【智能优化算法】基于蜉蝣算法求解多目标优化问题附matlab代码

1 内容介绍

本文介绍了一种称为 Mayfly 算法 (MA) 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 的性能也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。婚舞和随机飞行的过程增强了算法探索性和利用性之间的平衡，帮助算法摆脱了局部最优。

2 仿真代码

% Project Title: A multiobjective mayfly optimization algorithm (MOMA) in MATLAB

% Researchers are allowed to use this code in their research projects.

% Please cite as:

% Zervoudakis, K., & Tsafarakis, S. (2020). A mayfly optimization algorithm.

% Computers & Industrial Engineering, 145, 106559.

% https://doi.org/10.1016/j.cie.2020.106559

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=100; % 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

% Merge

Pareto=[Mayfly;Mayflyf];

% Non-Dominated Sorting

[Pareto, F]=ParetoSorting(Pareto);

% Calculate Crowding Distance

Pareto=CalcCD(Pareto,F);

% Sort Population

Pareto=SortSolutions(Pareto);

Pareto=Pareto(F{1});

% Truncate

if numel(Pareto)>nPareto

Pareto=Pareto(1:nPareto);

end

%% Mayfly Main Loop

for it=1:MaxIt

for i=1:nPop

leader=Pareto(randi(size(Pareto,2)));

% Update Females

if i<=nPopf

if Dominates(Mayfly(i),Mayflyf(i))

rmf=norm(Mayfly(i).Position-Mayflyf(i).Position);

Mayflyf(i).Velocity = g*Mayflyf(i).Velocity ...

+a3*exp(-beta*rmf^2).*(Mayfly(i).Position-Mayflyf(i).Position);

else

e=unifrnd(-1,+1,ProblemSize);

Mayflyf(i).Velocity = g*Mayflyf(i).Velocity+fl*(e);

end

% Apply Velocity Limits

Mayflyf(i).Velocity = max(Mayflyf(i).Velocity,VelMin);

Mayflyf(i).Velocity = min(Mayflyf(i).Velocity,VelMax);

% Update Position

Mayflyf(i).Position = Mayflyf(i).Position + Mayflyf(i).Velocity;

% Velocity Mirror Effect

IsOutside=(Mayflyf(i).Position<LowerBound | Mayflyf(i).Position>UpperBound);

Mayflyf(i).Velocity(IsOutside)=-Mayflyf(i).Velocity(IsOutside);

% Apply Position Limits

Mayflyf(i).Position = max(Mayflyf(i).Position,LowerBound);

Mayflyf(i).Position = min(Mayflyf(i).Position,UpperBound);

% Evaluation

Mayflyf(i).Cost=ObjectiveFunction(Mayflyf(i).Position);

Mayflyf(i).Best.Position=Mayflyf(i).Position;

Mayflyf(i).Best.Cost=Mayflyf(i).Cost;

end

% Update Males

% Update Velocity

if Dominates(leader,Mayfly(i))

rpbest=norm(Mayfly(i).Best.Position-Mayfly(i).Position);

rgbest=norm(leader.Position-Mayfly(i).Position);

Mayfly(i).Velocity = g*Mayfly(i).Velocity ...

+a1*exp(-beta*rpbest^2).*(Mayfly(i).Best.Position-Mayfly(i).Position) ...

+a2*exp(-beta*rgbest^2).*(leader.Position-Mayfly(i).Position);

else

e=unifrnd(-1,+1,ProblemSize);

Mayfly(i).Velocity = g*Mayfly(i).Velocity+dance*(e);

end

% Apply Velocity Limits

Mayfly(i).Velocity = max(Mayfly(i).Velocity,VelMin);

Mayfly(i).Velocity = min(Mayfly(i).Velocity,VelMax);

% Update Position

Mayfly(i).Position = Mayfly(i).Position + Mayfly(i).Velocity;

% Velocity Mirror Effect

IsOutside=(Mayfly(i).Position<LowerBound | Mayfly(i).Position>UpperBound);

Mayfly(i).Velocity(IsOutside)=-Mayfly(i).Velocity(IsOutside);

% Apply Position Limits

Mayfly(i).Position = max(Mayfly(i).Position,LowerBound);

Mayfly(i).Position = min(Mayfly(i).Position,UpperBound);

