A decomposition based estimation of distribution algorithm for multiobjective traveling salesman problems

The traveling salesman problem (TSP) is a well known NP-hard benchmark problem for discrete optimization. However, there is a lack of TSP test instances for multiobjective optimization and some current TSP instances are combined to form a multiobjective TSP (MOTSP). In this paper, we present a way to systematically design MOTSP instances based on current TSP test instances, of which the degree of conflict between the objectives is measurable. Furthermore, we propose an approach, named multiobjective estimation of distribution algorithm based on decomposition (MEDA/D), which utilizes decomposition based techniques and probabilistic model based methods, to tackle the newly designed MOTSP test suite. In MEDA/D, an MOTSP is decomposed into a set of scalar objective sub-problems and a probabilistic model, using both priori and learned information, is built to guide the search for each sub-problem. By the cooperation of neighbor sub-problems, MEDA/D could optimize all the sub-problems simultaneously and thus find an approximation to the original MOTSP in a single run. The experimental results show that MEDA/D outperforms MOACO and MOEA/D-ACO, two ant colony based methods, on most of the given test instances and MEDA/D is insensible to its control parameters.