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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 $T_i$ ...
John Smith's user avatar
1 vote
1 answer
71 views

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 \...
Joris Kinable's user avatar
0 votes
0 answers
45 views

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 ...
jayant's user avatar
  • 109
-1 votes
1 answer
79 views

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

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:...
wenny's user avatar
  • 1
0 votes
1 answer
93 views

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 ...
Rami's user avatar
  • 1
0 votes
1 answer
39 views

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 ...
BADJARA Mohamed el Amine's user avatar
1 vote
1 answer
77 views

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, ...
Basma Ben Mahmoud's user avatar
1 vote
0 answers
44 views

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. ...
Mohammad Reza Salehizadeh's user avatar
2 votes
1 answer
92 views

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 ...
Caterina De Franco's user avatar
3 votes
3 answers
391 views

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

I am an electrical engineer who is working in network problem and I was trying to solve a multi objective function $\begin{array}{*{20}{c}} {\min }&{{f_1}\left( x \right)}\\ \end{array}$ $\begin{...
Tuong Nguyen Minh's user avatar
0 votes
0 answers
49 views

Objective/Cost Function Normalization (MPC)

I am trying to develop an MPC. In this MPC, I predict the temperature and try to bring the sensor value to the desired setpoint temperature. I predict the temperature in the next 180 minutes for the ...
Clankk's user avatar
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3 votes
0 answers
124 views

Continuous optimization with a Euclidean TSP objective

I am trying to solve a problem of the form $$\min_{x_1,\dots,x_n} f(x_1,\dots,x_n)$$ subject to a constraint that $\mathrm{length}(\mathrm{TSP}(x_1,\dots,x_n))\leq c$, where $x_1,\dots,x_n$ are all ...
Tom Solberg's user avatar
1 vote
1 answer
620 views

How to get hypervolume calculation for Pareto Front in python?

I hope that this Stack Exchange channel is the right place for this. I'm trying to analyze a multiobjective optimization problem. I'm wanting to use the hypervolume calculation to benchmark the ...
BSplitter's user avatar
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1 vote
0 answers
61 views

MOO: Variable is both a decision variable and an objective

I'm trying to solve a Multi-Objective Optimization Problem to find the set of Pareto Optimal Solutions. I have a list of decision variables (x1, x2, x3) and a list of objectives (o1, o2, x3). As you ...
veeman's user avatar
  • 21
5 votes
1 answer
159 views

Numerically stable way to optimize a lexicographical preference between two objective functions?

I am solving a mixed-integer program whose decision variables are $x \in \{0, 1\}^n$ and $y \in \mathbb{R}^m$, where $0 \leq y_j \leq u_j$ for constant upper bounds. My primary objective function is ...
Max's user avatar
  • 544
1 vote
0 answers
49 views

Rank individuals of population after multi objective optimization using MCDM algorithm

I am trying to solve a multi objective optimization problem. It has 5 objectives. I am able to do optimization using NSGA2 algorithm of pymoo library in python. ...
MSS's user avatar
  • 111
1 vote
3 answers
99 views

Breaking symmetry

Suppose resources r1 and r2 are both able to perform jobs j1 and j2. The duration of the jobs being done is d. I would like to model the following rule: Within a time horizon H, perform j1 on r2 only ...
Clement's user avatar
  • 2,252
2 votes
0 answers
34 views

Maximizing value of nodes visited in fixed time

Consider the following three problems. The first is intended to be a simplification of the second that might be amenable to solution methods the second is not amenable to. First problem: Assume we ...
Aldo Leopold's user avatar
1 vote
1 answer
87 views

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

The multi-objective optimization problem settings are as defined below: Objective 1: Minimize $f_1(X_1,X_2)=C_0+C_1(1/X_1)+C_2(X_2/X_1)$ Objective 2: Minimize $f_2(X_1,X_2)=D_0+D_1X_1+D_2X_2+D_3(X_2/...
vp_050's user avatar
  • 179
1 vote
1 answer
134 views

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 ...
user4168715's user avatar
1 vote
2 answers
311 views

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 ...
PeterBe's user avatar
  • 1,652
0 votes
0 answers
46 views

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 ...
Tassos's user avatar
  • 1
-1 votes
1 answer
72 views

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 ...
Ashok Khatri's user avatar
-1 votes
3 answers
220 views

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 ...
MSS's user avatar
  • 111
0 votes
0 answers
71 views

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.
Abhishek Shukla's user avatar
2 votes
3 answers
118 views

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 ...
avilog's user avatar
  • 21
2 votes
1 answer
186 views

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 ...
Mrinmoy Chakraborty's user avatar
1 vote
0 answers
61 views

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?
Mansour's user avatar
  • 11
1 vote
2 answers
379 views

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 ...
PeterBe's user avatar
  • 1,652
3 votes
1 answer
110 views

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 ...
Nico Konrad's user avatar
4 votes
3 answers
595 views

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: ...
Soroosh Noorzad's user avatar
1 vote
0 answers
52 views

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 ...
Dinc's user avatar
  • 11
1 vote
1 answer
123 views

How to model this problem with multiple objectives?

