Multi-objective evolutionary algorithm based on RBF network for solving the stochastic vehicle routing problem

Solving the multi-objective vehicle routing problem with stochastic demand (MO-VRPSD) is challenging due to its non-deterministic property and conflicting objectives. Most multi-objective evolutionary algorithm dealing with this problem update current population without any guidance from previous searching experience. In this paper, a multi-objective evolutionary algorithm based on artificial neural networks is proposed to tackle the MO-VRPSD. Particularly, during the evolutionary process, a radial basis function network (RBFN) is exploited to learn the potential knowledge of individuals, generate hypothesis and instantiate hypothesis. The RBFN evaluates individuals with different scores and generates new individuals with higher quality while taking into account the non-dominated relationship between individuals. Moreover, integrated with a specific non-dominated sorting strategy, i.e., ENS-SS, along with several effective heuristic operations, the proposed algorithm performs favorably for solving the MO-VRPSD. The experimental results based on the modified Solomon benchmark instances verified the effectiveness of the respective components, and the superiority to other multi-objective evolutionary algorithms.