MILP - Multidimensional optimization

Question

Ngai Nang Wong 2018-8-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/416530-milp-multidimensional-optimization

回答： BOWEN LI 2019-7-19

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Hi guys, I am currently working on an optimization problem:-

I have to assign my workers (i) to perform different tasks (j) under different sections (k) of different projects(L).

So I created a simple model : Maximize P = X(ijkl)*Y(ijkl) and Y(ijkl) is binary variable

The assignment method are based on the performance data X(ijlk), e.g. workers (i) have 20 marks in task (j) under section (k) in project (L).

But I have problem in creating the performance data in matlab. I have tried to create 4-D matrix but error occur. Can anyone give me some advise?

Thank you. Jim

---Updated---

Here is my code

l = {'P1','P2',};
k = {'S1','S2','S3','S4'};
j = {'T1','T2','T3','T4','T5','T6','T7', 'T8'};
i = {'W1','W2','W3','W4','W5','W6','W7','W8'};
Y = optimvar('Y',i,j,k,l,'LowerBound',0,'UpperBound',1,'Type','integer');
X = rand(8,8,4,2)
Optimprob = optimproblem('ObjectiveSense','maximize','Objective',sum(sum(Y.*X)));
[soln,fval,exitflag,output] = solve(Optimprob);

and turns out error is occur:-

Error using optimproblem (line 52) Objective must be a scalar OptimizationExpression or a struct containing a scalar OptimizationExpression.

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Alan Weiss 2018-8-28

Please show us some code and the full error message.

Alan Weiss

MATLAB mathematical toolbox documentation

Ngai Nang Wong 2018-8-28

I edited the question with my code, thank you so much!

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Answer 1

Aurele Turnes 2018-9-11

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https://ww2.mathworks.cn/matlabcentral/answers/416530-milp-multidimensional-optimization#answer_336366

编辑：Aurele Turnes 2018-9-11

在 MATLAB Online 中打开

Your objective is

obj = sum(sum(Y.*X))

which is not scalar, but a 1-by-1-by-4-by-2 ND array.

Currently, the problem-based optimization only supports linear and mixed-integer linear problems: https://www.mathworks.com/help/optim/problem-based-lp-milp.html

All these solvers expect the objective to return a scalar value, so the objective is expected to be a 1-by-1 expression.