Entropy-based evolutionary diversity optimisation for the traveling salesperson problem

Nikfarjam, Adel; Bossek, Jakob; Neumann, Aneta; Neumann, Franz‐Josef

doi:10.1145/3449639.3459384

Cited by 25 publications

(11 citation statements)

References 23 publications

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“…They first introduced a sampling-based greedy algorithm to obtain diversity; then, they present an EDO approach to improve the results. To the best of our knowledge only Do et al (2020Do et al ( , 2021; Nikfarjam et al (2021) investigated EDO to compute diverse sets of tours for the TSP. Do et al ( 2020) introduced two distance-based diversity measures and studied simple EAs with k-OPT neighborhood search operators exclusively.…”

Section: Related Workmentioning

confidence: 99%

“…Do et al ( 2020) introduced two distance-based diversity measures and studied simple EAs with k-OPT neighborhood search operators exclusively. This is while Nikfarjam et al (2021) employed an entropy-based diversity measure focusing on diversifying segments of solutions. They both worked under the assumption of an optimal tour being known a-priori.…”

Section: Related Workmentioning

confidence: 99%

“…The entropy of a population P is minimal if and only if P includes µ copies of a single tour. In this setting the minimum entropy value is Nikfarjam et al (2021) showed that the maximum entropy value occurs when all edges appear roughly the same number of times in the population. Connect two sub-tours based on the neighbourhood search B.…”

Section: Domentioning

confidence: 99%

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Computing Diverse Sets of High Quality TSP Tours by EAX-Based Evolutionary Diversity Optimisation

Nikfarjam,

Bossek,

Neumann

et al. 2021

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Evolutionary algorithms based on edge assembly crossover (EAX) constitute some of the best performing incomplete solvers for the well-known traveling salesperson problem (TSP). Often, it is desirable to compute not just a single solution for a given problem, but a diverse set of high quality solutions from which a decision maker can choose one for implementation. Currently, there are only a few approaches for computing a diverse solution set for the TSP. Furthermore, almost all of them assume that the optimal solution is known. In this paper, we introduce evolutionary diversity optimisation (EDO) approaches for the TSP that find a diverse set of tours when the optimal tour is known or unknown. We show how to adopt EAX to not only find a high-quality solution but also to maximise the diversity of the population. The resulting EAX-based EDO approach, termed EAX-EDO is capable of obtaining diverse high-quality tours when the optimal solution for the TSP is known or unknown. A comparison to existing approaches shows that they are clearly outperformed by EAX-EDO.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Computing Diverse Sets of High Quality TSP Tours by EAX-Based Evolutionary Diversity Optimisation

Nikfarjam,

Bossek,

Neumann

et al. 2021

Preprint

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“…For TSP instances, it has been shown that such approaches are able to create TSP instances with desired properties (such as good or bad performance behaviour) with a much wider range in the feature space [13]. Furthermore, recent investigations have used and analyzed EDO methods to create diverse sets of high quality solutions for the TSP and other permutation problems [14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Exploring the Feature Space of TSP Instances Using Quality Diversity

Bossek,

Neumann

2022

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Generating instances of different properties is key to algorithm selection methods that differentiate between the performance of different solvers for a given combinatorial optimization problem. A wide range of methods using evolutionary computation techniques has been introduced in recent years. With this paper, we contribute to this area of research by providing a new approach based on quality diversity (QD) that is able to explore the whole feature space. QD algorithms allow to create solutions of high quality within a given feature space by splitting it up into boxes and improving solution quality within each box. We use our QD approach for the generation of TSP instances to visualize and analyze the variety of instances differentiating various TSP solvers and compare it to instances generated by a (µ + 1)-EA for TSP instance generation.

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“…For the same purposes, the star discrepancy and indicators from the multi-objective optimisation frameworks have been studied in Neumann et al [2018] and Neumann et al [2019], respectively. The use of distance-based diversity measures and entropy have been studied in Do et al [2020], Nikfarjam et al [2021b] to generate a diverse set of solutions for the TSP. Nikfarjam et al [2021a] introduced a modified Edge Assembly Crossover (EAX) to achieve higher diversity in TSP tours.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Diversity Optimisation for The Traveling Thief Problem

Nikfarjam¹,

Neumann²,

Neumann³

2022

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There has been a growing interest in the evolutionary computation community to compute a diverse set of high-quality solutions for a given optimisation problem. This can provide the practitioners with invaluable information about the solution space and robustness against imperfect modelling and minor problems' changes. It also enables the decision-makers to involve their interests and choose between various solutions. In this study, we investigate for the first time a prominent multi-component optimisation problem, namely the Traveling Thief Problem (TTP), in the context of evolutionary diversity optimisation. We introduce a bi-level evolutionary algorithm to maximise the structural diversity of the set of solutions. Moreover, we examine the inter-dependency among the components of the problem in terms of structural diversity and empirically determine the best method to obtain diversity. We also conduct a comprehensive experimental investigation to examine the introduced algorithm and compare the results to another recently introduced framework based on the use of Quality Diversity (QD). Our experimental results show a significant improvement of the QD approach in terms of structural diversity for most TTP benchmark instances.

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Entropy-based evolutionary diversity optimisation for the traveling salesperson problem

Cited by 25 publications

References 23 publications

Computing Diverse Sets of High Quality TSP Tours by EAX-Based Evolutionary Diversity Optimisation

Computing Diverse Sets of High Quality TSP Tours by EAX-Based Evolutionary Diversity Optimisation

Exploring the Feature Space of TSP Instances Using Quality Diversity

Evolutionary Diversity Optimisation for The Traveling Thief Problem

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