Volleyball premier league algorithm with ACO and ALNS for simultaneous pickup–delivery location routing problem

The reverse logistics problem, which involves customer returns and incurs high additional logistics costs, has become a topic of increasing interest. This problem is modeled as the location routing problem with simultaneous pickup and delivery under time constraints (LRPSPDTW), which is a more complex version of the location routing problem (LRP). Previous studies have shown that existing algorithms are unable to provide satisfactory solution accuracy for this problem. In order to address this, a novel algorithm called the hybrid volleyball premier league (HVPL) algorithm is proposed. Drawing inspiration from the competition mechanism of the original volleyball premier league (VPL) algorithm, the HVPL algorithm incorporates adaptive large neighborhood search (ALNS) and improved ant colony optimization (ACO) as sub-algorithms, allowing them to work together synergistically and strike a balance between exploration and exploitation. The learning and elimination phases of the VPL algorithm have been redesigned to enhance convergence speed. Furthermore, the Bellman's algorithm has been enhanced to determine depot locations and construct vehicle paths for the solution. Prior to solving the LRPSPDTW problem, benchmark testing was conducted using 35 latest benchmark functions. Experimental results and Friedman mean rank test demonstrated that HVPL exhibits superior exploration and exploitation capabilities. HVPL was subsequently tested on 66 instances based on the modified Solomon's benchmark and the NEO research group benchmarks, and the results showcased its outperformance over other methods in the majority of cases.