Population-Based Incremental Learning Algorithm for a Serial Colored Traveling Salesman Problem

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem. This paper investigate a class of CTSP, called serial CTSP (S-CTSP). Each of its salesmen has his exclusive cities and shares some cities with its neighbor(s) in a serial manner. It can be used to model the scheduling problem of multimachine engineering systems with linearly arranged machines. S-CTSP is NP-hard. Developing effective and efficient approaches to S-CTSP is important to enable its industrial applications. This paper presents a population-based incremental learning (PBIL) approach to it. After analyzing its solution space, we set up some probability matrix models to guide the individual search of the algorithm. Then, a distance penalty is introduced into the state transfer function that can select the cities with small penalty values by the Roulette method to form a good route. By adding a powerful local search operation, 2-opt, to the algorithm, we can further enhance its search ability. Extensive simulation is conducted and its results show that the augmented PBIL is effective and well outperforms the genetic algorithms and CPLEX.