Exact and Heuristic Algorithms for Routing AGV on Path with Precedence Constraints

A new problem arises when an automated guided vehicle (AGV) is dispatched to visit a set of customers, which are usually located along a fixed wire transmitting signal to navigate the AGV. An optimal visiting sequence is desired with the objective of minimizing the total travelling distance (or time). When precedence constraints are restricted on customers, the problem is referred to as traveling salesman problem on path with precedence constraints (TSPP-PC). Whether or not it is NP-complete has no answer in the literature. In this paper, we design dynamic programming for the TSPP-PC, which is the first polynomial-time exact algorithm when the number of precedence constraints is a constant. For the problem with number of precedence constraints, part of the input can be arbitrarily large, so we provide an efficient heuristic based on the exact algorithm

The Convex-hull-and-k-line Travelling Salesman Problem

We present a polynomial time solution algorithm for the so-called Convex-hull-and-k-line TSP: This is a special case of the Euclidean TSP where n- 111 of the cities lie on the convex hull and m of the cities lie on k almost parallel line segments in the interior of the hull such that the carrying lines of all these segments intersect the hull in two common edges. Our result contains and generalizes three earlier results that are due to Cutler (1980)) to Rote (1992), and to Deineko, Van Dal and Rote (1994)