Integrating machine learning (ML) techniques into metaheuristics is an efficient approach in single-objective optimization. Indeed, high-quality solutions often contain relevant knowledge, that can be used to guide the heuristic towards promising areas. In multiobjective optimization, the quality of solutions is evaluated according to multiple criteria that are generally conflicting. Therefore, the ML techniques designed for single-objective optimization can not be directly adapted for multi-objective optimization. In this paper, we propose to enhance the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) with a clustering-based learning mechanism. To be more precise, solutions are grouped regarding a metric based on their quality on each criterion, and the knowledge from the solutions of the same group is merged. Experiments are conducted on the multi-objective vehicle routing problem with time windows. The results show that MOEA/D with learning outperforms the original version. CCS CONCEPTS• Mathematics of computing → Combinatorial optimization; • Computing methodologies → Machine learning approaches.

Local search (LS) algorithms are efficient metaheuristics to solve vehicle routing problems (VRP). They are often used either individually or integrated into evolutionary algorithms. For example, the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) can be enhanced with a local search replacing the mutation step based on a single move operator traditionally. LS are based on an efficient exploration of the neighborhoods of solutions. Many methods have been developed over the years to improve the efficiency of LS. In particular, the exploration strategy of the neighborhood and the pruning of irrelevant neighborhoods are important concepts that are frequently considered when designing a LS. In this paper, we focus on a bi-objective vehicle routing problem with time windows (bVRPTW) where the total traveling cost and the total waiting time have to be minimized. We propose two neighborhood strategies to improve an existing LS, efficient on the single-objective VRPTW. First, we propose a new strategy to explore the neighborhood of a solution. Second, we propose a new strategy for pruning the solution neighborhood that takes into account the second criterion of our bVRPTW namely the waiting time between customers. Experiments on Solomon's instances show that using LS with our neighborhood strategies in the MOEA/D gives better performance. Moreover, we can achieve some best-known solutions considering the traveling cost minimization only.

Knowledge Discovery (KD) mechanisms (e.g. data mining, neural networks) receive more and more interest over the years. A KD mechanism uses an extraction procedure, namely Kext, to discover knowledge, and an injection procedure, namely Kinj, to exploit knowledge. However such mechanisms are not often applied to multi-objective combinatorial problems, due to the optimization of many objectives, which can lead to learning conflicting knowledge. The key is to know how the components of the KD mechanism should coexist and interact with the knowledge. In this article, we work with the MOEA/D algorithm, and existing Kinj and Kext components. We propose different interactions between the components of the KD mechanism, by using different numbers of knowledge groups (dedicated to the storage of the knowledge) and different strategies for the injection component. The variants are evaluated through the bi-objective Vehicle Routing Problem with Time Windows (bVRPTW). Our results show, that using five knowledge groups and an intensification strategy for the injection procedure leads to better results.