Speed-up techniques for solving large-scale biobjective TSP

In this paper, we present the Two-Phase Pareto Local Search (2PPLS) method with speed-up techniques for the heuristic resolution of the biobjective traveling salesman problem. The 2PPLS method is a state-of-the-art method for this problem. However, because of its running time that strongly grows with the instances size, the method can be hardly applied to instances with more than 200 cities. We thus adapt some speed-up techniques used in single-objective optimization to the biobjective case. The proposed method is able to solve instances with up to 1000 cities in a reasonable time with no, or very small, reduction of the quality of the generated approximations.

[1]  Piotr Czyzżak,et al.  Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization , 1998 .

[2]  Jon Jouis Bentley,et al.  Fast Algorithms for Geometric Traveling Salesman Problems , 1992, INFORMS J. Comput..

[3]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[4]  Xavier Gandibleux,et al.  Metaheuristics for Multiobjective Optimisation , 2004, Lecture Notes in Economics and Mathematical Systems.

[5]  Evripidis Bampis,et al.  A Dynasearch Neighborhood for the Bicriteria Traveling Salesman Problem , 2004, Metaheuristics for Multiobjective Optimisation.

[6]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[7]  Thibaut Lust,et al.  Two Phase Stochastic Local Search Algorithms for the Biobjective Traveling Salesman Problem , 2007 .

[8]  Forschungsinstitut für Diskrete.  Chained Lin-Kernighan for Large Traveling Salesman Problems , 2003 .

[9]  Andrzej Jaszkiewicz,et al.  On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment , 2002, IEEE Trans. Evol. Comput..

[10]  Pierre Hansen,et al.  First vs. best improvement: An empirical study , 1999, Discret. Appl. Math..

[11]  Thomas Stützle,et al.  Pareto Local Optimum Sets in the Biobjective Traveling Salesman Problem: An Experimental Study , 2004, Metaheuristics for Multiobjective Optimisation.

[12]  E. L. Ulungu,et al.  MOSA method: a tool for solving multiobjective combinatorial optimization problems , 1999 .

[13]  Pierre Hansen,et al.  Bicriterion Path Problems , 1980 .

[14]  Matthias Ehrgott,et al.  Bound sets for biobjective combinatorial optimization problems , 2007, Comput. Oper. Res..

[15]  Y. Aneja,et al.  BICRITERIA TRANSPORTATION PROBLEM , 1979 .

[16]  Jacques Teghem,et al.  Two-phase Pareto local search for the biobjective traveling salesman problem , 2010, J. Heuristics.

[17]  Matthias Ehrgott,et al.  Multicriteria Optimization , 2005 .

[18]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[19]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[20]  Thomas Stützle,et al.  A Two-Phase Local Search for the Biobjective Traveling Salesman Problem , 2003, EMO.

[21]  J. K. Lenstra,et al.  Local Search in Combinatorial Optimisation. , 1997 .

[22]  Marco Laumanns,et al.  Why Quality Assessment Of Multiobjective Optimizers Is Difficult , 2002, GECCO.

[23]  Matthieu Basseur.  Design of cooperative algorithms for multi-objective optimization: application to the flow-shop scheduling problem , 2006, 4OR.

[24]  Gerald S. Rogers,et al.  Mathematical Statistics: A Decision Theoretic Approach , 1967 .

[25]  David S. Johnson,et al.  8. The traveling salesman problem: a case study , 2003 .

[26]  Anthony Przybylski,et al.  The Biobjective Assignment Problem , 2006 .