A learning enhanced golden ball algorithm for the vehicle routing problem with backhauls and time windows

The vehicle routing problem and its variants are staples in addressing logistics problems. This widespread practicality combined with the computation complexity of these problems has led to a significant amount of research through the years. In this paper, a learning enhanced golden ball algorithm is developed to address the vehicle routing problem with backhaul and time windows. The meta-heuristic is inspired by competitive soccer league concepts. Many modifications to previous golden ball algorithm implementations were required but three new elements have been developed. First, a forbidden list technique improves the initial solutions used by the algorithm. Second, a new operator, flexible crossover, is proposed to improve solutions. Finally, a structural change to the sequence of operations was implemented to increase the search domain and thereby reduce the chance of having the algorithm get stuck at a local optimum. The algorithm was applied to 45 well-known standard problems from the literature that other researchers have used to test different approaches. So, each instance has best-known solutions that have been improved through the years using a variety of approaches. The algorithm proposed here found equivalent or superior solutions to 40 of the 45 problems. Further, stable solutions were found for larger problems using a desktop computer in less than two hours so this could be useful in practice.