On the Effect of Populations in Evolutionary Multi-Objective Optimisation

Giel, Oliver; Lehre, Per Kristian

doi:10.1162/evco_a_00013

Cited by 58 publications

(49 citation statements)

References 29 publications

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“…In general, parameter settings characterize the capacity of an EA when solving a problem instance, and a certain capacity is needed for each EA to obtain results of a certain quality within a certain probability. For certain types of multi-objective problems, it has been proved that only population-based MOEAs can obtain the Pareto-optimal fronts efficiently and single individual-based MOEAs fail to achieve the same goal [19]. While the population holds a crucial role in any EAs, especially MOEAs, it is notoriously difficult to determine the proper population sizes for solving the problem instance under concern beforehand in practice.…”

Section: Parameter Settings and The Interleaved Multi-start Scheme (Ims)mentioning

confidence: 99%

Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm with the Interleaved Multi-start Scheme

Luong

Poutré

Bosman

2018

Swarm and Evolutionary Computation

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The Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) has been shown to be a promising solver for multi-objective combinatorial optimization problems, obtaining an excellent scalability on both standard benchmarks and real-world applications. To attain optimal performance, MO-GOMEA requires its two parameters, namely the population size and the number of clusters, to be set properly with respect to the problem instance at hand, which is a non-trivial task for any EA practitioner. In this article, we present a new version of MO-GOMEA in combination with the so-called Interleaved Multi-start Scheme (IMS) for the multi-objective domain that eliminates the manual setting of these two parameters. The new MO-GOMEA is then evaluated on multiple benchmark problems in comparison with two well-known multi-objective evolutionary algorithms (MOEAs): Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D). Experiments suggest that MO-GOMEA with the IMS is an easy-to-use MOEA that retains the excellent performance of the original MO-GOMEA.

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Section: Parameter Settings and The Interleaved Multi-start Scheme (Ims)mentioning

confidence: 99%

Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm with the Interleaved Multi-start Scheme

Luong

Poutré

Bosman

2018

Swarm and Evolutionary Computation

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“…We consider OneMinMax and LOTZ (see Definition 2.2 and 2.3) which are benchmark functions that facilitate the theoretical analysis. These functions have previously been used in the theoretical analysis of evolutionary algorithms and our choice therefore allows for comparisons with previous approaches such as the ones investigated in [10,11,13].…”

Section: Preliminariesmentioning

confidence: 99%

Design and analysis of diversity-based parent selection schemes for speeding up evolutionary multi-objective optimisation

Osuna

Gao

Neumann

et al. 2020

Theoretical Computer Science

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Parent selection in evolutionary algorithms for multi-objective optimisation is usually performed by dominance mechanisms or indicator functions that prefer non-dominated points. We propose to refine the parent selection on evolutionary multi-objective optimisation with diversity-based metrics. The aim is to focus on individuals with a high diversity contribution located in poorly explored areas of the search space, so the chances of creating new non-dominated individuals are better than in highly populated areas. We show by means of rigorous runtime analysis that the use of diversity-based parent selection mechanisms in the Simple Evolutionary Multi-objective Optimiser (SEMO) and Global SEMO for the well known bi-objective functions OneMinMax and LOTZ can significantly improve their performance. Our theoretical results are accompanied by experimental studies that show a correspondence between theory and empirical results and motivate further theoretical investigations in terms of stagnation. We show that stagnation might occur when favouring individuals with a high diversity contribution in the parent selection step and provide a discussion on which scheme to use for more complex problems based on our theoretical and experimental results.

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“…The OneMinMax problem, originally introduced by Giel and Lehre [13], is defined as the bicriteria optimization problem over the set of binary strings as f : …”

Section: Oneminmaxmentioning

confidence: 99%

“…We start by analyzing the OneMinMax problem introduced in [13], which is the multi-objective version of the famous OneMax problem. We show that as long as µ is large enough to cover the entire Pareto front, (µ + 1) SIBEA computes the whole Pareto front in expected polynomial time.…”

Section: Introductionmentioning

confidence: 99%

Population size matters

Nguyen

Sutton

Neumann

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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Using the hypervolume indicator to guide the search of evolutionary multi-objective algorithms has become very popular in recent years. We contribute to the theoretical understanding of these algorithms by carrying out rigorous runtime analyses. We consider multi-objective variants of the problems OneMax and LeadingOnes called OneMinMax and LOTZ, respectively, and investigate hypervolume-based algorithms with population sizes that do not allow coverage of the entire Pareto front. Our results show that LOTZ is easier to optimize than OneMinMax for hypervolume-based evolutionary multi-objective algorithms which is contrary to the results on their single-objective variants and the well-studied (1+1) EA.

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On the Effect of Populations in Evolutionary Multi-Objective Optimisation

Cited by 58 publications

References 29 publications

Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm with the Interleaved Multi-start Scheme

Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm with the Interleaved Multi-start Scheme

Design and analysis of diversity-based parent selection schemes for speeding up evolutionary multi-objective optimisation

Population size matters

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