Advancing large-scale cement vehicle distribution: the modified salp swarm algorithm

The vehicle routing problem (VRP) is a paramount combinatorial optimisation challenge, extensively used across various transportation logistics and distribution systems. The capacity-utilised vehicle routing problem (CVRP) stands as a notable variant, necessitating a nuanced interplay between the exploration and exploitation phases due to its discrete nature. While the salp swarm algorithm (SSA) enjoys recognition in the optimisation domain for its streamlined design and efficacy, its foundational architecture is inherently suited for continuous optimisation tasks. Addressing this gap, our paper presents a refined iteration of SSA, termed mSSA. By ingeniously integrating the core principles of SSA with the opposition-based learning (OBL) approach and incorporating the roulette wheel selection (RWS) mechanism, mSSA is meticulously crafted to navigate the discrete challenges posed by expansive CVRP instances. To affirm the robustness of mSSA, our research undertook performance evaluations in three distinct CVRPs: initially, an 8-customer assignment to validate stability, followed by two practical tests involving the distribution of cement to 30 and 50 customers in Vietnam. Empirical findings consistently highlight mSSA's dominant performance against other meta-heuristic techniques tailored for CVRP. This positions mSSA as a formidable tool in decision-making processes, particularly for optimising cement delivery using limited-capacity vehicles.