Characterizing Permutation-Based Combinatorial Optimization Problems in Fourier Space

Elorza, Anne; Hernando, Leticia; Lozano, José A.

doi:10.1162/evco_a_00315

Cited by 2 publications

(3 citation statements)

References 28 publications

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“…The Hamming Distance is a first-order representation of the separation between two distinct fireflies. The number of elements in the sequence that do not match is the Hamming distance between two fireflies, as indicated in Equation (8).…”

Section: ) Hamming Distancementioning

confidence: 99%

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Single Depot Multiple Travelling Salesman Problem Solved With Preference-Based Stepping Ahead Firefly Algorithm

Nand,

Chaudhary,

Sharma

2024

IEEE Access

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Firefly Algorithm (FA) mimics the flashing light characteristic of fireflies to solve optimization problems. An area where its utilization is limited is Travelling Salesman Problem (TSP). There are a number of algorithms utilized to solve the problem; however, there is still scope to do better in terms of solution quality. In this study, stepping ahead FA is proposed to solve the single depot Multiple Travelling Salesman Problem (MTSP) with threshold strategy. Rooted in the discrete FA (dFA), dFA-Step introduces a discrete transformation and threshold strategy to enhance optimization. The algorithm combines a unique stepping ahead mechanism with a threshold acceptance preference operator, achieving a balance between exploration and exploitation. The deterministic threshold acceptance approach facilitates the selection of sub-best solutions while the integration of neighborhood operators, like reverse cyclic permutation and swap transformation, enables exploration of solutions superior and closely aligned with the best solutions. The experimental results are compared with selected novel works from the literature where the results show competitive performance of the proposed algorithm in terms of solution quality. The proposed method gives insight in preference operator and stepping ahead mechanism for other researchers to utilize in discrete domains such as robotics and scheduling.INDEX TERMS Combinatorial problem, firefly algorithm, multiple travelling salesman problem, swarm intelligence.

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Section: ) Hamming Distancementioning

confidence: 99%

“…Combinatorial optimization, extensively studied, focuses on selecting the best objects from a finite set to achieve the optimal solution [8], [9]. This discrete optimization problem…”

Section: Introductionmentioning

confidence: 99%

Single Depot Multiple Travelling Salesman Problem Solved With Preference-Based Stepping Ahead Firefly Algorithm

Nand,

Chaudhary,

Sharma

2024

IEEE Access

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“…( 12) without ambiguity. Kondor [15] and Elorza et al [8] proved that in some permutation problems, like QAP, the nonzero matrices f (𝜌 𝜆 ) have rank 1 or 2. This fact could be used to reduce the number of considered unknowns.…”

Section: Fourier-based Surrogate Modelsmentioning

confidence: 99%

Fourier Transform-based Surrogates for Permutation Problems

Chicano

Derbel

Vérel

2023

Proceedings of the Genetic and Evolutionary Computation Conference

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In the context of pseudo-Boolean optimization, surrogate functions based on the Walsh-Hadamard transform have been recently proposed with great success. It has been shown that lower-order components of the Walsh-Hadamard transform have usually a larger influence on the value of the objective function. Thus, creating a surrogate model using the lower-order components of the transform can provide a good approximation to the objective function. The Walsh-Hadamard transform in pseudo-Boolean optimization is a particularization in the binary representation of a Fourier transform over a finite group, precisely defined in the framework of group representation theory. Using this more general definition, it is possible to define a Fourier transform for the functions over permutations. We propose in this paper the use of surrogate functions based on the Fourier transforms over the permutation space. We check how similar the proposed surrogate models are to the original objective function and we also apply regression to learn a surrogate model based on the Fourier transform. The experimental setting includes two permutation problems for which the exact Fourier transform is unknown based on the problem parameters: the Asteroid Routing Problem and the Single Machine Total Weighted Tardiness.

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Characterizing Permutation-Based Combinatorial Optimization Problems in Fourier Space

Cited by 2 publications

References 28 publications

Single Depot Multiple Travelling Salesman Problem Solved With Preference-Based Stepping Ahead Firefly Algorithm

Single Depot Multiple Travelling Salesman Problem Solved With Preference-Based Stepping Ahead Firefly Algorithm

Fourier Transform-based Surrogates for Permutation Problems

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