Developing a guaranteed-accuracy heuristic learning algorithm for travelling salesman problems

This research investigates the feasibility of applying a guaranteed-accuracy heuristic learning algorithm to address the traveling salesman problem. The research focuses on tour construction. The advantage of tour construction heuristic is its simplicity in concept. However, tour construction heuristic often results in a sub-optimal solution and the tour often needs to be improved after it is built by changing the tour configuration until a better solution is found. This paper will describe the application of a real time admissible heuristic learning algorithm that allows the tour configuration to change as the tour is built. A learning threshold approach will also be introduced to allow solution with known quality to be found. 1. Introduction In traveling salesman problem (TSP), a salesman is to complete a tour of a number of cities by visiting each city exactly once, and the tour must begin and end with the same city so that the total distance travelled is minimum. There are many industrial optimisation problems that can be formulated as TSP. Examples of such applications include transportation and logistics applications, scheduling and timetabling problems. TSP is inherently intractable. It belongs to a group of problems known as NP -complete in which no efficient algorithm could be constructed to find optimal solution in polynomial time (Garey and Johnson, 1979). The computation time required to solve the n-city TSP using an exhaustive enumerative approach becomes increasingly high as the size of the problem increases. The commonly used approach to solve TSP is the composite approach (Lawler et. al, 1985). In the composite approach, the tour is first constructed using tour construction heuristic and then tour improvement heuristic is applied to obtain a shorter tour. The main feature of tour improvement heuristics is its ability to change tour configuration using the edge-exchange process so that a shorter tour is found. However, in tour construction heuristics, where the tour is built from scratch and the city is added one at a time until a complete tour is found, part of the tour that is already built remains unchanged throughout the tour construction process and no attempt is made to change or undo part of the tour that has been built. Reinelt (1994) points out that in gen eral, constructing a tour using only tour construction heuristics alone will not lead to optimal solution. It often needs to be improved using tour improvement heuristics such as 2 -opt or 3 -opt heuristics, which made improvement to the tour by exchanging edges until a shorter tour is found. In addition, tour construction heuristic often relies on local knowledge to construct a tour. The selection and insertion criteria in various tour construction heuristics often rely on local distance information to deter mine which city is to be selected and added to the tour. This research is based on the following rationale: “If the tour configuration of the partially completed tour can be changed during the tour construction process, similar to the approach of tour improvement heuristics, then it is more likely to lead to optimal solution. This way