粒子群优化算法 - 数学建模社区-数学中国

% 粒子群优化算法 (PSO) 示例
: t4 u1 O" X# [2 P3 V
9 w/ \ R5 S" ^6 p! ?
% 参数设置) k0 k" Q3 J+ N
numParticles = 30; % 粒子数量" c& o9 Z/ Q0 c9 R1 z
numDimensions = 2; % 问题维度
6 L: ^3 e$ H- c: P. i# ^
maxIterations = 100; % 最大迭代次数; C/ d- Y `- D$ G& _
bounds = [-10, 10]; % 搜索边界
, s7 ]$ |3 |% b/ w
: C) S3 |7 E! y+ D% N* Y M
% 初始化粒子位置和速度
: \, I0 \6 |4 I M" U& a/ R8 \
positions = rand(numParticles, numDimensions) * (bounds(2) - bounds(1)) + bounds(1);; z& z& }9 D( @! F
velocities = rand(numParticles, numDimensions) * 2 - 1;8 s3 Z) u5 q# }: A
0 l9 h2 U" Y7 ]; K m) z8 H
% 适应度值预分配
4 n3 a/ V$ J* M0 N
fitness = ones(numParticles, 1) * Inf;
; s$ G! R" U( s2 O
personalBestPositions = positions; $ `( H) d( S% }7 I. o0 @' E! @
personalBestFitness = fitness; 1 s% Q$ z3 E+ G0 R
globalBestPosition = zeros(1, numDimensions);
* h! E% [1 a1 U# s
globalBestFitness = Inf;0 ~8 F! r( c, H' S
9 a) r! j( N7 g0 ^' A* {* t
% 目标函数 (Rosenbrock函数)
$ z2 Y# T5 \, l6 w1 X# E7 a) Q
objectiveFunction = @(x) sum(100*(x(:,2) - x(:,1).^2).^2 + (1 - x(:,1)).^2);
' ]* X; R5 X& I* D& \6 I+ i
. o* k; X0 }3 `* Q# Z
% PSO主循环& X6 T9 f F4 R R- m x
for iter = 1:maxIterations: b6 _9 ^4 |$ ]* e8 T& O
% 计算适应度
0 h& b- h2 y/ }/ K. t
fitness = objectiveFunction(positions);% E" _: o3 j% u0 ]$ w! n0 {" @
8 {$ U: h- P4 X
% 更新个人最佳和全局最佳 i; e, _8 M( @( F6 l4 D
for i = 1:numParticles
: Q; h3 p' A+ n. F
if fitness(i) < personalBestFitness(i)3 t4 Q% U7 Q0 r7 p/ U
personalBestFitness(i) = fitness(i);. U* Z5 T! T* J5 A: J
personalBestPositions(i, :) = positions(i, :);
: W% Z% k# T! _. M9 E* o f8 |
end
# k( X9 t& K1 q: u# F2 z
end
l! k3 u' t6 e# A0 |
$ A, @ L4 _( s& G! m1 d+ W* E
[minFitness, minIndex] = min(personalBestFitness);# h- N9 ~# P5 G# h. L8 f* ~9 s
if minFitness < globalBestFitness
+ C7 d5 @1 r! F; l# s) x- p+ c& ]
globalBestFitness = minFitness;
7 p7 L* F( ^9 e
globalBestPosition = personalBestPositions(minIndex, :);
/ ~5 m- T% S) s/ _; @0 r
end' b, y$ ~$ C" g3 G9 S/ o
$ t8 P$ m" D5 O. x* F/ p
% 更新速度和位置
( C2 ^- U' Z( q) {
inertiaWeight = 0.7; % 惯性权重. M7 X0 y. R( l1 @; k
cognitiveWeight = 1.5; % 个体学习因子
- O' u/ r$ h* ?* s
socialWeight = 1.5; % 社会学习因子* R7 _* x" J4 v4 J1 h+ S! g/ Y
7 L0 A' S3 M- f1 {0 F4 t: ?" l9 e
for i = 1:numParticles! u# @, L: A4 L1 U
r1 = rand(1, numDimensions);
$ b2 L( T9 B" B, r& B8 g
r2 = rand(1, numDimensions);
, f" G3 k; _- n- w' }
f2 `2 Q1 F- x3 B- p9 K
% 更新速度! L" V" c3 I) K( z% _
velocities(i, :) = inertiaWeight * velocities(i, :) + ...) i3 ~% ?5 N8 Y2 A T T
cognitiveWeight * r1 .* (personalBestPositions(i, :) - positions(i, :)) + ...' O" S# d% h1 @6 q: Q0 J/ m4 N
socialWeight * r2 .* (globalBestPosition - positions(i, :));
8 y5 S, N7 b: y9 L
. \; h* i- z, J3 k( p
% 更新位置
q, v" S4 H) W+ v
positions(i, :) = positions(i, :) + velocities(i, :);3 i w3 G7 ?& q$ K% T
; W' _( z' V$ x1 r
% 限制在边界内
0 i6 n/ U/ Z6 c3 n$ ]" Z
positions(i, :) = max(min(positions(i, :), bounds(2)), bounds(1));
/ O A$ q# C0 ?( g( d' \# A$ X
end
& W/ |: s) T8 j( O: ~0 a& _
( }- L$ f# O3 X3 n4 g& D l
% 可选的日志输出
3 w, Q& [+ ]/ \6 }2 l% x O
disp(['Iteration ' num2str(iter) ': Best Fitness = ' num2str(globalBestFitness)]);
! [; L1 E& b# E" }7 S1 Q
end
) i- I5 u* c. X! K" L. J( X2 F
" j) I! M; y1 C9 k, i+ v
% 输出结果' \0 \( h R3 ]2 t; X9 _
disp(['全局最佳位置: ', num2str(globalBestPosition)]);/ [* j+ a. p/ S! Q5 W+ X
disp(['全局最佳适应度: ', num2str(globalBestFitness)]);
# Z8 T. l4 W( _3 K9 Y9 _
```

复制代码