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Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and…

Neural and Evolutionary Computing · Computer Science 2020-06-22 Yali Wang , André Deutz , Thomas Bäck , Michael Emmerich

Choices in scientific research and management require balancing multiple, often competing objectives.Multiple-objective optimization (MOO) provides a unifying framework for solving multiple objective problems. Model selection is a critical…

Applications · Statistics 2018-10-26 Perry Williams , William Kendall , Mevin Hooten

Multi-task learning (MTL), which aims to improve performance by learning multiple tasks simultaneously, inherently presents an optimization challenge due to multiple objectives. Hence, multi-objective optimization (MOO) approaches have been…

Artificial Intelligence · Computer Science 2021-10-08 Simyung Chang , KiYoon Yoo , Jiho Jang , Nojun Kwak

Constrained submodular optimization problems play a key role in the area of combinatorial optimization as they capture many NP-hard optimization problems. So far, Pareto optimization approaches using multi-objective formulations have been…

Neural and Evolutionary Computing · Computer Science 2024-06-21 Frank Neumann , Günter Rudolph

In single-objective optimization, it is well known that evolutionary algorithms also without further adjustments can tolerate a certain amount of noise in the evaluation of the objective function. In contrast, this question is not at all…

Neural and Evolutionary Computing · Computer Science 2023-08-25 Matthieu Dinot , Benjamin Doerr , Ulysse Hennebelle , Sebastian Will

We propose an algorithm and a new method to tackle the classification problems. We propose a multi-output neural tree (MONT) algorithm, which is an evolutionary learning algorithm trained by the non-dominated sorting genetic algorithm…

Neural and Evolutionary Computing · Computer Science 2022-02-21 Varun Ojha , Giuseppe Nicosia

In this paper, an evolutionary many-objective optimization algorithm based on corner solution search (MaOEA-CS) was proposed. MaOEA-CS implicitly contains two phases: the exploitative search for the most important boundary optimal solutions…

Artificial Intelligence · Computer Science 2018-06-11 Xinye Cai , Haoran Sun , Chunyang Zhu , Zhenyu Li , Qingfu Zhang

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

Machine Learning · Statistics 2015-11-13 Mengdi Wang , Yichen Chen , Jialin Liu , Yuantao Gu

In this paper we present an evolutionary optimization approach to solve the risk parity portfolio selection problem. While there exist convex optimization approaches to solve this problem when long-only portfolios are considered, the…

Portfolio Management · Quantitative Finance 2015-04-14 Ronald Hochreiter

When and why can evolutionary multi-objective optimization (EMO) algorithms cover the entire Pareto set? That is a major concern for EMO researchers and practitioners. A recent theoretical study revealed that (roughly speaking) if the…

Neural and Evolutionary Computing · Computer Science 2018-04-20 Naoki Hamada , Keisuke Goto

This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation…

Artificial Intelligence · Computer Science 2013-01-18 Pedro Larrañaga , Ramon Etxeberria , Jose A. Lozano , Jose M. Pena

Creating diverse sets of high quality solutions has become an important problem in recent years. Previous works on diverse solutions problems consider solutions' objective quality and diversity where one is regarded as the optimization goal…

Neural and Evolutionary Computing · Computer Science 2024-01-17 Anh Viet Do , Mingyu Guo , Aneta Neumann , Frank Neumann

Problems defined on binary decision spaces have been intensively studied in the theory of multi-objective evolutionary algorithms (MOEAs). In contrast, no mathematical runtime analyses exist so far for MOEAs dealing with decision variables…

Neural and Evolutionary Computing · Computer Science 2026-05-15 Mingfeng Li , Zheng Cheng , Weijie Zheng , Benjamin Doerr

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 the field of evolutionary multi-objective optimization, the approximation of the Pareto front (PF) is achieved by utilizing a collection of representative candidate solutions that exhibit desirable convergence and diversity. Although…

Neural and Evolutionary Computing · Computer Science 2024-07-10 Peng Chen , Jing Liang , Kangjia Qiao , Ponnuthurai Nagaratnam Suganthan , Xuanxuan Ban

Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems. However, these algorithms depends largely on problem characteristics, and there is a need to improve their performance for a wider…

Neural and Evolutionary Computing · Computer Science 2019-10-17 Shouyong Jiang , Hongru Li , Jinglei Guo , Mingjun Zhong , Shengxiang Yang , Marcus Kaiser , Natalio Krasnogor

Most multimodal multi-objective evolutionary algorithms (MMEAs) aim to find all global Pareto optimal sets (PSs) for a multimodal multi-objective optimization problem (MMOP). However, in real-world problems, decision makers (DMs) may be…

Neural and Evolutionary Computing · Computer Science 2023-06-13 Wenhua Li , Xingyi Yao , Kaiwen Li , Rui Wang , Tao Zhang , Ling Wang

Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of…

Neural and Evolutionary Computing · Computer Science 2015-06-24 Shayan Poursoltan , FranK Neumann

Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a…

Neural and Evolutionary Computing · Computer Science 2025-01-27 Saba Sadeghi Ahouei , Denis Antipov , Aneta Neumann , Frank Neumann

In the domain of multi-objective optimization, evolutionary algorithms are distinguished by their capability to generate a diverse population of solutions that navigate the trade-offs inherent among competing objectives. This has catalyzed…

Neural and Evolutionary Computing · Computer Science 2025-01-07 Yuxin Ma , Zherui Zhang , Ran Cheng , Yaochu Jin , Kay Chen Tan