Global Convexity in the Bi-Criteria Traveling Salesman Problem
نویسندگان
چکیده
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.
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