Constrained multi-objective optimization problems (CMOPs) are challenging because of the difficulty in handling both multiple objectives and constraints. While some evolutionary algorithms have demonstrated high performance on most CMOPs, they exhibit bad convergence or diversity performance on CMOPs with small feasible regions. To remedy this issue, this paper proposes a coevolutionary framework for constrained multi-objective optimization, which solves a complex CMOP assisted by a simple helper problem. The proposed framework evolves one population to solve the original CMOP and evolves another population to solve a helper problem derived from the original one. While the two populations are evolved by the same optimizer separately, the assistance in solving the original CMOP is achieved by sharing useful information between the two populations. In the experiments, the proposed framework is compared to several state-of-the-art algorithms tailored for CMOPs. High competitiveness of the proposed framework is demonstrated by applying it to 47 benchmark CMOPs and the vehicle routing problem with time windows.

Dynamic vehicle routing problems (DVRPs) have become a hot research topic due to their significance in logistics, although it is still very challenging for existing algorithms to solve DVRPs due to the dynamically changing customer requests during the optimization. In this paper, we propose a pairwise proximity learning-based ant colony algorithm, termed PPL-ACO, for tackling DVRPs. In PPL-ACO, a pairwise proximity learning method is suggested to predict the local visiting order of customers in the optimal route after the occurrence of changes, which is on the basis of learning from the optimal routes found before the changes occur. A radial basis function network is used to learn the local visiting order of customers based on the proximity between each pair of customer nodes, by which the optimal routes can be quickly tracked after changes occur. Experimental results on 22 popular DVRP instances show that the proposed PPL-ACO significantly outperforms four state-of-the-art approaches to DVRPs. More interestingly, the results on five large-scale DVRP instances demonstrate the superiority of the proposed PPL-ACO in solving large-scale DVPRs with up to 1000 customers. The results on a real case of Nankai Strict, Tianjin, China also verifies that the proposed PPL-ACO is more effective and efficient than the four compared approaches in solving real-world DVRPs.

The shelter location is very important for evacuation planning in natural disasters, and evolutionary algorithms have demonstrated their effectiveness in solving this challenging problem. However, few evolutionary algorithms have been reported focusing on the shelter location under uncertainty of road networks due to the expensive cost of calculating the evacuation distance for individual evaluation. To address this issue, in this paper we propose a clustering-based surrogate-assisted multi-objective evolutionary algorithm, termed AR-MOEA+SA, in the framework of a recently developed evolutionary algorithm AR-MOEA. In AR-MOEA+SA, a surrogate model, the radial basis function (RBF), is adopted to approximately calculate the evacuation distance under uncertainty of road networks. Due to the fact that there often exist a large number of communities needing to be considered in shelter location, a clustering strategy is suggested to convert the surrogate of high-dimensional problem into the one of low-dimensional problem in the proposed AR-MOEA+SA for efficiently building the RBF network. A population initialization strategy is also suggested in AR-MOEA+SA to enhance the quality of training data in the early stages of evolution. Experimental results on a variety of test instances demonstrate the superiority of the proposed AR-MOEA+SA over the original version of AR-MOEA in terms of both computational efficiency and solution quality.