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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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 ...
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70 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
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3 votes
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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: ...
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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 ...
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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 ...
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4 votes
1 answer
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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 ...
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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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4 votes
2 answers
130 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-...
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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 ...
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Multiserver Queue Theory Optimization problem

I have a design optimization problem where I need to connect a customer with a server via call. The scenario is as follows: Customer-1 is connected with $N$ servers out of a total pool of $P$ servers....
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How to use PROMETHEE multicriteria method in R

I used TOPSIS multicriteria method to select the best number of clusters out of the 34 options. As weights I used 0.5 for each criterion. The ...
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2 answers
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How to normalize the objective functions of multi-objective optimization for a MPC?

I have a MPC with two objective functions, one that minimises fuel consumption and one that minimises the travel time of a vessel. I want to combine these two objectives into one weighted objective, ...
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3 votes
1 answer
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Goal Programming -- Best practice for standardizing magnitude of deviations across goals?

A certain goal program I've been working on has three goals that each operate at different scales. Two of the goals stay between 0-10, so any deviation from the goal is generally only a couple of &...
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2 votes
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How to normalize the objective functions of multi-objective optimization into uniform form?

In my bi-objective model, the range of solution value for the first objective is large than the second objective. I decide to obtain a single solution by the weighted sum approach and solve it using ...
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Relationship between Hypervolume and population size, number of generations, and number of functional evaluations?

I have a multi-objective optimization with the following properties: Objective function: two non-linear functions and one linear function Decision variable: two real variables (Bounded) Constraint: ...
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1 answer
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How to compute Generational Distance, Inverted Generational Distance, Epsilon Indicator, and Hypervolume for a Pareto front?

In order to find the quality indicators like Generational Distance, Inverted Generational Distance, Epsilon Indicator, and HyperVolume for a Pareto front I want to normalize the values of ...
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Designing Multi Floor Architectural Layouts

Architectural layouts define the position and shape of rooms in 3D space, where windows and water pipes are and as well as how humans travel between rooms (among other things). There is a lot of ...
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8 votes
4 answers
548 views

Are simulations a form of multi-objective optimization?

Where is the line when an approach is called multi-objective optimization? For example: Problem Presume I want to optimize an optimization problem, for example nurse rostering, with 2 soft constraints:...
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8 votes
3 answers
292 views

Do you know production deployments of multi-objective optimization?

In mathematical optimization software, defining the weight and level (hard/soft) of each of the objectives/constraints is often difficult for the business people at software development time, due to ...
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1 vote
2 answers
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Branch and bound method for solving non-convex integer non-linear multi-objective optimization problem?

Following are the characteristics of my problem: Objective function: two non-linear functions and one linear function Decision variable: two integer variables ($X_1$ and $X_2$) Constraint: three (two ...
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5 votes
1 answer
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What methods are used to solve multi-objective optimization problem with non-linear objective functions and integer decision variables?

Case 1: NLP When either the objective function or at least one of the constraints or both are non-linear it is a NLP. We use generalized reduced gradient or Quadratic Programming to solve NLP. However,...
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1 answer
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A lexicographic objective function

I am trying to solve a multi-objective vehicle routing problem, I want to implement a lexicographic objective function, I have already defined a function for each objective. if someone has an idea of ...
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4 votes
1 answer
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How to linearize a non-convex optimization objective function?

The non-convex multi-objective optimization problem in my case is defined below: Objective 1: Minimize $f_1(X_1,X_2)=C_0+C_1(1/X_1)+C_2(X_2/X_1)+C_3X_1+C_4X_2+C_5(X_2^2/X_1)$ Objective 2: Minimize $...
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2 votes
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How to interpret this problem of multicriteria decision

I am trying to optimise a cost function that consists of three parameters (A,B,C) using weighted sum approach for the selection of optimal technique out of three techniques. Parameter A unit is in ...
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3 votes
1 answer
204 views

Bin Packing with CP Solver

[ [0,5], [0,4], [1,6], [2,4], [3,6], [3,2], [4,5], [5,5], [6,4], [7,3], [8,2], [8,3], [9,5], [10,3]] ...
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2 votes
3 answers
274 views

Does a pre-calculated lower bound of an MILP problem help?

I have an MILP model, say $$ \begin{array}{rl} \mbox{minimize} &f_1(x) + f_2(x)\\ \mbox{subject to} &x\in X \end{array} $$ which is hard to solve. And I find it simple to solve the two ...
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Which multi-objective optimization algorithm should one select?

The multi-objective optimization problem in my case is defined below: Objective 1: Minimize $f_1(X_1,X_2)=C_1X_1+C_2X_2+C_3X_1^2+C_4X_2^2+C_5X_1^2X_2^2$ Objective 2: Minimize $f_2(X_1,X_2)=D_1X_1+...
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1 answer
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How define variable in CPLEX and What is diffrence between decision variables and variable in CPLEX

I want to code a problem by CPLEX, in this problem I have variables and decision variables, how define them? In this picture you can see the variables: which we have: I use these codes for variables:...
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What is a good approach to deciding which jobs (from a list of HPC jobs) should be ran locally vs. on the cloud given time & cost constraints?

