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# MILP - Multidimensional optimization

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Ngai Nang Wong on 28 Aug 2018
Answered: BOWEN LI on 19 Jul 2019
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.

#### 2 Comments

Alan Weiss on 28 Aug 2018
Please show us some code and the full error message.
Alan Weiss
MATLAB mathematical toolbox documentation
Ngai Nang Wong on 28 Aug 2018
I edited the question with my code, thank you so much!

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### Answers (2)

Aurele Turnes on 11 Sep 2018
Edited: Aurele Turnes on 11 Sep 2018
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.

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BOWEN LI on 19 Jul 2019
Hi, I am working on a similar question as yours, have you solved this question?

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