A memetic NSGA-II for the bi-objective mixed capacitated general routing problem

The mixed capacitated general routing problem (MCGRP) is concerned with the determination of the optimal vehicle routes to service a set of customers located at nodes and along edges or arcs on a mixed weighted graph representing a complete transportation network. Although MCGRP generalizes many other routing problems and yields better models for several practical problems such as newspaper delivery and urban waste collection , this is still an underinvestigated problem. Furthermore, most of the studies have focused on the optimization of just one objective, that is, cost minimization. Keeping in mind the requirement of industries nowadays, MCGRP has been addressed in this paper to concurrently optimize two crucial objectives, namely, minimization of routing cost and route imbalance. To solve this bi-objective form of MCGRP, a multi-objective evolutionary algorithm (MOEA), coined as Memetic NSGA-II, has been designed. It is a hybrid of non-dominated sorting genetic algorithm-II (NSGA-II), a dominance based local search procedure (DBLSP), and a clone management principle (CMP). The DBLSP and CMP have been incorporated into the framework of NSGA-II with a view to empowering its capability to converge at/or near the true Pareto front and boosting diversity among the trade-off solutions, respectively. In addition, the algorithm also contains a set of three well-known crossover operators (X-set) that are employed to explore different parts of the search space. The algorithm was tested on a standard benchmark of twenty three standard MCGRP instances of varying complexity. The computational experiments verify the effectiveness of Memetic NSGA-II and also show the energetic effects of using DBLSP, CMP and X-set together while finding the set of potentially Pareto optimal solutions.