Cost of buy with price 26 is 2*26 + c = 152 in your setting. Note that although you don't generate energy, Cg_i(0,a,b,c) = c - thus you always add c to the cost of buying energy which obviously is not correct. Or do you want to treat c as fixed costs that always have to be paid - independent of whether energy is generated or not ?
fmincon get the wrong answer
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i have a optimization problem that fmincon get the wrong answer, there are a demand power(2) that can be generate or buy with different price, the codes are as follow:
a = 0.005;
b = 6;
c = 100;
% Define the cost function for generating energy (quadratic cost function) for the current microgrid
Cg_i = @(Ec, a, b, c) a * Ec^2 + b * Ec + c;
% Given prices
prices = [33, 26];
mprice = 27; % Given value of mprice
% Define the cost function for buying energy
Cb_i = @(Ec, price) price * Ec;
% Given total energy constraint
Ec_total = 2; % Given value of Ec_total
% Define the objective function
objective = @(X) Cg_i(X(1), a, b, c) + Cb_i(X(2), prices(1)) + Cb_i(X(3), prices(2)) + Cb_i(X(4), mprice);
% Initial guess for Ec_g, Ec1, Ec2
initial_guess = [Ec_total / 3, Ec_total / 3, Ec_total / 3, Ec_total / 3];
% initial_guess = [0, 0, Ec_total, 0];
% Linear equality constraint for the sum of Ec_g, Ec1, Ec2
Aeq = [1, 1, 1, 1];
beq = Ec_total;
% Options for fmincon
options = optimoptions('fmincon', 'Display', 'iter');
% Define solver options
% Call fmincon with specified options
X = fmincon(objective, initial_guess, [], [], Aeq, beq, [0, 0, 0,0], [], [], options)
the matlab answer is X=[2 0 0 0]; that means generat 2 and no buy, that obviously is wrong because cost of buy with price 26 is 26*2=52 while generating cost is 112!
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Torsten
2024-5-12
编辑：Torsten
2024-5-12
3 个评论
Torsten
2024-5-13
编辑：Torsten
2024-5-14
One way is to use "ga": it can handle discontinuous objective functions:
rng("default")
a = 0.005;
b = 6;
c = 100;
% Define the cost function for generating energy (quadratic cost function) for the current microgrid
Cg_i = @(Ec, a, b, c) (a * Ec^2 + b * Ec + c)*(Ec>0);
% Given prices
prices = [33, 26];
mprice = 27; % Given value of mprice
% Define the cost function for buying energy
Cb_i = @(Ec, price) price * Ec;
% Given total energy constraint
Ec_total = 2; % Given value of Ec_total
% Define the objective function
objective = @(X) Cg_i(X(1), a, b, c) + Cb_i(X(2), prices(1)) + Cb_i(X(3), prices(2)) + Cb_i(X(4), mprice);
% Initial guess for Ec_g, Ec1, Ec2
initial_guess = [Ec_total / 3, Ec_total / 3, Ec_total / 3, Ec_total / 3];
% initial_guess = [0, 0, Ec_total, 0];
% Linear equality constraint for the sum of Ec_g, Ec1, Ec2
Aeq = [1, 1, 1, 1];
beq = Ec_total;
X = ga(objective,4,[],[],Aeq,beq,zeros(4,1),inf(4,1))
objective(X)
Torsten
2024-5-14
编辑：Torsten
2024-5-14
Maybe somebody sees the problem - I don't know why "fmincon" has to shift the initial guess to [1 1 2 1] . In my opinion, [0 0 2 0] as given should satisfy lower and upper bounds as well as the linear equality constraint.
% Given total energy constraint
Ec_total = 2; % Given value of Ec_total
% Initial guess for Ec_g, Ec1, Ec2
initial_guess = [0, 0, Ec_total, 0];
% Linear equality constraint for the sum of Ec_g, Ec1, Ec2
Aeq = [1, 1, 1, 1];
beq = Ec_total;
% Options for fmincon
options = optimoptions('fmincon', 'Display', 'iter');
% Define solver options
% Call fmincon with specified options
[X,fval,flag] = fmincon(@objective, initial_guess, [], [], Aeq, beq, zeros(1,4), inf(1,4), [], options)
objective(X)
function value = objective(X)
X
a = 0.005;
b = 6;
c = 100;
% Define the cost function for generating energy (quadratic cost function) for the current microgrid
Cg_i = @(Ec, a, b, c) a * Ec^2 + b * Ec + c;
% Given prices
prices = [33, 26];
mprice = 27; % Given value of mprice
% Define the cost function for buying energy
Cb_i = @(Ec, price) price * Ec;
% Define the objective function
value = Cg_i(X(1), a, b, c) + Cb_i(X(2), prices(1)) + Cb_i(X(3), prices(2)) + Cb_i(X(4), mprice);
end
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