Elite-based multi-objective improved iterative local search algorithm for time-dependent vehicle-drone collaborative routing problem with simultaneous pickup and delivery

This paper focuses on solving a time-dependent multi-objective vehicle-drone collaborative routing problem with simultaneous pickup and delivery, in which multiple visits per drone trip, simultaneous pickup and delivery, soft time windows, and time-dependent road network are considered. With the maximum completion time and total violation time as the optimization objectives, we first formulate the mathematical model of the problem. Then, in order to effectively solve the problem, an Elite-based multi-objective improved iterative local search algorithm developed within a collaborative optimization framework is proposed. Specifically, the multi-objective problem is decomposed into two subproblems, each of which is solved by minimizing a single objective. Meanwhile, the algorithm uses an elite set to record non-dominated solutions, guide the search, and achieve information exchange between subproblems. In the proposed algorithm, an individual is encoded as a vector consisting of two parts, a customer sequence and a sequence recording the customers' visiting modes, and can be decoded into subroutes for the vehicle and drone. To guarantee the feasibility of the solution, an adjustment method is proposed to repair the individual. In addition, based on individual representation and problem characteristics, six neighborhood structures are designed, through which new individuals can be generated. Then, by using the neighborhood structures, a problem-specific local search strategy and an iterative local search strategy are proposed to improve the search capability of the algorithm. Experimental tests and analyses demonstrate the correctness of the established mathematical model and the effectiveness of the proposed algorithm in solving this complex vehicle-drone collaborative routing problem.