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
  • 38.8k
2 votes

How to set an objective to minimize the variance in ratio of allocation

In case your solver doesn't provide a constraint to use absolute value like gurobi.absconstraint & since you have minimize as objective any $\vert x-c \vert $ can be written with constraints as $ ...
Sutanu Majumdar's user avatar
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
  • 6,427
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
  • 6,427
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
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
  • 8,717
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
  • 6,427
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
  • 8,717
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
  • 38.8k
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
  • 38.8k
1 vote

Multi objective optimization is giving wrong results

Pymoo always minimize so, as you did, it is needed to convert max priority to min -priority. If your results are expressed in terms of priority instead of -priority, and sorted in base of the first ...
Enrique Gabriel Baquela's user avatar
1 vote

Multi objective optimization is giving wrong results

I don't know how pymoo works under the hood but the moment you are minimizing something like $g(x) = c^Tx - p^Tx $ without any scaling or hierarchial factor, it would minimize the whole func. Rather ...
Sutanu Majumdar's user avatar
1 vote
Accepted

Multi objective optimization is giving wrong results

It seems right to me. If you want to maximise priority, you would have to sacrifice cost-wise. Hence, the costs goes up. If you want to minimise costs, you cannot select all the high-priority nodes, ...
Sune's user avatar
  • 6,427
1 vote

Is there a name for this variation of the generalized assignment problem?

The problem sounds like a parallel resource scheduling problem with preemption. One of the efficient way to solve the problem (as an LP) is to define that as a bipartite graph in which the first group ...
A.Omidi's user avatar
  • 8,717
1 vote

Is there a name for this variation of the generalized assignment problem?

It's similar to knapsack problem. I am referring to wiki links here from here you can refer to other additional academic papers. Also check this general wiki as well on general assignment problem. ...
Sutanu Majumdar's user avatar
1 vote

Solving a Global Optimization problem using Differential Evolutionary Algorithm using R

(This is too long for a comment.) What I meant with my comment is this: given two candidate solutions to an optimization model, it is easy to figure out which is better. Insert each solution into the ...
Enrico Schumann's user avatar
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
  • 6,427

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