This question is related to How to deal this L0 norm of a vector of L2 or L1 norms in objective? I have an optimization variable denoted as ${\bf A\in\mathbb{C}^{100\times 5}}=\begin{bmatrix}{\bf a}_1&...
KGM's user avatar
  • 2,377
3 votes
0 answers
96 views

Pygmo2: What is the point of evolving an archipelago in a loop if number of generations already set in algo

I want to solve a multi-objective problem with nsga2 or moead taking advantage of the parallelism available in pygmo library. I have seen a very nice example on github posted below. However I am not ...
Sophie's user avatar
  • 31
2 votes
1 answer
91 views

Need a multi-optimization environment or plugin in Anylogic

currently I am working on a model to simulate the supply chain of a group of warehouses in a country using Anylogic. Then I need to multi-optimize these outputs to get the best one based on optimizing ...
Hussam Aoun's user avatar
3 votes
1 answer
119 views

OptaPlanner Collaboration with Anylogic

Is there a way that i can let Anylogic Collaborate with OptaPlanner? I need to do both Simulation and Optimization for a logistic project.
Hussam Aoun's user avatar
2 votes
0 answers
68 views

Multi-objective optimization with known variable dependencies (via a graph) -- what is this called?

Suppose that I am trying to solve a standard multi-objective optimization problem: $$ \min_{ \begin{array}{c} \textbf{x} \in S \end{array} } \left [ f_1(\textbf{x}),f_2(\...
Astrid's user avatar
  • 121
2 votes
1 answer
107 views

Could non-supported efficient solutions in multi-objective optimization problem be an optimal solution of a parameterized single-objective problem?

Since all supported efficient solutions in a multi-objective optimization problem are actually the optimal solutions for some weighted sum scalarization single-objective optimization problem with the ...
Brown's user avatar
  • 173
2 votes
1 answer
247 views

Multi-objective optimization for resource allocation

Say I have several portfolios of the format: Product Name Product Amount Price per unit A_1 10 2 B_1 20 6 ... ... ... Z_1 30 7 We can call this $\text{Portfolio}_{1}$. Similarly, $\text{...
BenBernke's user avatar
  • 185
1 vote
0 answers
38 views

Multicollinearity w.r.t decisions in optimal control/reinforcement learning learning/resource allocation problem

Consider the following optimization/control problem: We aim to maximize the cumulative reward $R$ during the horizon $H$ by every day allocating a portion of total budget $B$ to our two different ...
chrisrichardsson's user avatar
1 vote
2 answers
296 views

How can we choose the right weight to solve multi-objective problem using weighted sum method?

I have a multi-objective problem with three objectives F1, F2, and F3. the problem was formulated as a weighted sum. Now I didn't know how I can choose the right weight for my problem
charafeddine's user avatar
3 votes
1 answer
216 views

What is the default weight allocation in solving multi-objective on CPLEX?

I am currently working on a multi-objective problem where I am trying to minimize cost and time. I am using Docplex to solve it, but I did not specify any weight using the following code: ...
Bree's user avatar
  • 115
3 votes
1 answer
444 views

Minimum cost flow problem with multiple arcs between nodes in Python / Google OR

Is it possible to work with multiple arcs between 2 nodes within Google OR? Or are there better modeling techniques? I want to optimize flow from supply to demand areas, where supply and demand are ...
Fabian's user avatar
  • 31
2 votes
1 answer
534 views

Is it possible to merge two objective functions using the LpSolve package in R?

I have been using the LpSolve package to solve a minimization problem in my final course work, but I need to reconcile this problem with a maximization problem. Conducting several researches, I ...
Éric Dias Rosso's user avatar
4 votes
1 answer
810 views

large scale optimization with Python

I am dealing with the following optimization problem: $$ \underset{x}{\min} q(x) $$ subject to $$ l_{x} \leq x \leq u_{x} \,\,\,\, \text{ and } \,\,\,\, l_{a} \leq Ax \leq u_{a}. $$ where $q(x)$ is a ...
AnTlr's user avatar
  • 43
3 votes
2 answers
1k views

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 ...
Nara Begnini's user avatar
1 vote
0 answers
47 views

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 ...
Nyxynyx's user avatar
  • 179
1 vote
2 answers
1k views

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 ...
MAJID majid's user avatar
4 votes
2 answers
181 views

How to fix unbalanced multi-commodity network flow with equal supply and demand?

I have a fairly large network with eleven commodities and arc capacities that are commodity-dependent (i.e. an arc may have a higher capacity for one commodity than another). I'm solving a protection-...
Emma Kuttler's user avatar
3 votes
2 answers
660 views

Designing a multi-commodity network flow optimizer

I'm trying to solve multi commodity multi source network flow optimization problem using Python-PuLP. Here is how my problem looks like: The numbers on the arcs represent the order of priority a ...
themlchic's user avatar