An edge memory-driven iterated search algorithm with bidirectional feedback for the capacitated vehicle routing problem

The fixed‑fleet Capacitated Vehicle Routing Problem (CVRP) is a canonical NP‑hard combinatorial optimization problem in logistics distribution. Conventional metaheuristic algorithms fail to fully exploit structural information embedded within historical routes and lack effective search guidance, which readily results in premature convergence. To remedy these limitations, this paper proposes an Edge Memory‑Driven Iterative Search algorithm with Bidirectional Feedback (EMIS‑BF). A dynamic edge memory matrix embedded with decay and upper‑lower bound constraints is devised to quantify high‑quality edge patterns and alleviate search stagnation. To couple global population exploration and memory‑guided local intensification, a closed‑loop bidirectional feedback mechanism is constructed, where forward feedback disseminates elite route structures and backward feedback feeds local optimization improvements back into the memory matrix to enable cross‑stage information exchange. Furthermore, a two‑stage hybrid search framework is established that integrates 2‑opt, 3‑opt, insertion and destroy‑and‑repair neighborhood operators alongside a probabilistic inferior‑solution acceptance rule to strike a balance between global‑exploration breadth and local‑exploitation depth. Numerical experiments are carried out on 83 standard A/B/E/P benchmark instances, with more than ten representative metaheuristics employed as comparative baselines. EMIS‑BF matches published best‑known solutions (BKS) on 68 test instances. The Friedman test combined with post‑hoc Bonferroni–Dunn statistical analysis shows that EMIS‑BF achieves the second‑best average rank among the twelve algorithms ranked on Sets A, B and P. The proposed algorithm yields statistically significant performance improvements over six baseline methods, while no statistically distinguishable performance gaps are observed between EMIS‑BF and the top‑five competitive solvers. Multiple independent runs further verify its robust performance and stable convergence behavior. The edge‑memory and feedback strategies provide valuable design references for hybrid swarm‑intelligence and metaheuristic optimization algorithms.