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4 votes

Multiple Travelling Salesmen - How to make the second slowest salesman matter?

You are dealing with a multi-objective problem. A common approach is to first consider your main goal, in your case that is $T_{max}$. Once you have found an optimal $T_{max}$, you adjust your ...
PeterD's user avatar
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4 votes

Problem of scaling or normalizing in multiobjective optimization problem when one objective function is much larger than the other?

I would suggest that you start by asking yourself (or the boss) why you want to reduce delay and why you want to reduce resource use. Ideally, these will translate into some sort of tangible costs. ...
prubin's user avatar
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3 votes

Multiple Travelling Salesmen - How to make the second slowest salesman matter?

In addition to the multiobjective approach suggested by @PeterD, another possibility is to penalize the total time taken by each agent in the objective. The objective would now be to minimize $T_{max} ...
prubin's user avatar
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2 votes
Accepted

Which exact method can find all pareto-optimal solutions of a multi-objective optimization problem

Whether a particular method is capable of generating all efficient solutions is often a question of what structure the MOOP (multi objective optimisation problem) has. In addition, you ask for methods ...
Sune's user avatar
  • 6,562
1 vote

Which exact method can find all pareto-optimal solutions of a multi-objective optimization problem

I would like to add the following resources that were mentioned by Gurobi experts and would be useful: These extreme points are non-dominated points on the Pareto front. It is possible to compute all ...
A.Omidi's user avatar
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1 vote

Do you have to normalize objectives when using the weighted sum approch?

It depends on what you want to achieve, but I would like to argue, contrary to the answer by @Merve Özer, that you do not need to (explicitly) normalize the objectives. If you have, two objective ...
Sune's user avatar
  • 6,562
1 vote
Accepted

How to get hypervolume calculation for Pareto Front in python?

It seems the Pymoo package has the machinery to compute the hypervolume. From the documentation, in the "Performance indicator" section, they describe several performance indicators (...
Sune's user avatar
  • 6,562
1 vote

Breaking symmetry

The problem you have sounds like a parallel resource scheduling model that may have some additional limitations. $(\text{R}_{2} \ | Cap | \sum_{j}w_{j})$. In the simplest form, it is still NP-hard, I ...
A.Omidi's user avatar
  • 8,940
1 vote

Breaking symmetry

Suppose you define a small penalty for each time a job is performed on the "wrong" resource. You now have a bicriterion optimization problem, one criterion being the original objective and ...
prubin's user avatar
  • 39.5k
1 vote

Metaheuristics or Exact algorithms to solve a non-linear multi-objective optimization problem?

Observe that all three objective functions are increasing functions of $X_2.$ For fixed $X_1,$ you want the smallest feasible value of $X_2.$ Constraint 4 is the only one that puts upward pressure on $...
prubin's user avatar
  • 39.5k
1 vote

Lexicographic objective to maximize the x-th highest value

As Mark L. Stone notes, some solvers (including CPLEX) handle lexicographic optimization directly. If you are using a solver that does not, but does allow you to modify branching, pruning etc. using ...
prubin's user avatar
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1 vote

How to use gurobi to describe the process of finding the rank of matrix without objective function?

In theory we can use the fact that rank = the number of non-zero singular values in a singular value decomposition (SVD). ...
Riley's user avatar
  • 166
1 vote

Exception from IBM ILOG CPLEX: CPLEX Error 5002: 'q1' is not convex.->

You did not identify the variables in your model. Presumably X is a variable. If either M_T or Consumption_M_T_R is a variable, then your objective function is a nonconvex quadratic function. If any ...
prubin's user avatar
  • 39.5k
1 vote

New considerations for efficient solutions in multiobjective optimization

Years ago two of my colleagues proposed an interactive approach. (This was for LPs, but should generalize to MIPs.) It requires reasonably fast solution time for the model. The gist was to optimize a ...
prubin's user avatar
  • 39.5k
1 vote

Weighted sum in the objective function

We typically normalize on seconds, minutes xor dollars, for as far as that is possible. And then leave it to a business stakeholder alignment meeting to tweak the weights. But normalization is not ...
Geoffrey De Smet's user avatar
1 vote

Problem of scaling or normalizing in multiobjective optimization problem when one objective function is much larger than the other?

You write in a comment that "you want to scale $f_1$ and $f_2$ so that they are as big as the others". If I understand you correctly, this may be impossible if you do not know the range of ...
Sune's user avatar
  • 6,562
1 vote

Problem of scaling or normalizing in multiobjective optimization problem when one objective function is much larger than the other?

In my opinion, the problem could be addressed by defining an appropriate reference system or rather an appropriate measurement scale. We can image $f_1$ and $f_2$ to be the coordinate of two vectors: ...
marco tognoli's user avatar

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