Theoretical Analysis of Local Search and Simple Evolutionary Algorithms for the Generalized Travelling Salesperson Problem

The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which metaheuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a cluste...

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Vydané v:Evolutionary computation Ročník 27; číslo 3; s. 525
Hlavní autori: Pourhassan, Mojgan, Neumann, Frank
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States 01.09.2019
Predmet:
Algorithms
Biological Evolution
Cluster Analysis
Computational Biology - methods
Computer Heuristics
Computer Simulation
Humans
Problem Solving
Search Engine
Generalized travelling salesperson problem
bi-level optimisation
parameterised complexity analysis
combinatorial optimisation
evolutionary algorithms
ISSN:1530-9304, 1530-9304
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Shrnutí:The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which metaheuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a cluster-based approach and a node-based approach, have been proposed by Hu and Raidl (2008) for solving this problem. In this article, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we point out the complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches when initialized on a particular point of the search space, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time. Then we turn our attention to analysing the behaviour of simple evolutionary algorithms that use these approaches. We show that the node-based approach solves the hard instance of the cluster-based approach presented in Corus et al. (2016) in polynomial time. Furthermore, we prove an exponential lower bound on the optimization time of the node-based approach for a class of Euclidean instances.
Bibliografia:ObjectType-Article-1
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ISSN:1530-9304
1530-9304
DOI:10.1162/evco_a_00233