% Evaluation

Mayfly(i).Cost=ObjectiveFunction(Mayfly(i).Position);

% Update Personal Best

if Dominates(Mayfly(i),Mayfly(i).Best)

Mayfly(i).Best.Position=Mayfly(i).Position;

Mayfly(i).Best.Cost=Mayfly(i).Cost;

elseif Dominates(Mayfly(i).Best,Mayfly(i))

% Do Nothing

else

if rand<0.5

Mayfly(i).Best.Position=Mayfly(i).Position;

Mayfly(i).Best.Cost=Mayfly(i).Cost;

end

% MATE

popc=repmat(empty_mayfly,nCrossover/2,2);

for k=1:nCrossover/2

% Select Parents

i1=randi(numel(Pareto));

i2=randi(numel(Pareto));

%p1=Mayfly(i1).Best;

%p2=Mayflyf(i2).Best;

% Apply Crossover

[popc(k,1).Position, popc(k,2).Position]=Crossover(Pareto(i1).Position,Pareto(i2).Position);

% Evaluation

popc(k,1).Position = max(popc(k,1).Position, LowerBound);

popc(k,1).Position = min(popc(k,1).Position, UpperBound);

popc(k,1).Cost=ObjectiveFunction(popc(k,1).Position);

% Evaluation

popc(k,2).Position = max(popc(k,2).Position, LowerBound);

popc(k,2).Position = min(popc(k,2).Position, UpperBound);

popc(k,2).Cost=ObjectiveFunction(popc(k,2).Position);

popc(k,1).Best.Position = popc(k,1).Position;

popc(k,1).Best.Cost = popc(k,1).Cost;

popc(k,1).Velocity= zeros(ProblemSize);

popc(k,2).Best.Position = popc(k,2).Position;

popc(k,2).Best.Cost = popc(k,2).Cost;

popc(k,2).Velocity= zeros(ProblemSize);

end

% break

popc=popc(:);

% Mutation

popm=repmat(empty_mayfly,nMutation,1);

for k=1:nMutation

i=randi(numel(Pareto));

popm(k)=Pareto(i);

popm(k).Position=Mutate(popm(k).Position,mu,LowerBound,UpperBound);

% Evaluation

popm(k).Position = max(popm(k).Position, LowerBound);

popm(k).Position = min(popm(k).Position, UpperBound);

popm(k).Cost=ObjectiveFunction(popm(k).Position);

end

% Create Merged Population

popc=[popc

popm]; %#ok

split=round((nCrossover/2+nMutation)/2);

males=popc(1:split);

Mayfly=[Mayfly

males]; %#ok

males=popc(split+1:nCrossover/2+nMutation);

Mayflyf=[Mayflyf

males]; %#ok

% SHORT

% Non-Dominated Sorting

[Mayfly, F]=ParetoSorting(Mayfly);

Mayfly=CalcCD(Mayfly,F);

[Mayfly, F]=SortSolutions(Mayfly);

[Mayflyf, F]=ParetoSorting(Mayflyf);

Mayflyf=CalcCD(Mayflyf,F);

[Mayflyf, F]=SortSolutions(Mayflyf);

Mayfly=Mayfly(1:nPop);

Mayflyf=Mayflyf(1:nPopf);

Pareto=[Pareto

Mayfly

Mayflyf]; %#ok

all=Pareto;

% Non-Dominated Sorting

[Pareto, F]=ParetoSorting(Pareto);

% Calculate Crowding Distance

Pareto=CalcCD(Pareto,F);

% Sort Population

[Pareto, F]=SortSolutions(Pareto);

% Store F1

Pareto=Pareto(F{1});

% Truncate

if numel(Pareto)>nPareto

Pareto=Pareto(1:nPareto);

end

% Show Iteration Information

disp(['Iteration ' num2str(it) ': Number of Solution in repository = ' num2str(numel(Pareto))]);

% Plot F1 Costs

figure(1);

PlotCosts(all,Pareto);

%pause(0.01);

g=g*gdamp;

dance = dance*dance_damp;

fl = fl*fl_damp;

end

%% Results

3 运行结果

4 参考文献

[1] Zervoudakis K , Tsafarakis S . A mayfly optimization algorithm[J]. Computers & Industrial Engineering, 2020, 145:106559.

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