Breakout local search for the traveling salesman problem with job-times

The traveling salesman problem with job-times combines two classic NP-hard combinatorial optimization problems: the traveling salesman problem and the scheduling problem. In this problem, a traveler visits sequentially n locations with given travel-times between locations and assigns, to each visited location, one of n jobs with location-dependent job-times. When a job is assigned to a specific location, the job starts to run at that location for its given duration. The goal of the problem is to find a job assignment to minimize the maximum completion time of the n jobs. This work presents an effective heuristic algorithm for the problem based on the breakout local search method. The algorithm employs a local search procedure to find high-quality local optimal solutions and a dedicated perturbation procedure to escape local optimum traps. The local search procedure is based on the 2-opt and j-swap moves adapted to the problem, while the perturbation procedure combines both informed and random 2-opt and j-swap operations. To speed up the search, we introduce a dedicated strategy to identify promising neighboring solutions. We evaluate the algorithm on the 310 benchmark instances in the literature. Computational results show that the proposed algorithm outperforms the previous methods, by reporting improved best results (new upper bounds) for 291 instances and equal best results for 16 other instances. The main search components of the algorithm are investigated to shed light on their contributions to the performance of the algorithm.