A multi-population cooperative coevolutionary algorithm for multi-objective capacitated arc routing problem

Capacitated Arc Routing Problem (CARP) has drawn much attention during the last few years. In addition to the goal of minimizing the total cost of all the routes, many real-world applications of CARP also need to balance these routes. The Multi-objective CARP (MO-CARP) commonly exists in practical applications. In order to solve MO-CARP efficiently and accurately, this paper presents a Multi-population Cooperative Coevolutionary Algorithm (MPCCA) for MO-CARP. Firstly, MPCCA applies the divide-and-conquer method to decompose the whole population into multiple subpopulations according to their different direction vectors. These subpopulations evolve separately in each generation and the adjacent subpopulations can share their individuals in the form of cooperative subpopulations. Secondly, multiple subpopulations are used to search different objective subregions simultaneously, so individuals in each subpopulation have a different fitness function, which can be modeled as a Single Objective CARP (SO-CARP). The advanced MAENS approach for single-objective CARP can be used to search each objective subregion. Thirdly, the internal elitism archive is used to construct evolutionary pool for each subregion, which greatly speeds up the convergence. Lastly, the fast nondominated ranking and crowding distance of NSGA-II are used for selecting the offspring and keeping the diversity. MPCCA is tested on 91 CARP benchmarks. The experimental results show that MPCCA obtains better generalization performance over the compared algorithms.