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

Amaal Ghazi Hamad Rafash,Enas Mohammed Hussein Saeed,Al-Sharify Mushtaq Talib

doi:10.15587/1729-4061.2021.234915

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

Highlights

Many complex optimization problems can be solved with many variables exactly over a very limited time for calculations
The aim of the study is to implement an algorithm that finds an optimal solution to the travelling salesman problem with a minimum number of iterations required and time
The aim of the Scatter Search is maintaining a group of various and high-quality candidate solution cases. The concept of this method is that the beneficial information on global optima is maintained in an elite and diverse solution set and that re-combining samples from the group may benefit from that information

Summary

Introduction

Many complex optimization problems can be solved with many variables exactly over a very limited time for calculations. This causes great interest in search algorithms, which find optimal solutions at reasonable times of work. One of these optimal problems is the Travelling Salesman Problem (TSP). TSP is looking for the shortest path to visit the city group and return to the starting point. Even though the problem statement is quite simple, it’s a problem of improving a well-known complex NP constraint that can be solved in a time limit. TSP is thoroughly studied and resolved using various top-end approaches, like research typography, evolutionary algorithms, neural networks, bee algorithm and ant colony system [1]

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