A Novel Crossover based Discrete Artificial Algae Algorithm for Solving Traveling Salesman Problem

Abstract

The Artificial Algae Algorithm (AAA) is a newly proposed metaheuristic algorithm that is inspired by microalgae behaviors. This algorithm has been proposed for solving continuous optimization problems and achieved good results for the continuous problems. In addition, binary versions of AAA are proposed in the literature. This paper presents a discrete version of AAA, which is named Discrete Artificial Algae Algorithm (DAAA). For discretization of AAA, Crossover operators (one-point and uniform) are used in the processes (helical movement, evolutionary process, and adaptation). In this study, in addition to crossover operators, transformation operators such as swapping, insertion, symmetry, and reversion are also used. DAAA’s performance was analyzed on a well-known discrete optimization problem called the Traveling Salesman Problem (TSP). DAAA was tested on thirty-two Benchmark instances of the TSP. These instances were small-sized, medium-sized, and large-sized. Firstly, the AAA processes (evolutionary process, adaptation, and helical movement) with the combination of nearest neighbor and transformation operators were tested for selected benchmark instances and this testing was called Process Analysis. After this process Analysis the best processes with which to continue were selected, and after this decision comparisons with other algorithms were started. The main comparison is between discrete Social Spider Algorithm (DSSA) and DAAA, and DAAA outperformed DSSA on most of the problems. Further, DAAA’s performance on some of the benchmark instances was compared with some of the well-known algorithms for TSP. In this comparison, DAAA has achieved better results than many other algorithms. Experimental results show that DAAA has the capability of solving discrete optimization problems and outperforming other algorithms.