MILP problem which is a function of time

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sibabalo noludwwe 2020-4-14

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https://ww2.mathworks.cn/matlabcentral/answers/517725-milp-problem-which-is-a-function-of-time

评论： sibabalo noludwwe 2020-5-1

i have solved my MILP problem using intlinprog, that part was fine. I am now extending the same problem but now it is depedent on time (i.e. I was to solve the optimization problem for each hour time step).

my question is: How do I extend my objective function and constraints to be time depedent?

thank you

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sibabalo noludwwe 2020-4-14

Thanks ill try that. May you refer me to a matlab site of how i can achieve to use my previous results for the next if possible

Ameer Hamza 2020-4-14

Please see my answer below for explanation.

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采纳的回答

Ameer Hamza 2020-4-14

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在 MATLAB Online 中打开

I have modified this example from the documentation: https://www.mathworks.com/help/optim/ug/intlinprog.html#mw_cd504ff9-629b-402f-acb0-7aa7c7926290 to explain the effect of using the solution from the previous time step as an initial point for the next iteration. In the following example, I used a for loop to solve an MILP problem 20 times, each time slightly varying the objective function.

First, check the code which does not use the solution from the last iteration as an initial guess of next iteration. The initial guess is always the same.

Aeq = [22    13    26    33    21     3    14    26
    39    16    22    28    26    30    23    24
    18    14    29    27    30    38    26    26
    41    26    28    36    18    38    16    26];
beq = [ 7872
       10466
       11322
       12058];
   
N = 8;
lb = zeros(N,1);
intcon = 1:N;
f = [2    10    13    17     7     5     7     3];
x0 = [8 62 23 103 53 84 46 34];
opts = optimoptions('intlinprog', 'Display', 'off');
tic
for i=1:20
    f(3:5) = randi([1 15], 1, 3); % objective function is changed in each iteration
    [x2,fval2] = intlinprog(f,intcon,[],[],Aeq,beq,lb,[],x0,opts);
end
toc

Time of execution

Elapsed time is 24.518613 seconds.

The following code update the initial guess

Aeq = [22    13    26    33    21     3    14    26
    39    16    22    28    26    30    23    24
    18    14    29    27    30    38    26    26
    41    26    28    36    18    38    16    26];
beq = [ 7872
       10466
       11322
       12058];
   
N = 8;
lb = zeros(N,1);
intcon = 1:N;
f = [2    10    13    17     7     5     7     3];
x0 = [8 62 23 103 53 84 46 34];
opts = optimoptions('intlinprog', 'Display', 'off');
tic
for i=1:20
    f(3:5) = randi([1 15], 1, 3);
    [x2,fval2] = intlinprog(f,intcon,[],[],Aeq,beq,lb,[],x0,opts);
    x0 = x2;
end
toc

Time of execution

Elapsed time is 8.489186 seconds.

This example shows a speed gain of about 3 times. The actual gain can vary from problem to problem, but still, it is better than just using a random initial guess.

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Ameer Hamza 2020-4-30

This is quite strange behavior. I couldn't see any reason why this should be happening. I recommend starting two instances of MATLAB and run both code line by line. You will definitely see the difference at some point.

sibabalo noludwwe 2020-5-1