Cloud computing has transformed the landscape of compute operations. Of course, there are still many labs/businesses with local, large-scale compute clusters. For those businesses who keep the ...
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3 votes
2 answers
196 views

Multi-objective function normalization

I am trying to solve the multi-objective function of my linear program. Are there another approaches other than the weighted sum approximation?
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6 votes
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What are useful plots/statistics/metrics when analyzing the solution sensitivity in multi-objective optimization?

Consider an optimization problem with $n>3$ objectives. For handling this there exists often two approaches: a) some weighting of the objectives, b) fix an order of objectives and then optimize ...
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1 vote
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Can I combine two objective functions if they have a relation between them?

I will use a meta-heuristic algorithm, to maximize the following objective functions: Objective function 1 $=\sum\limits_{r=1}^{M} \sum\limits_{s=r+1}^{M} \sum\limits_{j=r+1}^{N} (r_{rj}w_j - r_{sj}...
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3 votes
0 answers
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Appropriate Rotation Matrix in Nonconvex Optimization with Barrier

Let $ x \in \mathbb{R}^n_+$ be a variable such that $\sum_{i=1}^n x_i = 1$. In other words, $x$ is in a probability simplex. I am working on barrier-like functions in nonconvex optimization over such ...
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3 votes
1 answer
152 views

Which method to use to solve this multi-objective conflicting objectives

I have the following multiobjective problem. I need to minimize the user-perceived latency while doing so aggressively minimizing user-perceived latency generates large switching cost (Reconfiguration ...
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6 votes
1 answer
486 views

Does the weighted sum approach find all pareto-optimal solutions in MILP

I use the weighted sum approach for a multiobjective optimization problem that is formulated as a MILP. This means that the objective function is linear. I read quite often that the weighted sum ...
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1 vote
2 answers
103 views

How this problem can be defined as MultiObjective optimisation

I need to optimize the end-to-end latency of a multi-component application. Assuming that the application has 10 components, component 1-5 is hosted by device 1, and device 2 is hosting the other 5 ...
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15 votes
4 answers
8k views

Which Python package is suitable for multiobjective optimization

I would like to start using Python for modelling and solving optimization problems. I would like to use both single-objective problems and multi-objective problems with a multidimensional objective ...
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3 votes
1 answer
107 views

Can Deep RL be used to find optimal division point in an application?

I need to optimise the end-to-end latency for a multi-service application while distributing it on multiple devices. The application is a series of services interconnected to each other. The goal is ...
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2 votes
0 answers
53 views

Algorithm for Trainyard Marshall optimization problem

The problem I am trying to solve is the 2014 RAS problem. The link is the following The problem Trains come to the humpyard where each compartment of a train gets humped or disassembled and then each ...
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2 votes
1 answer
543 views

Defining and comparing utilization rates for delivery service

I'm currently working on a case for a food delivery service and wondered whether my notion of "driver utilization" makes any sense. My data set contains an hourly overview of the number of active ...
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4 votes
1 answer
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Is Multidisciplinary Design Optimization / Collaborative Optimization used anywhere outside of the Mechanical Engineering context?

I recently stumbled across the concept of Multidisciplinary Design Optimization (MDO), sometimes referred to as Multi-Disciplinary Optimization or Multidisciplinary Systems Design Optimization (MSDO), ...
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9 votes
5 answers
406 views

How to model a TSP where the salesman can choose between flight, train and bus for every single connection?

I want to model a multiobjective TSP where the salesman can choose between a flight, train and bus to go from city $i$ to city $j$. The aim of this multiobjective optimization problem is to minimize ...
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4 votes
1 answer
135 views

Software for multi-objective optimization

I am looking to solve a multi-objective chance-constrained blending problem. Are there any suggestions about the software to use to try and solve a problem like this?
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4 votes
0 answers
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Best method to optimise the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimise the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for ...
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8 votes
1 answer
362 views

How to resolve this issue in multi-objective optimization?

I have the following multiobjective optimization problem. The objectives are non-conflicting. The Optimization Problem: $$\underset{\large{a^{(l)}_{c,u},f^{(l)}_{c,u},z_{l,t},l\in\mathcal{L}}}{\max}\...
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9 votes
1 answer
74 views

Using Spatial Multi Criteria Analysis for simultaneously locating various facilities?

Is it possible to use SMCA (Spatial Multi Criteria Analysis) for determining simultaneously where to locate various facilities? Suppose, for example, I'm planing to build a new city and everything ...
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4 votes
0 answers
205 views

How can I formulate this multi-objective optimization problem?

Now, for each system $X$ $(X=A,B,C,E)$, my objective is $$\max\min\frac{s_{x_u}}{d_{x_u}}$$ here, $x=a$ for system A, $x=b$ for system B and follows... and for the whole system, my objective is $$\max\...
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16 votes
1 answer
1k views

Are there any benefits to using Gurobi's built-in "blended" multi-objective functionality?

The newer versions of Gurobi include a couple of built-in functionalities for multi-objective optimization: blended objectives and hierarchical (lexicographically ordered) objectives. Suppose we ...
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