mopso算法matlab
时间: 2023-09-06 13:12:51 浏览: 42
以下是一个基于MATLAB实现的MOPSO算法示例:
```matlab
%% MOPSO algorithm for multi-objective optimization
% Problem definition
CostFunction = @(x) ZDT(x); % Cost function
nVar = 30; % Number of decision variables
VarSize = [1 nVar]; % Size of decision variables matrix
VarMin = 0; % Lower bound of decision variables
VarMax = 1; % Upper bound of decision variables
% MOPSO algorithm parameters
MaxIt = 100; % Maximum number of iterations
nPop = 100; % Population size
nRep = 100; % Repository size
w = 0.5; % Inertia weight
wdamp = 0.99; % Inertia weight damping ratio
c1 = 1; % Personal learning coefficient
c2 = 2; % Global learning coefficient
nGrid = 7; % Number of grid in each dimension
alpha = 0.1; % Inflation rate of grid
% Initialization
empty_particle.Position = [];
empty_particle.Velocity = [];
empty_particle.Cost = [];
empty_particle.Best.Position = [];
empty_particle.Best.Cost = [];
particle = repmat(empty_particle, nPop, 1);
for i = 1:nPop
particle(i).Position = unifrnd(VarMin, VarMax, VarSize);
particle(i).Velocity = zeros(VarSize);
particle(i).Cost = CostFunction(particle(i).Position);
particle(i).Best.Position = particle(i).Position;
particle(i).Best.Cost = particle(i).Cost;
end
rep = particle;
Grid = CreateGrid(rep, nGrid, alpha);
for i = 1:numel(rep)
rep(i) = UpdateRepository(rep(i), Grid);
end
BestSol.Cost = inf;
for i = 1:nPop
if particle(i).Best.Cost < BestSol.Cost
BestSol = particle(i).Best;
end
end
BestCosts = zeros(MaxIt, 1);
% MOPSO main loop
for it = 1:MaxIt
for i = 1:nPop
% Update velocity
particle(i).Velocity = w*particle(i).Velocity ...
+ c1*rand(VarSize).*(particle(i).Best.Position - particle(i).Position) ...
+ c2*rand(VarSize).*(BestSol.Position - particle(i).Position);
% Update position
particle(i).Position = particle(i).Position + particle(i).Velocity;
% Apply lower and upper bounds
particle(i).Position = max(particle(i).Position, VarMin);
particle(i).Position = min(particle(i).Position, VarMax);
% Evaluation
particle(i).Cost = CostFunction(particle(i).Position);
% Update personal best
if particle(i).Cost < particle(i).Best.Cost
particle(i).Best.Position = particle(i).Position;
particle(i).Best.Cost = particle(i).Cost;
end
% Update repository
rep = UpdateRepository(rep, particle(i));
end
% Update grid
Grid = CreateGrid(rep, nGrid, alpha);
% Repair empty repository
if numel(rep) < nRep
rep(end+1:nRep) = empty_particle;
end
% Select best non-dominated solutions
rep = FindParetoSet(rep);
% Find crowding distance
rep = CalculateCrowdingDistance(rep);
% Sort repository by crowding distance
[~, SortOrder] = sort([rep.CrowdingDistance]);
rep = rep(SortOrder);
% Truncate repository
rep = rep(1:nRep);
% Update best solution
BestSol.Cost = inf;
for i = 1:nPop
if particle(i).Best.Cost < BestSol.Cost
BestSol = particle(i).Best;
end
end
BestCosts(it) = BestSol.Cost;
% Display iteration information
disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestSol.Cost)]);
% Damping inertia weight
w = w*wdamp;
end
% Results
figure;
PlotCosts(BestCosts);
xlabel('Iteration');
ylabel('Best Cost');
title('MOPSO');
```
请注意,这个示例使用了两个辅助函数 `CreateGrid()` 和 `PlotCosts()`,它们的代码如下:
```matlab
function Grid = CreateGrid(rep, nGrid, alpha)
% Create grid structure
Grid = struct();
Grid.Lower = min([rep.Cost], [], 2);
Grid.Upper = max([rep.Cost], [], 2);
Grid.Width = Grid.Upper - Grid.Lower;
Grid.Width(Grid.Width == 0) = 1;
% Initialize grid
Empty.GridIndex = [];
Empty.Members = [];
Empty.N = 0;
Grid.Matrix = repmat(Empty, nGrid, 1);
% Assign solutions to grid
for i = 1:numel(rep)
GridIndex = floor((rep(i).Cost - Grid.Lower)./Grid.Width*alpha + 1);
if GridIndex == 0
GridIndex = 1;
end
Grid.Matrix(GridIndex).Members(end+1) = i;
Grid.Matrix(GridIndex).N = numel(Grid.Matrix(GridIndex).Members);
Grid.Matrix(GridIndex).GridIndex = GridIndex;
end
end
function rep = UpdateRepository(rep, particle)
% Add new solution to repository
rep(end+1) = particle;
% Remove dominated solutions
rep = FindParetoSet(rep);
% Calculate crowding distance
rep = CalculateCrowdingDistance(rep);
end
function PlotCosts(Costs)
plot(Costs, 'LineWidth', 2);
grid on;
end
```
这个示例使用了一个简单的测试函数 `ZDT()`,它的代码如下:
```matlab
function y = ZDT(x)
n = numel(x);
f1 = x(1);
g = 1 + 9/29*sum(x(2:end));
h = 1 - sqrt(f1/g);
f2 = g*h;
y = [f1 f2];
end
```
注意,这个函数是一个两个目标的测试函数,可以在MOPSO算法中使用。如果你想使用其他的问题,只需要替换 `CostFunction`、`nVar`、`VarSize`等变量即可。