Knowledge Application to Crossover Operators in Genetic Algorithm for Solving the Traveling Salesman Problem

Abstract

Genetic Algorithm often bears with Premature Convergence for solving combinatorial optimization problems but can be improved by modification at different prospectives. In this research, an effective knowledge is applied in the procedure of Genetic Algorithm used for solving TSP. The key concept for the proposed GA is a modification in the crossover operators by applying knowledge of smallest distant cities (shortest edge) assuming that it would improve the process to find the shortest path, by optimizing the new generations. As TSP is represented as a graph, considering cities as nodes and paths as edges, in the proposed approach, crossover point selection for crossover operators is selected upon the basis of minimum edge in the given graph. To test the effect of the proposed method of knowledge application, Linear Order Crossover, Cycle Crossover Operator, and Sequential Constructive Crossover are modified and results are proved on the randomly generated data sets for TSP. This optimization not only improved the shortest path but also reduced the problem of Premature Convergence.

A Decomposition Algorithm for Dynamic Car Sequencing Problems with Buffers

“…For the crossover method, we use the PMX crossover operator [34], a crossover operator that is guaranteed to produce valid chromosomes. PMX determines the crossover region by randomly selecting two crossover points, and the crossover region is populated directly to the offspring chromosome, for genes outside the crossover region in the offspring, which needs to be determined based on the mapping relationship established by the crossover region.…”