Solution of maximum scatter traveling salesman problem through evolutionary approaches

This paper is concerned with a variant of the traveling salesman problem (TSP) called the maximum scatter traveling salesman problem (MSTSP). The goal of MSTSP is to find a Hamiltonian cycle that maximizes the minimum length edge of the cycle. This problem has real -world applications in domains such as manufacturing and medical imaging. Both symmetric and asymmetric versions of the problem are considered in this paper. To address this problem, we have developed two evolutionary approaches. Our first approach is based on a genetic algorithm, whereas the second approach is based on a differential evolution algorithm. Initial solution generation procedure, variation operators (crossover and mutation) used in our approaches are designed considering the characteristics of this problem. The solutions obtained through variation operators are improved further through a local search that is specially adapted for MSTSP. For benchmarking, we have compared the performance of our proposed approaches with the state-of-the-art approaches available in the literature. Our approaches obtained better quality solutions in a shorter time for both symmetric and asymmetric versions of the problem, thereby clearly demonstrating their effectiveness in solving MSTSP.