Solving permutational routing problems by population-based metaheuristics

In this paper we consider two routing problems: traveling salesman problem (TSP, fundamental problem of the combinatorial optimization) and the TSP with times of traveling, times of processing and due dates where the objective is to minimize the total weighted tardiness (TSPTWT). Since problems are NP-hard in the strong sense, we propose a metaheuristic algorithm to determine a good suboptimal solution. We present an algorithm based on the idea of researching and analyzing local optima. TSP with times of traveling, times of processing and due dates, and with the total weighted tardiness cost function is identical with the single machine total weighted tardiness problem with sequence-dependent setup times. It was possible to find the new best known solutions for 81 of 120 benchmark instances of this scheduling problem using the method proposed here.