粒子群算法添加约束条件
时间: 2023-08-05 18:02:35 浏览: 92
在粒子群算法中添加约束条件可以通过定义约束条件函数来实现。约束条件函数的调用语法与目标函数相同,但返回一个值数组。例如,假设我们的目标函数是banana(x),约束条件函数是con(x),我们可以使用pyswarm库中的pso函数来进行优化。下面是一个示例代码:
```python
from pyswarm import pso
def banana(x):
x1 = x[0]
x2 = x[1]
return x1**4 - 2*x2*x1**2 + x2**2 + x1**2 - 2*x1 + 5
def con(x):
x1 = x[0]
x2 = x[1]
return [-(x1 - 0.25)**2 + 0.75*x2]
lb = [-3, -1] # 变量的下界
ub = [2, 6] # 变量的上界
xopt, fopt = pso(banana, lb, ub, f_ieqcons=con)
# 最优解应该在x=[0.5, 0.76]处,目标函数值为4.5,约束条件值为0
```
在上述代码中,我们定义了目标函数banana(x)和约束条件函数con(x)。然后,我们使用pso函数进行优化,指定了变量的下界lb和上界ub,并通过f_ieqcons参数传递约束条件函数。最后,我们得到了最优解xopt和目标函数值fopt。
这样,我们就可以在粒子群算法中添加约束条件。
相关问题
粒子群算法添加约束条件的matlab代码
以下是一个基本的粒子群算法添加约束条件的MATLAB示例代码:
```
function [x, fval] = constrained_pso(obj_func, lb, ub, constraint_func)
% obj_func为目标函数句柄,lb、ub为变量的上下限界限,constraint_func为约束条件句柄
% 返回最优解x和目标函数值fval
% 初始化参数
nVar = length(lb); % 变量的数量
nPop = 50; % 粒子群中的粒子数量
maxIter = 100; % 最大迭代次数
w = 0.7; % 惯性权重
c1 = 1.5; % 个体学习因子
c2 = 2; % 群体学习因子
Vmax = (ub - lb) * 0.1; % 粒子速度上限
% 初始化粒子位置和速度
X = repmat(lb, nPop, 1) + rand(nPop, nVar) .* repmat(ub-lb, nPop, 1);
V = rand(nPop, nVar) .* Vmax;
% 计算每个粒子的适应度值
f = zeros(nPop, 1);
for i = 1:nPop
f(i) = obj_func(X(i,:));
end
% 初始化全局最优粒子位置和适应度值
[~, gbest] = min(f);
xbest = X(gbest,:);
% 迭代寻优
for t = 1:maxIter
% 更新速度和位置
for i = 1:nPop
% 更新速度
V(i,:) = w*V(i,:) + c1*rand(1,nVar).*(xbest-X(i,:)) + c2*rand(1,nVar).*(X(gbest,:)-X(i,:));
% 限制速度在上下限范围内
V(i,V(i,:) > Vmax) = Vmax(V(i,:) > Vmax);
V(i,V(i,:) < -Vmax) = -Vmax(V(i,:) < -Vmax);
% 更新位置
X(i,:) = X(i,:) + V(i,:);
% 限制位置在上下限范围内
X(i,X(i,:) > ub) = ub(X(i,:) > ub);
X(i,X(i,:) < lb) = lb(X(i,:) < lb);
end
% 计算适应度值
for i = 1:nPop
f(i) = obj_func(X(i,:)); % 计算函数值
if constraint_func(X(i,:)) > 0 % 判断是否还符合约束条件
f(i) = inf; % 若不符合,则赋予无穷大的函数值,以便后面的处理
end
end
% 更新全局最优粒子位置和适应度值
[fmin, gbest] = min(f);
if fmin < obj_func(xbest) % 若全局最优粒子位置符合约束条件
xbest = X(gbest,:);
else % 若不符合,则从剩余粒子中随机选择一个符合约束条件的粒子作为全局最优粒子
remaining_particles = find(f ~= inf);
gbest = remaining_particles(randi([1,length(remaining_particles)]));
xbest = X(gbest,:);
end
end
x = xbest;
fval = obj_func(xbest);
end
```
其中,约束条件句柄constraint_func的编写方式可以参考以下示例:
```
function [c, ceq] = constraint_func(x)
c(1) = x(1) + x(2) - 2; % 不等式约束条件,c(x) < 0
ceq = []; % 等式约束条件,ceq(x) = 0
end
```
在这个示例中,只有一个不等式约束条件:x1 + x2 < 2。如果需要添加更多的约束条件,可以在constraint_func函数中继续添加。当任意一个约束条件不满足时,对应的粒子将被赋予一个无穷大的适应度值,以便后面的处理。同时,全局最优粒子的更新也需要根据约束条件进行判断和调整,以保证寻优结果符合约束条件。
粒子群算法添加约束条件相关的论文有哪些?
以下是一些粒子群算法添加约束条件相关的论文:
1. "A Particle Swarm Optimization Algorithm for Constrained Optimization Problems," by Maurice Clerc and James Kennedy.
2. "Particle Swarm Optimization with Constraints Handling," by Xin-She Yang.
3. "Particle Swarm Optimization for Constrained Optimization Problems: A Survey," by Shima Azizi, Mohammad Tavakoli, and Ahmad Khademzadeh.
4. "A Hybrid Particle Swarm Optimization Approach for Constrained Optimization Problems," by Hamed Fazlollahtabar and Hassan Ghassemian.
5. "An Improved Particle Swarm Optimization with Adaptive Constraint Handling Strategy for Constrained Optimization Problems," by Jinxia Liu, Yanling Wei, and Weidong Wang.
6. "Constrained Particle Swarm Optimization Algorithm for Nonlinear Constrained Optimization," by Venkatesan M, Rajendran P, and Thangavel K.
7. "Particle Swarm Optimization Algorithm with Adaptive Penalty Function for Constrained Optimization Problems," by Qiao Zhang and Bo Xiao.
8. "Robust Particle Swarm Optimization for Constrained Optimization Problems," by Xin-She Yang.
9. "A Hybrid Particle Swarm Optimization Algorithm for Constrained Optimization Problems," by Xiaohui Yan, Ye Tian, and Weiwei Cheng.
10. "Constrained Multi-objective Particle Swarm Optimization Based on Decomposition and Local Search," by Mingyong Yin, Fei Xiao, and Wei Wang.