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Related papers: On Upper Approximations of Pareto Fronts

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This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously…

Optimization and Control · Mathematics 2021-09-22 Arne Herzel , Stephan Helfrich , Stefan Ruzika , Clemens Thielen

Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the…

Machine Learning · Computer Science 2019-06-24 Biswajit Paria , Kirthevasan Kandasamy , Barnabás Póczos

We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…

Optimization and Control · Mathematics 2015-01-13 Bram L. Gorissen , Dick den Hertog

In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…

Optimization and Control · Mathematics 2022-05-04 Fritz Bökler , Sophie N. Parragh , Markus Sinnl , Fabien Tricoire

In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…

Optimization and Control · Mathematics 2023-08-07 Abhishek Roy , Geelon So , Yi-An Ma

Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…

Neural and Evolutionary Computing · Computer Science 2021-01-05 Gurpreet Singh , Soumyajit Gupta , Matthew Lease

In this paper, we deal with the Front Steepest Descent algorithm for multi-objective optimization. We point out that the algorithm from the literature is often incapable, by design, of spanning large portions of the Pareto front. We thus…

Optimization and Control · Mathematics 2023-03-17 Matteo Lapucci , Pierluigi Mansueto

We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the…

Data Structures and Algorithms · Computer Science 2015-01-16 Tobias Brunsch , Heiko Röglin

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of…

Optimization and Control · Mathematics 2011-07-18 Alberto Lovison

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 multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…

Optimization and Control · Mathematics 2024-02-29 Weitian Wu , Xinmin Yang

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

Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…

Robotics · Computer Science 2022-06-02 Alexander Botros , Armin Sadeghi , Nils Wilde , Javier Alonso-Mora , Stephen L. Smith

We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{\mathbf{x} \in \mathbf{S}}\{ (f_1(\mathbf{x}), f_2(\mathbf{x})) \}$, where $f_1$ and $f_2$ are two…

Optimization and Control · Mathematics 2014-06-17 Victor Magron , Didier Henrion , Jean-Bernard Lasserre

We present a review that unifies decision-support methods for exploring the solutions produced by multi-objective optimization (MOO) algorithms. As MOO is applied to solve diverse problems, approaches for analyzing the trade-offs offered by…

Artificial Intelligence · Computer Science 2023-11-21 Zuzanna Osika , Jazmin Zatarain Salazar , Diederik M. Roijers , Frans A. Oliehoek , Pradeep K. Murukannaiah

Although synthetic test problems are widely used for the performance assessment of evolutionary multi-objective optimization algorithms, they are likely to include unrealistic properties which may lead to overestimation/underestimation. To…

Neural and Evolutionary Computing · Computer Science 2020-09-29 Ryoji Tanabe , Hisao Ishibuchi

Multi-objective optimization is a widely studied problem in diverse fields, such as engineering and finance, that seeks to identify a set of non-dominated solutions that provide optimal trade-offs among competing objectives. However, the…

Neural and Evolutionary Computing · Computer Science 2024-01-15 Arash Heidari , Sebastian Rojas Gonzalez , Tom Dhaene , Ivo Couckuyt

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…

Neural and Evolutionary Computing · Computer Science 2026-04-17 Liam Wigney , Frank Neumann

In general, a multi-objective optimization problem does not have a single optimal solution but a set of Pareto optimal solutions, which forms the Pareto front in the objective space. Various evolutionary algorithms have been proposed to…

Neural and Evolutionary Computing · Computer Science 2020-06-16 Hisao Ishibuchi , Lie Meng Pang , Ke Shang

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M-1)-dimensional topological…

Optimization and Control · Mathematics 2018-12-14 Ken Kobayashi , Naoki Hamada , Akiyoshi Sannai , Akinori Tanaka , Kenichi Bannai , Masashi Sugiyama