LCS-Based Selective Route Exchange Crossover for the Pickup and Delivery Problem with Time Windows

Abstract

The pickup and delivery problem with time windows (PDPTW) is an NP-hard discrete optimization problem of serving transportation requests using a fleet of homogeneous trucks. Its main objective is to minimize the number of vehicles, and the secondary objective is to minimize the distance traveled during the service. In this paper, we propose the longest common subsequence based selective route exchange crossover (LCS-SREX), and apply this operator in the memetic algorithm (MA) for the PDPTW. Also, we suggest the new solution representation which helps handle the crossover efficiently. Extensive experimental study performed on the benchmark set showed that using LCS-SREX leads to very high-quality feasible solutions. The analysis is backed with the statistical tests to verify the importance of the elaborated results. Finally, we report one new world’s best routing schedule found using a parallel version of the MA exploiting LCS-SREX.