The Traveling Salesman Problem (TSP) is an important combinatorial optimization problem tackled by many researchers. A variety of existing algorithms aim at optimal or near optimal solutions to specific TSP instances. Nevertheless, as the number of cities increases, TSP becomes an NP hard problem. This research puts forward a novel approach to the TSP that employs sequences of Natural Computing Heuristics (NCH). NCHs describe a set of techniques that mimic aspects of nature as an approach to solving otherwise computationally-intractable problems. In particular, this research has applied the following five NCHs: simulated annealing (SA), genetic algorithm (GA), ant colony optimization (ACO), hill climbing (HC), and inver-over evolutionary algorithm (EA). Sequences are mapped to permutations of the heuristics, and those investigated consist of one, two, or three-heuristic combinations. The hypothesis of this research is that by investigating sequences of NCHs, one can viably predict heuristic combinations that can solve realistic TSP instances. The focus of this research is twofold: (1) to investigate the feasibility of multi-heuristic sequences as sufficient heuristics to TSP, and (2) to determine if patterns and behaviors can be extracted from the sequence experiments. Specifically, the patterns and behaviors of this investigation included percent optimality, elapsed time, city count, iterations, algorithmic scope, and city data layout. In addition, this research leveraged and expanded on insights of the Krink-Lovberg Life Cycle Model, an earlier study that used sequences of algorithms.
The TSP instances investigated include previously studied problems of number-of-cities varying from a small number up to 101, 159, 280, 439, 575, and 1002 cities. The research encompassed three experiments with increasing complexity: each of the five NCH by themselves on small city size problems, sequences of all 20 pairs and all 60 triplets of NCH on small city size problems, and the 10 best second-experiment sequences and some of the best known single algorithms on the larger number-of-city problems. An analysis of the results on the larger number of cities showed that sequences beginning with GA and ending with ACO performed best, and that ACO by itself also performed well.
