Discrete ITÔ algorithm to the coloured travelling salesman problem

The Coloured Travelling Salesman Problem CTSP, a generalised version of the Multiple Travelling Salesman Problem MTSP, has been proposed to model some real-world applications. This work proposes a discrete ITO DITO algorithm to solve CTSP. It combines the continuous ITO stochastic process with Ant Colony Optimisation ACO algorithm. First, the stochastic drift and volatility terms of ITO process are designed to be suitable for solving combinatorial optimisation problems, such as TSP and CTSP. And then, inspired by ACO, the generative model for a feasible solution of CTSP is constructed via the distance between cities and the experience gathered in the searching process. The experiments results show that the performance of DITO is superior to some state-of-the-art meta-heuristic algorithms in terms of the quality of the solution and computational time.