In this paper, the Periodic Capacitated Arc Routing Problem (PCARP) is investigated. PCARP is an extension of the well-known CARP from a single period to a multi-period horizon. In PCARP, two objectives are to be minimized. One is the number of required vehicles (nv), and the other is the total cost (tc). Due to the multi-period nature, given the same graph or road network, PCARP can have a much larger solution space than the single-period CARP counterpart. Furthermore, PCARP consists of an additional allocation sub-problem (of the days to serve the arcs), which is interdependent with the routing sub-problem. Although some attempts have been made for solving PCARP, more investigations are yet to be done to further improve their performance especially on large-scale problem instances. It has been shown that optimizing nv and tc separately (hierarchically) is a good way of dealing with the two objectives. In this paper, we further improve this strategy and propose a new Route Decomposition (RD) operator thereby. Then, the RD operator is integrated into a Memetic Algorithm (MA) framework for PCARP, in which novel crossover and local search operators are designed accordingly. In addition, to improve the search efficiency, a hybridized initialization is employed to generate an initial population consisting of both heuristic and random individuals. The MA with RD (MARD) was evaluated and compared with the state-of-the-art approaches on two benchmark sets of PCARP instances and a large data set which is based on a real-world road network. The experimental results suggest that MARD outperforms the compared state-of-the-art algorithms, and improves most of the best-known solutions. The advantage of MARD becomes more obvious when the problem size increases. Thus, MARD is particularly effective in solving large-scale PCARP instances. Moreover, the efficacy of the proposed RD operator in MARD has been empirically verified.
Graphical abstract
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Improved memetic algorithm for Capacitated Arc Routing Problem
