Knowledge-Guided Memetic Algorithm for Capacitated Arc Routing Problems with Time-Dependent Service Costs

Abstract: The capacitated arc routing problem with time-dependent service costs (CARPTDSC) is a challenging combinatorial optimization problem that arises from winter gritting applications. CARPTDSC has two main challenges about time consumption. First, it is an NP-hard problem. Second, the time-dependent service costs of tasks require frequent evaluations during the search process, significantly increasing computational effort. These challenges make it difficult for existing algorithms to perform efficient searches, often resulting in limited efficiency. To address these issues, this paper proposes a knowledge-guided memetic algorithm with golden section search and negatively correlated search (KGMA-GN), where two knowledge-guided strategies are introduced to improve search efficiency. First, a knowledge-guided initialization strategy (KGIS) is proposed to generate high-quality initial solutions to speed up convergence. Second, a knowledge-guided small-step-size local search strategy (KGSLSS) is proposed to filter out invalid moves, thereby reducing unnecessary evaluations and saving the computation time. Experimental results on five benchmark test sets, including both small- and larger-scale instances, demonstrate that KGMA-GN achieves higher search efficiency than the state-of-the-art methods. Moreover, the ablation study further confirms that the knowledge-guided local search operators in KGSLSS can significantly reduce runtime compared to traditional operators, especially for the knowledge-guided swap operator, which achieves more than a tenfold improvement in speed.