVars[m])+ (random.nextDouble() - 0.5) * 2 * (spiderMonkeys[random.nextInt(spiderMonkeys.length)].curVars[m] - spiderMonkeys[k].curVars[m]);moveSpiderMonkey(spiderMonkeys[k], m, moveDist);}spiderMonkeys[k].curObjValue = getObjValue(spiderMonkeys[k].curVars);spiderMonkeys[k].fit = 1 / spiderMonkeys[k].curObjValue;break;}}}for (int j = 0; j < spiderMonkeys.length; j++) {for (int m = 0; m < spiderMonkeys[j].curVars.length; m++) {positionArr[curC][c][m] = spiderMonkeys[j].curVars[m];}c++;}spiderMonkeyList.set(i, spiderMonkeys);}curC++;}// 局部领导者阶段（LLP：所有的蜘蛛猴都有机会更新自己）private void LLP() {int c = 0;for (int i = 0; i < spiderMonkeyList.size(); i++) {SpiderMonkey[] spiderMonkeys = spiderMonkeyList.get(i);SpiderMonkey localLeader = localLeaderList.get(i);for (int j = 0; j < spiderMonkeys.length; j++) {// 以一定几率更新自己if (random.nextDouble() <= LLP_PR) {SpiderMonkey tempSpiderMonkey = copySpiderMonkey(spiderMonkeys[j]);for (int m = 0; m < varNum; m++) {double moveDist = random.nextDouble() * (localLeader.curVars[m] - tempSpiderMonkey.curVars[m])+ (random.nextDouble() - 0.5) * 2 * (spiderMonkeys[random.nextInt(spiderMonkeys.length)].curVars[m] - tempSpiderMonkey.curVars[m]);moveSpiderMonkey(tempSpiderMonkey, m, moveDist);}tempSpiderMonkey.curObjValue = getObjValue(tempSpiderMonkey.curVars);tempSpiderMonkey.fit = 1 / tempSpiderMonkey.curObjValue;if(greedy){if(tempSpiderMonkey.fit > spiderMonkeys[j].fit){spiderMonkeys[j] = tempSpiderMonkey;}}else{spiderMonkeys[j] = tempSpiderMonkey;}}for (int m = 0; m < spiderMonkeys[j].curVars.length; m++) {positionArr[curC][c][m] = spiderMonkeys[j].curVars[m];}c++;}spiderMonkeyList.set(i, spiderMonkeys);}curC++;}// 初始化蜘蛛猴种群private void initSpiderMonkeys() {positionArr = new double[3 * maxGen][spiderMonkeyNum][varNum];SpiderMonkey[] spiderMonkeys = new SpiderMonkey[spiderMonkeyNum];SpiderMonkey localLeader = null;for (int i = 0; i < spiderMonkeyNum; i++) {spiderMonkeys[i] = getRandomSpiderMonkey();if (i == 0) {bestSpiderMonkey = copySpiderMonkey(spiderMonkeys[0]);localLeader = copySpiderMonkey(spiderMonkeys[0]);} else {if (bestSpiderMonkey.fit < spiderMonkeys[i].fit) {bestSpiderMonkey = copySpiderMonkey(spiderMonkeys[i]);localLeader = copySpiderMonkey(spiderMonkeys[0]);}}}spiderMonkeyList.add(spiderMonkeys);localLeaderList.add(localLeader);}// 获取一个随机生成的蜘蛛猴SpiderMonkey getRandomSpiderMonkey() {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 SpiderMonkey(vars.clone(), objValue, 1 / objValue);}// 控制spiderMonkey在第m个维度上移动n个距离public void moveSpiderMonkey(SpiderMonkey spiderMonkey, int m, double n) {// 移动spiderMonkey.curVars[m] += n;// 超出定义域的判断if (spiderMonkey.curVars[m] < lb[m]) {spiderMonkey.curVars[m] = lb[m];}if (spiderMonkey.curVars[m] > ub[m]) {spiderMonkey.curVars[m] = ub[m];}}/*** @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;}// 复制蜘蛛猴SpiderMonkey copySpiderMonkey(SpiderMonkey old) {return new SpiderMonkey(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SMO_Solver solver = new SMO_Solver();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);}}}

优化流程（图太大了，所以放最后…）