Global convexity in the bi-criteria Traveling Salesman problem

This work studies the solution space topology of the Traveling Salesman Problem or TSP, as a bi-objective optimization problem. The concepts of category and range of a solution are introduced for the first time in this analysis. These concepts relate each solution of a population to a Pareto set, presenting a more rigorous theoretical framework than previous works studying global convexity for the multi-objective TSP. The conjecture of a globally convex structure for the solution space of the bi-criteria TSP is confirmed with the results presented in this work. This may support successful applications using state of the art metaheuristics based on Ant Colony or Evolutionary Computation. IFIP International Conference on Artificial Intelligence in Theory and Practice - Evolutionary Computation Red de Universidades con Carreras en Informática (RedUNCI)