多目标蜉蝣优化算法（Matlab代码实现）

💥1 概述

    蜉蝣算法 (MA)由Konstantinos Zervoudakis于2020年提出的新方法来解决优化问题。受蜉蝣飞行行为和交配过程的启发，该算法结合了群体智能和进化算法的主要优点。为了评估所提出算法的性能，使用了 38 个数学基准函数，包括 13 个 CEC2017 测试函数，并将结果与七种最先进的著名元启发式优化方法的结果进行了比较。MA 的性能还通过多目标优化中的收敛行为以及使用现实世界的离散流水车间调度问题进行评估。比较结果证明了所提方法在收敛速度和收敛速度方面的优越性。婚礼舞蹈和随机飞行的过程增强了算法探索和利用属性之间的平衡，并帮助其摆脱局部最优。

📚2 运行结果

部分代码：

clc; clear; close all;
 %% Problem Definition
 % Objective Functions
 ANSWER=listdlg('PromptString','Choose Objective Function','SelectionMode','single', 'ListString', {'1. ZDT', '2. ZDT2', '3. ZDT3'});
 if eq(ANSWER,1); ObjectiveFunction=@(x) ZDT(x); funcname='ZDT';
 elseif eq(ANSWER,2); ObjectiveFunction=@(x) ZDT2(x); funcname='ZDT2';
 elseif eq(ANSWER,3); ObjectiveFunction=@(x) ZDT3(x); funcname='ZDT3';
 else; disp('Terminated'); return
 end
 ProblemSize=[1 10];       % Decision Variables Size
 LowerBound=0;             % Decision Variables Lower Bound
 UpperBound=1;             % Decision Variables Upper Bound
 %% Mayfly Parameters
 methname='Mayfly Algorithm';
 MaxIt=1000;         % Maximum Number of Iterations
 nPop=20; nPopf=20;          % Population Size (males and females)
 nPareto=50;       % Repository Size
 g=0.8;                % Inertia Weight
 gdamp=1;            % Inertia Weight Damping Ratio
 a1=1.0;             % Personal Learning Coefficient
 a2=1.5;  a3=1.5;           % Global Learning Coefficient
 beta=2;             % Distance sight Coefficient
 dance=0.77;          % Mutation Coefficient
 dance_damp=0.99;    % Mutation Coefficient Damping Ratio
 fl=0.77;                       % Random flight
 fl_damp=0.99;
 % Mating Parameters
 nCrossover=20;  % Number of Parnets (Offsprings)
 nMutation=round(0.5*nPop);        % Number of Mutants
 mu=0.02;                                % Mutation Rate
 % Velocity Limits
 VelMax=1*(UpperBound-LowerBound)*5; VelMin=-VelMax;
 %% Initialization
 %run initial
 empty_mayfly.Position=[];
 empty_mayfly.Velocity=[];
 empty_mayfly.Cost=[];
 empty_mayfly.Best.Position=[];
 empty_mayfly.Best.Cost=[];
 empty_mayfly.Rank=[];
 empty_mayfly.DominationSet=[];
 empty_mayfly.DominatedCount=[];
 empty_mayfly.CrowdingDistance=[];
 Mayfly=repmat(empty_mayfly,nPop,1);
 Mayflyf=repmat(empty_mayfly,nPopf,1);
 for i=1:nPop
     % Initialize Male Position
     Mayfly(i).Position=unifrnd(LowerBound,UpperBound,ProblemSize);
     % Initialize Velocity
     Mayfly(i).Velocity=zeros(ProblemSize);
     % Evaluation
     Mayfly(i).Cost=ObjectiveFunction(Mayfly(i).Position);
     % Update Personal Best
     Mayfly(i).Best.Position=Mayfly(i).Position;
     Mayfly(i).Best.Cost=Mayfly(i).Cost;
     % Initialize female Position
     if i<=nPopf
         Mayflyf(i).Position=unifrnd(LowerBound,UpperBound,ProblemSize);
         Mayflyf(i).Velocity=zeros(ProblemSize);
         Mayflyf(i).Cost=ObjectiveFunction(Mayflyf(i).Position);
         Mayflyf(i).Best.Position=Mayflyf(i).Position;
         Mayflyf(i).Best.Cost=Mayflyf(i).Cost;
     end
 end

🎉3 参考文献

[1]Zervoudakis, K., & Tsafarakis, S. (2020). A mayfly optimization algorithm. Computers & Industrial Engineering, 145, 106559. https://doi.org/10.1016/j.cie.2020.106559

 

​​🌈​​4 Matlab代码实现