Comparative Study of Different Memetic Algorithm Configurations for the Cyclic Bandwidth Sum Problem

Abstract

The Cyclic Bandwidth Sum Problem (CBSP) is an NP-Hard Graph Embedding Problem which aims to embed a simple, finite graph (the guest) into a cycle graph of the same order (the host) while minimizing the sum of cyclic distances in the host between guest's adjacent nodes. This paper presents preliminary results of our research on the design of a Memetic Algorithm (MA) able to solve the CBSP. A total of 24 MA versions, induced by all possible combinations of four selection schemes, two operators for recombination and three for mutation, were tested over a set of 25 representative graphs. Results compared with respect to the state-of-the-art top algorithm showed that all the tested MA versions were able to consistently improve its results and give us some insights on the suitability of the tested operators.

Dynamic Multi-Armed Bandit Algorithm for the Cyclic Bandwidth Sum Problem

“…Only recently the CBSP has received more attention in the optimization and operation research communities where the following approaches have been proposed: a local search based approach [17], a constructive greedy heuristic [18], hybrid metaheuristic algorithms [15], and a reformulation of the evaluation function [19].…”

“…In our previous work we tested the combinations of a smaller set of genetic operators, resulting in 24 MA versions [15]. While all of them were able to produce significant better results than MACH and GVNS, the best MA version showed hints of premature convergence related to the survival selection scheme.…”

“…In our previous work (see [15]) we implemented four selection schemes (roulette, stochastic, random, and binary tournament), two crossover mechanisms (cyclic and orderbased), as well as three mutation operators (cyclic insertion, reduced 3-swap, and cumulative swap). Survival of individuals was determined by the (µ + λ) strategy, allowing only the fittest among parents and offspring to survive.…”

“…Survival of individuals was determined by the (µ + λ) strategy, allowing only the fittest among parents and offspring to survive. For more details about those operators we refer the reader to [15]. Additionally to those operators, in this work we incorporated the (µ, λ) survival strategy that directly replaces the parent population by the offspring.…”

“…In a previous work [15] 24 Memetic Algorithms (MA) versions for the CBSP, produced by the combination of a small set of genetic operators, were extensively evaluated. The experimental results showed that all of them were able to produce significant better results than the state-of-the-art reference methods.…”