An enhanced Moth-flame optimization algorithm for permutation-based problems
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RESEARCH PAPER
An enhanced Moth‑flame optimization algorithm for permutation‑based problems Ahmed Helmi1 · Ahmed Alenany1 Received: 23 October 2019 / Revised: 10 March 2020 / Accepted: 18 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Moth-flame optimizer (MFO) is one of the recently proposed metaheuristic optimization techniques which has been successfully used in wide range of applications. However, there are two issues with the MFO algorithm. First, as a stochastic technique, MFO may prematurely converge at some local minima during the search process. Second, the original MFO was developed for continuous search space problems and is not directly applicable to, e.g., permutation-based problems (PBP). In this paper, a novel perturbation strategy is introduced to the MFO algorithm to avoid probable local minima regions. This strategy works as follows: if the best solution obtained so far doesn’t improve for a given number of consecutive iterations, the current population of solutions is perturbed using some crossover mechanism as an attempt to explore new promising neighbourhoods in the search space. In addition, smallest position values mapping technique is employed in order for the proposed, termed CrossMFO (COMFO), algorithm to be applicable to PBP problems. It is noticed that, despite these modifications, the proposed COMFO has the same time complexity order as the original MFO. Extensive simulation experiments are conducted to compare the proposed COMFO to the MFO, other enhanced versions of MFO, and some metaheuristic optimizers in solving the well-known Travelling Salesman Problem (TSP). Empirical results show that the solutions obtained using MFO are improved by a factor of 24–47% on average for large TSP instances having more than 100 cities using COMFO and can even reach 38–58% using different settings. In addition, compared to other algorithms in the literature, the proposed algorithm provides, on average, better solutions. Hence, it can be considered a promising and efficient technique for this type of problems. Keywords Metaheuristics · Combinatorial optimization problems (COP) · Moth-flame optimization (MFO) · Travelling salesman problem (TSP) · Crossover function · Local minima
1 Introduction Metaheuristic-based techniques inspired by the behaviour of natural phenomena [1], swarm intelligence [2], or physical processes [3] have been extensively used in wide range of applications in science and engineering [4–8]. The era of metaheuristic techniques started by Genetic Algorithm (GA) which was introduced by Holland in 1960 [9] inspired by the theory of evolution in biology. The paradigm of GA is almost followed by all next members in the field. For example, particle swarm optimization (PSO), which is a widely used technique, imitates the social behaviour of swarms. * Ahmed Helmi [email protected] 1
Department of Computer and Systems Engineering, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
Each individual in the swarm updates its current kno
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