A Heuristic Enhancing Artificial Immune System for Three-dimensional Loading Capacitated Vehicle Routing Problem

This study addresses the Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP), a highly complex NP-hard problem that combines vehicle routing with spatially constrained three-dimensional bin packing. To tackle this challenge, we propose an enhanced Artificial Immune System (En-AIS) that integrates a novel local search heuristic called “Bring-i-to-j,” designed to improve routing feasibility and loading efficiency. The En-AIS algorithm is further refined through rigorous parameter tuning using a full factorial design and ANOVA analysis. Comparative experiments were conducted against conventional AIS and the Firefly Algorithm (FA) across 27 benchmark instances. Results demonstrate that En-AIS consistently outperforms both baseline methods in terms of solution quality, achieving an average improvement of 15–20% while maintaining competitive computational times. These findings highlight the algorithm’s robustness and its practical potential for application in logistics and supply chain optimization tasks involving joint routing and loading decisions.