A memetic algorithm with fuzzy-based population control for the joint order batching and picker routing problem

The joint order batching and picker routing problem (JOBPRP) is a combinatorial optimization problem that occurs during in the order-picking operation of warehouse management. It consists of simultaneous assignment of customer orders to batches and routing of picking operations in the batches such that the total travel distance is minimized. In this paper, we develop a memetic algorithm with fuzzy-based population control (MA-FPC) to solve the JOBPRP. MA-FPC takes advantage of the hierarchical nature of the problem to design a batch exchange crossover (BEX) operator and a two-level local improvement procedure. BEX transfers complete batches from parent solutions to offsprings. Local improvement systematically employs a combined heuristic and exact routing approach to solve the picker routing problem. Furthermore, fuzzy -based population control is used to dynamically regulate population diversity during the search, which removes individuals from or adds individuals to the population. In numerical experiments, MA-FPC significantly outperforms state-of-the-art point-based and population-based algorithms developed for the order batching problem and JOBPRP with respect to solution quality in reasonable running times. Our algorithm improves the previous best-known solutions for 57 of the 64 benchmark instances.