Hybrid ITÖ Algorithm for Maximum Scatter Colored Traveling Salesman Problem

Abstract This research presents a new problem maximum scatter colored traveling salesman problem (MSCTSP), the objective of MSCTSP is to find Hamiltonian cycles with the minimal edge as max as possible, it is used to simulate the real-world applications of network and transport. Since MSCTSP has been proved to be a NP-hard problem, population-based algorithms can be used for solving it. However, the performances are not satisfactory. Thus, it is necessary to develop novel algorithms to obtain high quality feasible solution. Based on the above reason, the paper proposes a novel hybrid ITÖ (HITÖ) algorithm, which integrates the two new strategies: crossover operator and mutation strategy, into the standard ITÖ. In the iteration course of HITÖ, the dual-chromosome coding is used to code a feasible solution of MSCTSP, and the stochastic drift and volatility operators are used to explore and exploit new unknown region. During the process, drift operator is performed by crossover operator, volatility operator is carried out by mutation strategy, and they are both affected by activity intensity of particles which functionally depends on the radius and temperature. Experiments display HITÖ shows an improvement over comparative algorithms on solution quality.