Why to Climb If One Can Jump: A Hill Jumping Algorithm for the Vehicle Routing Problem with Time Windows

Abstract

The most common approaches to solve the variants of the well-known vehicle routing problem are based on metaheuristic hill-climbing search. The deficiency of these methods is slow local search based hill climbing that often is restricted to limited local neighborhood. In this paper we suggest a novel new two-phase metaheuristic that escapes the local minima with jumps of varying size, instead of step by step local hill climbing. The initial solution is first generated with a powerful ejection pool heuristic. The key idea of the improvement phase is to combine large neighborhood search with standard guided local search metaheuristic in a novel way, allowing improved search diversification and escape from local minima in more efficient way through jumps. The algorithm has been tested on the standard Gehring and Homberger benchmarks for the vehicle routing problem with time windows and the results indicate very competitive performance. We found 12 new and 43 matched best-known solutions and the best overall results for all problem sizes at comparable computation times.