Bees traplining metaphors for the vehicle routing problem using a decomposition approach

In this study, the bees traplining metaphor was adopted for the Bees Algorithm (BA) and the Combinatorial Bees Algorithm (BA_C) and applied to solve the vehicle routing problem. The two-parameter Continuous and Combinatorial Bees Algorithms (BA₂ and BA_C2), equipped with a traplining metaphor intensifier, Bees Routing Optimiser (BRO), were used to solve the capacitated vehicle routing problem with a decomposition approach. In the first phase of the proposed method, the two-parameter Bees Algorithm (BA₂) was employed to solve the capacitated facility location problem, resulting in clusters of customers that did not violate the vehicles’ capacity. Then, BA_C2 combined with BRO was used to produce the routing plan for each cluster. BA₂ and BA_C2 implement the traplining foraging technique of bees, which integrates their exploratory and exploitative search mechanisms, to simplify parameter setting and use their threat avoidance tactics to intensify the solution. The results of comparisons with other BA versions indicate that the proposed algorithm improves the accuracy of the basic version by at least 4% while speeding it up fourfold.