Tabu Search on the Geometric Traveling Salesman Problem

Abstract

I Abstract The Traveling Salesman Problem (TSP) is probably the most well-known problem of its genre: Combinatorial Optimization. New heuristics, built on the concept of local search, i.e. continuously to make transitions from one solution to another in the search for better solutions have shown to be successful, especially for medium-to large-scale problems (+1000 cities). This thesis presents a new classiication of TSP-transitions and evaluates a new tabu search implementation for the geometric TSP. The use of complex TSP transitions in a tabu search context is investigated; among these transitions are the classical Lin-Kernighan transition and a new transition, called the Flower transition. The neighbour-hood of the complex transitions is reduced strategically by using computational geometry forming a so-called variable candidate set of neighbouring solutions; the average quality of candidate set solutions is controlled by parameter. A new diversiication method based on a notion of solution-distance is used. The experimental achievements are comparable to the best published results in the literature.