Abstract
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.
Highlights
A traveling salesman problem on path (TSPP for short) arises in dispatching an automated guided vehicle (AGV) to visit a set of locations along the wire which transmits signal to navigate the AGV
Arbitrarily large, so we provide an efficient heuristic based on the exact algorithm
The exact algorithm is based on dynamic programming, which takes into consideration the last vertices in all precedence constraints visited by the salesman rather than all the vertices visited
Summary
A traveling salesman problem on path (TSPP for short) arises in dispatching an automated guided vehicle (AGV) to visit a set of locations along the wire which transmits signal to navigate the AGV. In this example, the AGV is travelling along the wire (in grey) to shuttle materials between the two conveyors to the four workstations. 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. The exact algorithm is based on dynamic programming, which takes into consideration the last vertices in all precedence constraints visited by the salesman rather than all the vertices visited. The dynamic programming for TSPP-PC is provided, and the dynamic programming can be proved to be the first polynomial-time exact algorithm for TSPP-PC with number of precedence constraints being a constant.
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