Using Group Theory to Generate Initial Population for a Genetic Algorithm for Solving Traveling Salesman

Abstract

In this chapter, we propose a novel algorithm that uses Genetic algorithm with group theory for initial population generation and also propose a novel crossover for solving Traveling Salesman Problem. In the group tour construction method, each individual/initial tour has distinct start city provided that population size is equal to total number of cities. In the initial population, each individual/tour has a distinct starting city. The distinct starting cites of each tour provide genetic material for exploration for the whole search space. Therefore, a heterogeneous starting city of a tour in initial population is generated to have rich diversity. Proposed crossover based on greedy method of sub-tour connection drives the efficient local search, followed by 2-opt mutation for improvement of tour for enhanced/optimal solution. The result of the proposed algorithm is compared with other standard algorithms followed by conclusion.