A hyper-heuristic based artificial bee colony algorithm for k-Interconnected multi-depot multi-traveling salesman problem

Abstract This paper addresses a newly introduced variant of traveling salesman problem, viz. k-Interconnected Multi-Depot Multi-Traveling Salesman Problem (k-IMDMTSP). This problem has the potential to address a variety of problems as it is a general problem that can change its characteristics according to the combination of parameter values. In fact, k-IMDMTSP can become an altogether different problem depending on the choice of its parameter values. According to the No Free Lunch Theorem [43], it is not possible to have a general algorithm that can outperform all algorithms across all problems emanating from k-IMDMTSP due to various parameter values. However, an appropriate combination of different algorithms can successfully deal with all such problems emanating from k-IMDMTSP. Here, we have made an attempt in this direction with the help of hyper-heuristics. A hyper-heuristic based artificial bee colony algorithm is proposed for k-IMDMTSP. A new solution encoding scheme is proposed for representing a k-IMDMTSP solution within the proposed approach, and its associated search space is analyzed theoretically. It has been proved that our encoding scheme yields a search space that is considerably smaller in comparison to encoding schemes used previously. Experimental results on standard benchmark instances show that the proposed approach outperforms other state-of-the-art approaches available in literature in terms of both solution quality and running time.