Questions tagged [multi-objective-optimization]
Multi-objective optimization is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Involve two or more optimization goals that are conflicting, meaning that improvement to one objective comes at the expense of another objective. The two methods for perform a multi-objetive-optimization are Pareto and scalarization.
103 questions
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Majorize instead of maximize
In my very limited knowledge of optimization there is always an objective function to minimize or maximize.
I have a problem where there are binary and integer variables. The objective is to find a ...
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Do we have to always normalize the objectives in multi-objective optimization problems?
I’m working on a multi-objective optimization problem using evolutionary algorithms such as NSGA-II or MOPSO, which rely on dominance comparisons. I’m wondering whether it is necessary to normalize ...
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Reference request - Multi-objective discrete optimization
I'm looking for references to do a review of research on solving discrete optimization problems with multiple objectives. Ideally a recent book / survey papers summarizing latest advances would be ...
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Model decomposition clarification
This is a follow-up question again. Now the two-step approach looks like this, the goal is to minimize the upward deviations from the mean $M_i$.
First stage:
\begin{align}
&\min \sum_{i\in I} C_i\...
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Column generation and lexicographic optimization
I have the following master problem:
\begin{align}
&\min \sum_{i\in I}\sum_{v\in V}C_{i}^v\Lambda_{iv}+\sum_{s\in S }^{}g_s\\\
&s.t.\\
&\sum_{i\in I}\sum_{v\in V}\chi_{itk}^v\cdot\Lambda_{...
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Which is the lowest, rightmost point over each set - reformulate max lexmin as MIP
For a bi-objective two-stage robust problem, we try to find the optimal objective value of
$$ \max_{x \in X} \left(\underset{y \in Y(x)}{\operatorname{lexmin}} \left\{ f_2 (x,y), f_1(x,y) \right\} \...
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How to perform a mathematical optimization with tight dependence between objectives and variables?
I am coding a physics simulation software where I need to perform mathematical optimization to find equilibrium positions of physical objects affected by several forces. There are 3 control variables, ...
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What should be the crowding distance of overlapping points?
When using an evolutionary algorithm like NSGA-II, we sort candidate solutions based on their domination level (rank) and their crowding distance (CD) to select the solutions that we will carry over ...
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How to find the feasible solution when the value of the objective function is known?
I am a network engineer working on a network optimization problem where we are exploring the use of Machine Learning to identify the Pareto boundary in a multi-objective optimization context. Our ...
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From Minimax to MILP
Definitions
Let
$S = \{ (x, y) | Ax + Dy \leqslant b\}$, and $\pi$ be its dual; And
$P_2(x) = \min_{(x, y) \in S} c^T_2 y$;
Problem
We aim to solve the following MILP.
$P = \max_{(x, y) \in S} c^T_1 ...
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Coverage Path Planning Dilemma (Trade-Off)
I have encountered a dilemma while I was trying to model a certain problem. Here is the description of the problem:
Imagine a 2D square area divided into square grids/cells. We have an agent (robot) ...
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How to reset hints in a CP-SAT model?
Pretty much the title. I have a cp model for which I have already provided a hint when minimizing a given objective function. I now want to provide a new hint to minimize the model with respect to a ...
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Can I tell a MILP solver to prefer solutions with fewer fractions?
I have a linear program
$$\max c^T x \text{ s.t. } A x\leq b, x\geq 0.$$
I would like a solution that, among all optimal solutions, has the largest number of integer variables. For example, if the ...
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Multiple Travelling Salesmen - How to make the second slowest salesman matter?
I'm building a Mixed Integer Linear Program for a variant of TSP I'm dealing with, where there are multiple salesmen. The way I have formulated the problem is that each agent has a time variable $T_i$ ...
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Lexicographic objective to maximize the x-th highest value
Given the following (stylized) IP:
\begin{align}
\mbox{minimize }& \sum_i c_ix_i&\\
\mbox{s.t. }&\sum_i x_i \leq Q & \\
& f(x_i) \geq L & \forall i \\
& 0 \...
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