An Improved Genetic Algorithm with a New Initialization Mechanism Based on Regression Techniques

Abstract

Genetic algorithm (GA) is one of the well-known techniques from the area of evolutionary computation that plays a significant role in obtaining meaningful solutions to complex problems with large search space. GAs involve three fundamental operations after creating an initial population, namely selection, crossover, and mutation. The first task in GAs is to create an appropriate initial population. Traditionally GAs with randomly selected population is widely used as it is simple and efficient; however, the generated population may contain poor fitness. Low quality or poor fitness of individuals may lead to take long time to converge to an optimal (or near-optimal) solution. Therefore, the fitness or quality of initial population of individuals plays a significant role in determining an optimal or near-optimal solution. In this work, we propose a new method for the initial population seeding based on linear regression analysis of the problem tackled by the GA; in this paper, the traveling salesman problem (TSP). The proposed Regression-based technique divides a given large scale TSP problem into smaller sub-problems. This is done using the regression line and its perpendicular line, which allow for clustering the cities into four sub-problems repeatedly, the location of each city determines which category/cluster the city belongs to, the algorithm works repeatedly until the size of the subproblem becomes very small, four cities or less for instance, these cities are more likely neighboring each other, so connecting them to each other creates a somehow good solution to start with, this solution is mutated several times to form the initial population. We analyze the performance of the GA when using traditional population seeding techniques, such as the random and nearest neighbors, along with the proposed regression-based technique. The experiments are carried out using some of the well-known TSP instances obtained from the TSPLIB, which is the standard library for TSP problems. Quantitative analysis is carried out using the statistical test tools: analysis of variance (ANOVA), Duncan multiple range test (DMRT), and least significant difference (LSD). The experimental results show that the performance of the GA that uses the proposed regression-based technique for population seeding outperforms other GAs that uses traditional population seeding techniques such as the random and the nearest neighbor based techniques in terms of error rate, and average convergence.