An artificial bee colony algorithm for the vehicle routing problem with backhauls and time windows

The vehicle routing problem with backhauls and time windows (VRPBTW) aims to find a feasible vehicle route that minimizes the total traveling distance while imposing capacity, backhaul, and time-window constraints. We present an enhanced artificial bee colony algorithm (EABCA), which is a meta-heuristic, to solve this problem. Three strategies - a forbidden list, the sequential search for onlookers, and the combination of 1-move intra-route exchange and λ-interchange technique - are introduced for EABCA. The proposed method was tested on a set of benchmark instances. The computational results show that the EABCA can produce better solutions than the basic ABCA, and it discovered many new best-known solutions