Enhancing vehicle routing problem solutions for sustainability: a multi-heuristic approach with load factor integration

PURPOSE: The research examines the effectiveness of combining multiple heuristic methods, specifically local search operators, with this incorporated load factor. While a single local search operator can improve solution quality, we hypothesize that using multiple operators in a search strategy leads to further optimization. METHODS: We analyze the performance of two powerful heuristics: the composite and multi-level methods. Both methods involve applying improvement schemes sequentially with various local search operators. The key difference lies in how the search is directed after implementing a scheme. We evaluate these methods using 46 well-established VRP instances. RESULTS: Our findings reveal that the multi-level heuristic, on average, achieves solutions comparable to the composite heuristic when using the same parameters. The difference in solution quality is minimal. Notably, the multi-level method exhibits significantly faster computation times. CONCLUSION: This performance analysis provides valuable insights for developing further refinement methods that integrate the load factor. Applying these methods to real-world case studies presents an exciting future direction. Businesses can leverage these findings to optimize their transportation services, leading to both economic and environmental benefits.