Development of an enhanced scatter search algorithm using discrete chaotic Arnold’s cat map

Authors

DOI:

https://doi.org/10.15587/1729-4061.2021.234915

Keywords:

scatter search, Arnold's cat map, chaotic, TSP, metaheuristic, optimization problems

Abstract

Solving optimization problems is an ever-growing subject with an enormous number of algorithms. Examples of such algorithms are Scatter Search (SS) and genetic algorithms. Modifying and improving of algorithms can be done by adding diversity and guidance to them. Chaotic maps are quite sensitive to the initial point, which means even a very slight change in the value of the initial point would result in a dramatic change of the sequence produced by the chaotic map Arnold's Cat Map. Arnold's Cat Map is a chaotic map technique that provides long non-repetitive random-like sequences. 

Chaotic maps play an important role in improving evolutionary optimization algorithms and meta-heuristics by avoiding local optima and speeding up the convergence. This paper proposes an implementation of the scatter search algorithm with travelling salesman as a case study, then implements and compares the developed hyper Scatter Arnold's Cat Map Search (SACMS) method against the traditional Scatter Search Algorithm. SACMS is a hyper Scatter Search Algorithm with Arnold's Cat Map Chaotic Algorithm. Scatter Arnold's Cat Map Search shows promising results by decreasing the number of iterations required by the Scatter Search Algorithm to get an optimal solution(s). Travelling Salesman Problem, which is a popular and well-known optimization example, is implemented in this paper to demonstrate the results of the modified algorithm Scatter Arnold's Cat Map Search (SACMS). Implementation of both algorithms is done with the same parameters: population size, number of cities, maximum number of iterations, reference set size, etc. The results show improvement by the modified algorithm in terms of the number of iterations required by SS with an iteration reduction of 10–46 % and improvements in time to obtain solutions with 65 % time reduction

Author Biographies

Amaal Ghazi Hamad Rafash, Al Ma’moon University College

PhD, Lecturer

Department of Computer Science

Enas Mohammed Hussein Saeed, Al- Mustansiriyah University

PhD, Lecturer

Department of Computer Science

Al-Sharify Mushtaq Talib, Taras Shevchenko National University of Kyiv

PhD, Assistant

Department of Radio Engineering and Radio Electronics Systems

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Published

2021-12-16

How to Cite

Rafash, A. G. H., Saeed, E. M. H., & Talib, A.-S. M. (2021). Development of an enhanced scatter search algorithm using discrete chaotic Arnold’s cat map. Eastern-European Journal of Enterprise Technologies, 6(4 (114), 15–20. https://doi.org/10.15587/1729-4061.2021.234915

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Section

Mathematics and Cybernetics - applied aspects