Restricted Dynamic Programming Heuristic for Precedence Constrained Bottleneck Generalized TSP

Abstract

We develop a restricted dynamical programming heuristic for a complicated traveling salesman problem: a) cities are grouped into clusters, resp. Generalized TSP; b) precedence constraints are imposed on the order of visiting the clusters, resp. Precedence Constrained TSP; c) the costs of moving to the next cluster and doing the required job inside one are aggregated in a minimax manner, resp. Bottleneck TSP; d) all the costs may depend on the sequence of previously visited clusters, resp. Sequence-Dependent TSP or Time Dependent TSP. Such multiplicity of constraints complicates the use of mixed integer-linear programming, while dynamic programming (DP) benefits from them; the latter may be supplemented with a branch-and-bound strategy, which necessitates a “DP-compliant” heuristic. The proposed heuristic always yields a feasible solution, which is not always the case with heuristics, and its precision may be tuned until it becomes the exact DP.