Augmented tour construction heuristics for the travelling salesman problem

Abstract

Tour construction heuristics serve as fundamental techniques in optimizing the routes of a traveling salesman. These heuristics remain significant as foundational methods for generating initial solutions to the Traveling Salesman Problem (TSP), facilitating subsequent applications of tour improvement heuristics. These heuristics effectively comprise the iterative application of city node selection and insertion. However, thus far, no attempts have been made to enhance the basic structure of tour construction heuristics to bring a better initial solution for the advanced heuristics. This study aims to enhance tour construction heuristics without compromising their theoretical complexity. Specifically, an iterative step of partial tour deconstruction has been introduced to the existing heuristics. This additional step has been implemented and evaluated with three highly performing tour construction heuristics: the farthest insertion heuristic, the max difference insertion heuristic, and the fast max difference insertion heuristic. The results demonstrate that augmenting these heuristics with the partial tour deconstruction step improves the best, worst, and average solutions while preserving their theoretical complexity