# 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.

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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 $T_i$ ...
1 vote
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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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### Looking for OR courses on following topics

Currently, I am self-teaching myself the following topics in OR; a.) Multiobjective optimization, b.) Deterministic/Probabilistic Inventory models c.) Deterministic/Stochastic Dynamic Programming. On ...
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### How to use gurobi to describe the process of finding the rank of matrix without objective functionļ¼

I have a general square matrix [[1,1,0],[1,1,0],[0,0,0]] (the element is on a binary field--Galois Fields) I want to find the rank of this matrix (like the function:...
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### Exception from IBM ILOG CPLEX: CPLEX Error 5002: 'q1' is not convex.->

I am currently solving a scheduling optimization problem regarding the fleet management of AGV/AMR. I always get the same error and I don't know where to start to solve it. Here's the code snippet for ...
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### New considerations for efficient solutions in multiobjective optimization

In multiobjective optimization, by using exact methods, we need to find the set of efficient solutions in the decision space or the set of non-dominated solutions in the criteria space. So, we must ...
1 vote
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### Weighted sum in the objective function

I am working on my actual model. The objective function aims to maximize the preferences related to each criterion pc to select the best contract that fits with the project characteristics( c1= size, ...
1 vote
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### satisfactory vs optimal decision making

In most classical game theoretic problems (situations in which more than one decision maker impacts the state of the environment), we assume that the decision-makers optimize their objective function. ...
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### Help with choosing the penalty parameters in the objective function

I'm working on a MIP optimization problem where I'm trying to reorganize a list of purchases (negative integer numbers) and requests (positive integer number) to maximize the number of positive values ...
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### Set optimality gap for each goal objective in FICO XPRESS

FICO XPRESS recently released a feature that supports multi-objective optimization. While it allows you to define a tolerance per objective (aka how much you can relax the previous objective), I am ...
1 vote
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### Which exact method can find all pareto-optimal solutions of a multi-objective optimization problem

I would like to know if there are methods that can gurantee to find all pareto-optimal solutions of a multi-objective optimization problem. I found some possible approaches but I don't know if they ...
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### When the Weighted Sum method yields a unique solution in MOLP?

I would like to ask if there are some specific conditions under which the Weighted Sum method yields a unique solution for MOLP or more general for convex problems. Let us assume that the number of ...
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### How to set an objective to minimize the variance in ratio of allocation

I am trying to write a model where I have to distribute fractions of rent from properties to loans. The objective is to distribute the rents as equally as possible given the loan balance. Say there ...
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### Multi objective optimization is giving wrong results

I am trying to solve a multi objective optimization problem. I have a set of nodes belonging to different counties and each node is associated with some cost and some priority. I want to select the ...
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### What are some important real life examples of multi objective optimization problem with box constraints to work on?

In the search of some of the important cutting edge many objective optimization problems to be solved using non-dominated sorting genetic algorithm (NSGA) and its variants.
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### Is there a name for this variation of the generalized assignment problem?

All the input variables are positive float (x > 0). We have $M$ agents with limited amount of time $t_1,\dots,t_M$, $N$ tasks $task_1,\dots,task_N$ associated with duration $d_1,\dots, d_N$. Cost ...
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### Solving a Global Optimization problem using Differential Evolutionary Algorithm using R

I need to determine the global optimum results of this objective function. I define the problem by minimizing the squared difference as represented in function $f(q_1,q_2,\alpha_1,\alpha_2)$ The ...
1 vote
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### Which Python package is suitable for finding the optimal non dominated set in multiobjective optimization?

I would like to know how to use pyhon or Cplex or both for finding the whole optimal pareto front for a biobjective mixed integer linear programming problem?
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### Do you have to normalize objectives when using the weighted sum approch?

Do you have to normalize objectives when using the weighted sum approch when having multiple objectives? Actually I thought that I should do it. But now I have run several experiments with different ...
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### Question about implementation method for optimization problem

Suppose we wanted to solve the following optimization problem: $$\inf_{x \geq 0}\sup_{y \in [0, 1];\ z > 0} f(x, y, z),$$ where $f(x, y, z)$ is some objective function with a closed form that can ...
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### Determining the optimize lambda in Multi-Objective Optimization

I have a convex optimization problem: Maximize obj1 Minimize obj2 Some constraint Now to solve this problem, I used lambda to make it one problem: ...
1 vote
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### Leontief utility function

For the Leontief utility function $$u_L(\lambda,y)=\min\{\lambda_1(r_1-y_1),\ldots,\lambda_m(r_m-y_m)\}$$ I would like to graphically show that, for $m=2$ and $\lambda\in\Lambda$ (for positive ...
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### How to calculate the trade-off between objectives in multi-objective optimization?

In the simple case, with only two objectives, I would like to know if it is possible to answer a question like: How many units of objective 1 do I need to reduce, in order to improve objective 2 by ...
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### Blended or hierarchical objectives if solving speed is more important

When optimizing a two objective task assignment problem, is it generally better to use blended objectives or hierarchical objectives if the speed to obtaining a near-optimal solution is more ...
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### weight choice in multi-objective weighted sum

I have a combinatorial optimization problem where there are three objectives F1, F2, and F3 to be minimized. The problem was formulated as a weighted sum where F=alphaF1+betaF2+gamma*F3. My question ...
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