Phased Genetic Programming for Application to the Traveling Salesman Problem

Abstract

The Traveling Salesman Problem (TSP) is a difficult permutation-based optimisation problem typically solved using heuristics or meta-heuristics which search the solution problem space. An alternative is to find sets of manipulations to a solution which lead to optimality. Hyper-heuristics search this space applying heuristics sequentially, similar to a program. Genetic Programming (GP) evolves programs typically for classification or regression problems. This paper hypothesizes that GP can be used to evolve heuristic programs to directly solve the TSP. However, evolving a full program to solve the TSP is likely difficult due to required length and complexity. Consequently, a phased GP method is proposed whereby after a phase of generations the best program is saved and executed. The subsequent generation phase restarts operating on this saved program output. A full program is evolved piecemeal. Experiments demonstrate that whilst pure GP cannot solve TSP instances when using simple operators, Phased-GP can obtain solutions within 4% of optimal for TSPs of several hundred cities. Moreover, Phased-GP operates up to nine times faster than pure GP.