A decomposition-based chemical reaction optimization for multi-objective vehicle routing problem for simultaneous delivery and pickup with time windows

A practical variant of the vehicle routing problem (VRP), with simultaneous delivery and pickup and time windows (VRPSDPTW) is a challenging combinatorial optimization problem that has five optimization objectives in transportation and distribution logistics. Chemical reaction optimization has been used to solve mono and multi-objective problems. However, almost all attempts to solve multi-objective problems have included continues problems less than four objectives. This paper studies discrete multi-objective VRPSDPTW using decomposition-based multi-objective optimization chemical reaction optimization. In the proposed algorithm, each decomposed sub-problem is represented by a chemical molecule. All of the molecules are divided into a few groups, with each molecule having several neighboring molecules. To balance the diversity and convergence, we designed operators of on-wall ineffective collision and inter-molecular ineffective collision for a local search, as well as operators of decomposition and synthesis to enhance global convergence. The proposed approach is compared with two different algorithms on hypervolume performance measures. Experimental results show that the proposed algorithm outperform the other algorithms in most benchmarks.