English
Related papers

Related papers: Computing the Pareto Front by Polynomial Eliminati…

200 papers

We study a general scalarization approach via utility functions in multi-objective optimization. It consists of maximizing utility which is obtained from the objectives' bargaining with regard to a disagreement reference point. The…

Optimization and Control · Mathematics 2024-01-26 Lorenzo Lampariello , Simone Sagratella , Valerio Giuseppe Sasso , Vladimir Shikhman

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective…

Optimization and Control · Mathematics 2021-02-08 Nikolai Krivulin

Operations research applications often pose multicriteria problems. Mathematical research on multicriteria problems predominantly revolves around the set of Pareto optimal solutions, while in practice, methods that output a single solution…

Data Structures and Algorithms · Computer Science 2013-03-12 Christina Büsing , Kai-Simon Goetzmann , Jannik Matuschke , Sebastian Stiller

Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously. However, it is often impossible to find one single solution to optimize all the tasks, since different tasks might conflict with each other.…

Machine Learning · Computer Science 2020-01-01 Xi Lin , Hui-Ling Zhen , Zhenhua Li , Qingfu Zhang , Sam Kwong

We introduce a nonmonotone extension of the Front Descent framework for multiobjective optimization. The method uses novel nonmonotone line searches that allow temporary increases in some objective functions. To our knowledge, this is the…

Optimization and Control · Mathematics 2025-09-03 Pierluigi Mansueto

Pairwise comparison matrices and the weight vectors obtained from them are important concepts in multi-criteria decision making. A weight vector calculated from a pairwise comparison matrix is called Pareto efficient if the approximation of…

Optimization and Control · Mathematics 2025-07-22 Kristóf Ábele-Nagy , Sándor Bozóki , Zsombor Szádoczki

We describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in Rp, and are typically only partially ordered. These can still be solved by a variable elimination algorithm, leading to a…

Artificial Intelligence · Computer Science 2012-10-19 Radu Marinescu , Abdul Razak , Nic Wilson

Multi-Objective Optimization (MOO) is an important problem in real-world applications. However, for a non-trivial problem, no single solution exists that can optimize all the objectives simultaneously. In a typical MOO problem, the goal is…

Machine Learning · Computer Science 2024-09-17 Zhang Haishan , Diptesh Das , Koji Tsuda

Consider an optimization problem with $n$ binary variables and $d+1$ linear objective functions. Each valid solution $x \in \{0,1\}^n$ gives rise to an objective vector in $\R^{d+1}$, and one often wants to enumerate the Pareto optima among…

Data Structures and Algorithms · Computer Science 2010-11-11 Ankur Moitra , Ryan O'Donnell

This work introduces MultiTRON, an approach that adapts Pareto front approximation techniques to multi-objective session-based recommender systems using a transformer neural network. Our approach optimizes trade-offs between key metrics…

Information Retrieval · Computer Science 2025-04-01 Timo Wilm , Philipp Normann , Felix Stepprath

The framework of decision-making, modeled as a Markov Decision Process (MDP), typically assumes a single objective. However, practical scenarios often involve tradeoffs between multiple objectives. We address this in the Linear Quadratic…

Optimization and Control · Mathematics 2025-01-16 Ali Jadbabaie , Devavrat Shah , Sean R. Sinclair

In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…

Optimization and Control · Mathematics 2025-10-06 Bikram Adhikary , Md Abu Talhamainuddin Ansary

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the…

Optimization and Control · Mathematics 2013-03-27 Xin-She Yang

Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for the desirability of a committee, Pareto optimality is a minimal and…

Computer Science and Game Theory · Computer Science 2018-03-20 Haris Aziz , Jerome Lang , Jerome Monnot

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…

Optimization and Control · Mathematics 2011-12-08 Jesus A. De Loera , Peter N. Malkin , Pablo A. Parrilo

This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical…

Optimization and Control · Mathematics 2026-01-29 V. S. Amaral , P. B. Assunção , D. R. Souza

We present a new inverse optimization methodology for multi-objective convex optimization that accommodates an input solution that may not be Pareto optimal and determines a weight vector that produces a Pareto optimal solution that…

Optimization and Control · Mathematics 2017-06-22 Timothy C. Y. Chan , Taewoo Lee

We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…

Data Structures and Algorithms · Computer Science 2008-05-20 Ilias Diakonikolas , Mihalis Yannakakis

In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…

Optimization and Control · Mathematics 2024-02-05 Ali Bencheikh , Mustapha Moulai , Ilies Badaoui

A key task in multi-objective optimization is to compute the Pareto subset or frontier $P$ of a given $d$-dimensional objective space $F$; that is, a maximal subset $P\subseteq F$ such that every element in $P$ is not-dominated (it is not…

Data Structures and Algorithms · Computer Science 2025-08-29 Konstantinos Karathanasis , Spyros Kontogiannis , Christos Zaroliagis