Fuzzy Superposition Operation and Knowledge-Driven Coevolutionary Algorithm for Integrated Production Scheduling and Vehicle Routing Problem With Soft Time Windows and Fuzzy Travel Times

This article investigates an integrated production scheduling and vehicle routing problem with soft time windows and fuzzy travel times, where orders are grouped into batches for production and delivered by a limited number of multitrip heterogeneous vehicles. A biobjective mixed integer nonlinear programming (MINLP) model is established, which takes total cost and total early and tardy weighted penalty time as optimization objectives. First, a fuzzy superposition operation is proposed to obtain the fuzzy weighted penalty time, and it is extended to a generalized fuzzy operation law in fuzzy sets and systems. Then, we propose a knowledge-driven coevolutionary algorithm (KDCEA) to solve this problem. The algorithm fuses dual-subpopulation coevolution based on different update strategies and a knowledge-driven strategy based on dynamic knowledge sets and problem-specific knowledge. Finally, the correctness of the MINLP model is verified by the CPLEX solver using the ϵ-constraint method. A computational experiment is conducted based on different scale instances and a real-world case, and the results show the superiority of KDCEA in solving this problem.