Multi-Strategy Quantum Differential Evolution Algorithm With Cooperative Co-Evolution and Hybrid Search for Capacitated Vehicle Routing

Capacitated Vehicle Routing Problem (CVRP) is a critical challenge in logistics optimization, which directly impact operational costs and service efficiency. While quantum differential evolution (QDE) algorithm offers potential advantages in solving combinatorial optimization problems, its application in CVRP is still limited due to the premature convergence, poor search capability and stagnation. To address these limitations, a novel multi-strategy QDE algorithm with cooperative co-evolution (CC) framework and hybrid local search strategy, namely MSCFLQDE is proposed to effectively solve the CVRP. Firstly, a new multi-population strategy with CC framework is designed to solve each sub-CVRP for enabling parallel optimization and preserving global constraints. Then an adaptive differential mutation mechanism is developed to balance the exploration and exploitation and accelerate the convergence. Thirdly, a new quantum rotation mode with the sorting coding rule is designed to adjust the search direction and reduce stagnation. In the later stage, a hybrid local search strategy is proposed to dynamically eliminate the redundant nodes and intersections. Finally, the experiment results on the five CVRPs (set A, set B, set P, set E, and set G) demonstrate that the MSCFLQDE has better search ability, higher convergence and stronger stability by comparing with the state-of-the-art algorithms(such as CCDE, CCDE-D, CCDE-R, CCDE-S, HGS, BILA, AGA-ES and TAMLS and so on), which achieves 5.53% shorter distances for P51_K10 by comparing with AGA-ES.