min F(S_1,S_2,):1.25 S_1^2+0.4S_2^2 Min ʄ (S_1,S_2,S_3 ): S_1^2+0.35S_2^2 2S_1^2+0.6S_2^2≤5100000 5S_1^2+3S_2^2 ≤14250000

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othman warde 2023-5-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1966224-min-f-s_1-s_2-1-25-s_1-2-0-4s_2-2-min-s_1-s_2-s_3-s_1-2-0-35s_2-2-2s_1-2-0-6s_2

编辑： Torsten 2023-5-17

Can you help me solve a bi-level programming problem that contains two levels and two constraints? How do I get the solution? I need the code, the solution, and the algorithm. Can you help me?

minF(s1,s2)=1.25S1^2 +0.4S2^2

minf(s1,s2)=s1^2+035s2^2

s.to 2s1^2+0.6s2^2 <=5100000

5s1^2+3s_2^2<=14250000

s1,s2>=0

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Torsten 2023-5-17

So you have two minimizations that can be solved independently from each other ? Or what do you want to tell us with your description of the problem ?

othman warde 2023-5-17

% Define the upper level objective function

upperLevelObj = @(s) 1.25*s(1)^2 + 0.4*s(2)^2;

% Define the lower level objective function

lowerLevelObj = @(s) s(1)^2 + 0.35*s(2)^2;

% Define the upper level constraint function

upperLevelConstr = @(s) [2*s(1)^2 + 0.6*s(2)^2 - 5100000;

5*s(1)^2 + 3*s(2)^2 - 14250000];

% Set up the optimization problem for the upper level

upperLevelProblem.objective = upperLevelObj;

upperLevelProblem.x0 = [0, 0]; % Initial guess for (s_1, s_2)

upperLevelProblem.Aineq = [];

upperLevelProblem.bineq = [];

upperLevelProblem.Aeq = [];

upperLevelProblem.beq = [];

upperLevelProblem.lb = [];

upperLevelProblem.ub = [];

upperLevelProblem.nonlcon = [];

upperLevelProblem.options = optimoptions('fmincon', 'Display', 'off');

% Solve the upper level problem

[sUpperOptimal, upperOptimalCost] = fmincon(upperLevelProblem);

% Set up the optimization problem for the lower level

lowerLevelProblem.objective = lowerLevelObj;

lowerLevelProblem.x0 = sUpperOptimal; % Use upper level optimal solution as initial guess

lowerLevelProblem.Aineq = [];

lowerLevelProblem.bineq = [];

lowerLevelProblem.Aeq = [];

lowerLevelProblem.beq = [];

lowerLevelProblem.lb = [];

lowerLevelProblem.ub = [];

lowerLevelProblem.nonlcon = upperLevelConstr;

lowerLevelProblem.options = optimoptions('fmincon', 'Display', 'off');

% Solve the lower level problem

[sLowerOptimal, lowerOptimalCost] = fmincon(lowerLevelProblem);

% Display the optimal values and costs

disp('Upper Level Optimal Solution:');

disp(['s_1 = ', num2str(sUpperOptimal(1))]);

disp(['s_2 = ', num2str(sUpperOptimal(2))]);

disp(['Upper Level Optimal Cost: ', num2str(upperOptimalCost)]);

disp('Lower Level Optimal Solution:');

disp(['s_1 = ', num2str(sLowerOptimal(1))]);

disp(['s_2 = ', num2str(sLowerOptimal(2))]);

disp(['Lower Level Optimal Cost: ', num2str(lowerOptimalCost)]);

Is that correct.........................؟؟؟؟؟؟؟؟؟؟؟

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Answer 1

Torsten 2023-5-17

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1966224-min-f-s_1-s_2-1-25-s_1-2-0-4s_2-2-min-s_1-s_2-s_3-s_1-2-0-35s_2-2-2s_1-2-0-6s_2#answer_1238009

编辑：Torsten 2023-5-17

在 MATLAB Online 中打开

My guess is you want to maximize, not minimize the objective function. The result of mimimizing it is obviously s_1 = s_2 = 0 in both cases.

% Define the upper level objective function
upperLevelObj = @(s) 1.25*s(1)^2 + 0.4*s(2)^2;
% Define the lower level objective function
lowerLevelObj = @(s) s(1)^2 + 0.35*s(2)^2;
% Define the upper level constraint function
upperLevelConstr = @(s) deal([2*s(1)^2 + 0.6*s(2)^2 - 5100000;
                              5*s(1)^2 + 3*s(2)^2 - 14250000],[]);
% Set up the optimization problem for the upper level
objective = upperLevelObj;
x0 = [0; 0]; % Initial guess for (s_1, s_2)
Aineq = [];
bineq = [];
Aeq = [];
beq = [];
lb = [0;0];
ub = [Inf ;Inf];
nonlcon = upperLevelConstr;
options = optimoptions('fmincon', 'Display', 'off', 'TolX',1e-16,'TolFun',1e-16);
% Solve the upper level problem
[sUpperOptimal, upperOptimalCost] = fmincon(objective,x0,Aineq,bineq,Aeq,beq,lb,ub,nonlcon,options);
% Set up the optimization problem for the lower level
objective = lowerLevelObj;
x0 = sUpperOptimal; % Use upper level optimal solution as initial guess
Aineq = [];
bineq = [];
Aeq = [];
beq = [];
lb = [0;0];
ub = [Inf;Inf];
nonlcon = upperLevelConstr;
options = optimoptions('fmincon', 'Display', 'off', 'TolX',1e-16,'TolFun',1e-16);
% Solve the lower level problem
[sLowerOptimal, lowerOptimalCost] = fmincon(objective,x0,Aineq,bineq,Aeq,beq,lb,ub,nonlcon,options);
% Display the optimal values and costs
disp('Upper Level Optimal Solution:');
Upper Level Optimal Solution:
disp(['s_1 = ', num2str(sUpperOptimal(1))]);
s_1 = 7.037e-08
disp(['s_2 = ', num2str(sUpperOptimal(2))]);
s_2 = 1.2715e-07
disp(['Upper Level Optimal Cost: ', num2str(upperOptimalCost)]);
Upper Level Optimal Cost: 1.2657e-14
disp('Lower Level Optimal Solution:');
Lower Level Optimal Solution:
disp(['s_1 = ', num2str(sLowerOptimal(1))]);
s_1 = 8.6229e-08
disp(['s_2 = ', num2str(sLowerOptimal(2))]);
s_2 = 1.4824e-07
disp(['Lower Level Optimal Cost: ', num2str(lowerOptimalCost)]);
Lower Level Optimal Cost: 1.5127e-14