Matlab在多变量优化中的应用

Question

我用Matlab fminsearch来最小化一个含有两个变量的方程，sum((interval-5).^2, 2)*factor，区间是包含5个值的向量。在步长为1的情况下，只能依次从值1到30中选择它们，其因子为0.1至0.9。

代码在下面。我认为区间值是正确的，但因子值是错误的。

区间值:3 4 5 6 7要素值: 0.6最终产出:6

我认为要素值应该是0.1，最终产出应该是1作为全局最小值。

%% initialization of problem parameters
minval = 1;
maxval = 30;
step = 1;
count = 5;

minFactor = 0.1;
maxFactor = 0.9;

%% the objective function
fun = @(interval, factor) sum((interval-5).^2, 2)*factor;

%% a function that generates an interval from its initial value
getinterval = @(start) floor(start) + (0:(count-1)) * step;
getfactor =@(start2) floor(start2 * 10)/10;

%% a modified objective function that handles constraints
objective = @(start, start2) f(start, fun, getinterval, minval, maxval, getfactor, minFactor, maxFactor);

%% finding the interval that minimizes the objective function
start = [(minval+maxval)/2 (minFactor+maxFactor)/2];
y = fminsearch(objective, start);
bestvals = getinterval(y(1));
bestfactor = getfactor(y(2));

eval = fun(bestvals,bestfactor);
disp(bestvals)
disp(bestfactor)
disp(eval)

代码使用以下函数f。

function y = f(start, fun, getinterval, minval, maxval, getfactor, minFactor, maxFactor)
   interval = getinterval(start(1));
   factor = getfactor(start(2));
   if (min(interval) < minval) || (max(interval) > maxval) || (factor<minFactor) || (factor>maxFactor)
       y = Inf;
       else
          y = fun(interval, factor);
       end
   end

我按亚当的建议尝试了GA功能。考虑到我的变量来自不同的范围和步骤，我将其改为两个不同的集合。这是我的零钱。

step1 = 1;
set1 = 1:step1:30;

step2 = 0.1;
set2 = 0.1:step2:0.9;

% upper bound depends on how many integer used for mapping
ub = zeros(1, nvar);
ub(1) = length(set1);      
ub(2) = length(set2); 

然后，我改变了目标函数

% objective function
function y = f(x,set1, set2)
    % mapping
    xmap1 = set1(x(1));
    xmap2 = set2(x(2));

    y = (40 - xmap1)^xmap2;

end

在我运行代码之后，我想我得到了我想要的答案。

Answer 1

集上ga()优化的说明

目标函数

f = xmap(1) -2*xmap(2)^2  + 3*xmap(3)^3 - 4*xmap(4)^4 + 5*xmap(5)^5;

设置

set = {1, 5, 10, 15, 20, 25, 30}

这套程序集包含7个元素：

set(1)

• index

• 索引1等于12到5.
• 索引7到30 set(7)

ga的输入将在1 to 7范围内。

下界是1，上界是7。

遗传算法的优化是通过计算适应度函数来完成的:对输入变量求f。

这里的技巧将是使用integer as input，稍后在评估f时使用上面讨论的mapping。

代码如下

% settting option for ga
opts = optimoptions(@ga, ...
                    'PopulationSize', 150, ...
                    'MaxGenerations', 200, ...
                    'EliteCount', 10, ...
                    'FunctionTolerance', 1e-8, ...
                    'PlotFcn', @gaplotbestf);

% number of variable
nvar = 5;   

% lower bound is 1
lb = ones(1, nvar);

step = 2.3;
set = 1:step:30;
limit = length(set);

% upper bound depends on how many integers are used for mapping
ub = limit.*lb;      

% maximization used the opposite of f as ga only does minimization
% asking ga to minimize -f is equivalent to maximizing f
fitness = @(x)-1*f(x, step, set);
[xbest, fbest, exitflag] = ga(fitness,nvar, [], [], [], [], lb, ub, [], 1:nvar, opts);  

% get the discrete integer value and find their corresponding value in the set
mapx = set(xbest)



% objective function
function y = f(x, step, set)
l = length(x);

% mapping
xmap = zeros(1, l);
for i = 1:l
    xmap(i) = set(x(i));
end



y = xmap(1) -2*xmap(2)^2  + 3*xmap(3)^3 - 4*xmap(4)^4 + 5*xmap(5)^5;

end