On local optima in multiobjective combinatorial optimization problems

Annals of Operations Research

Volumn 156, Issue 1, 2007, Pages 83-97

  Paquete, Luis ^a   Schiavinotto, Tommaso ^b   Stützle, Thomas ^c  

^a Centro de Sistemas Inteligentes   (Portugal)

^b SCUOLA NORMALE SUPERIORE   (Italy)

^c UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Local optima; Local search; Multiobjective combinatorial optimization

Indexed keywords

EID: 34548685671     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-007-0230-0     Document Type: Article

References (34)

1. Aarts, E. H. L., & Lenstra, J. K. (Eds.). (1997). Local search in combinatorial optimization. Chichester: Wiley.
2. Angel, E., Bampis, E., & Gourvés, L. (2004a). Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem. Theoretical Computer Science, 310, 135-146.
3. Angel, E., Bampis, E., & Gourvés, L. (2004b). A dynasearch neighborhood for the bicriteria traveling salesman problem. In X. Gandibleux, M. Sevaux, K. Sörensen & V. T'kindt (Eds.), Lecture notes in economics and mathematical systems : Vol. 535. Metaheuristics for multiobjective optimisation (pp. 153-176). Berlin: Springer.
4. Deb, K. (1999). Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evolutionary Computation, 7(3), 205-230.
5. Ehrgott, M. (2000). Lecture notes in economics and mathematical systems: Vol. 491. Multicriteria optimization. Heidelberg: Springer.
6. Ehrgott, M., & Gandibleux, X. (2004). Approximative solution methods for combinatorial multicriteria optimization. TOP, 12(1), 1-90.
7. Emelichev, V., & Perepelitsa, V. (1991). Complexity of vector optimization problems on graphs. Optimization, 6, 903-918.
8. Emelichev, V., & Perepelitsa, V. (1992). On the cardinality of the set of alternatives in discrete many-criterion problems. Discrete Mathematics and Applications, 2(5), 461-471.
9. Erlebach, T., Kellerer, H., & Pferschy, U. (2002). Approximating multiobjective knapsack problems. Management Science, 48(12), 1603-1612.
10. Fonseca, C., Fleming, P., Zitzler, E., Deb, K., & Thiele, L. (Eds.). (2003). Lecture notes in computer science: Vol. 2632. Evolutionary multi-criterion optimization (EMO 2003). Berlin: Springer.
11. Hamacher, H., & Ruhe, G. (1994). On spanning tree problems with multiple objectives. Annals of Operations Research, 5, 209-230.
12. Hansen, M., & Jaszkiewicz, A. (1998). Evaluating the quality of approximations to the non-dominated set (Technical report IMM-REP-1998-7). Institute of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark.
13. Hansen, P. (1979). Bicriterion path problems. In Lecture notes in economics and mathematical systems : Vol. 177. Multiple criteria decision making theory and application (pp. 109-127). Berlin: Springer.
14. Hansen, P., & Mladenović, N. (2002). Variable neighborhood search. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics (pp. 145-184). Norwell: Kluwer Academic.
15. Hoos, H. H., & Stützle, T. (2004). Stochastic local search-foundations and applications. San Francisco: Morgan Kaufmann.
16. Jörnsten, K., Andersen, K., & Lind, M. (1996). On bicriterion minimal spanning trees: an approximation. Computers & Operations Research, 23(12), 1171-1182.
17. Knowles, J., & Corne, D. (1999). The Pareto archived evolution strategy: a new base line algorithm for multiobjective optimisation. In Proceedings of the 1999 congress on evolutionary computation (CEC'99) (pp. 98-105). Washington.
18. Knowles, J., & Corne, D. (2000). Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation, 8(2), 149-172.
19. Knowles, J., & Corne, D. (2004). Bounded Pareto archiving: theory and practice. In X. Gandibleux, M. Sevaux, K. Sörensen & V. T'kindt (Eds.), Lecture notes in economics and mathematical systems : Vol. 535. Metaheuristics for multiobjective optimisation (pp. 39-64). Berlin: Springer.
20. Kung, H., Luccio, F., & Preparata, F. (1975). On finding the maxima of a set of vectors. Journal of the Association for Computing Machinery, 22(4), 469-476.
21. Laumanns, M., Thiele, L., Zitzler, E., Welzl, E., & Deb, K. (2002). Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem. In J. M. Guervos et al. (Eds.), Lecture notes in computer science : Vol. 2439. Proceedings of PPSN-VII (pp. 44-53). Berlin: Springer.
22. Moscato, P. (1999). Memetic algorithms: a short introduction. In D. Corne & M. Dorigo (Eds.), New ideas in optimization (pp. 219-234). London: McGraw-Hill.
23. Papadimitriou, C. H., & Yannakakis, M. (2000). On the approximability of trade-offs and optimal access of web sources. In Proceedings of the 41st annual symposium on foundations of computer science (FOCS 2000) (pp. 86-92).
24. Paquete, L., Chiarandini, M., & Stützle, T. (2002). A study of local optima in the multiobjective traveling salesman problem (Technical report AIDA-02-07). Fachgebiet Intellektik, Fachbereich Informatik, Technische Universität Darmstadt. Presented at the multiobjective metaheuristics workshop (MOMH 2002), Paris, 4-5 November 2002.
25. Paquete, L., Chiarandini, M., & Stützle, T. (2004). Pareto local optimum sets in the biobjective traveling salesman problem: an experimental study. In X. Gandibleux, M. Sevaux K. Sörensen & V. T'kindt (Eds.), Lecture notes in economics and mathematical systems : Vol. 535. Metaheuristics for multiobjective optimisation (pp. 177-200). Berlin: Springer.
26. Paquete, L., & Stützle, T. (2003). A two-phase local search for the biobjective traveling salesman problem. In C. Fonseca, P. Fleming, E. Zitzler, K. Deb & L. Thiele (Eds.), Lecture notes in computer science : Vol. 2632. Evolutionary multi-criterion optimization (EMO 2003) (pp. 479-493). New York: Springer.
27. Paquete, L., & Stützle, T. (2006). A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices. European Journal of Operational Research, 169(3), 943-959.
28. Ruhe, G., & Fruhwirth, B. (1990). ε-optimality for bicriteria programs and its application to minimum cost flows. Computing, 44(1), 21-34.
29. Schott, J. R. (1995). Fault tolerant design using single and multicriteria genetic algorithm optimization. Master's thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA.
30. Serafini, P. (1986). Some considerations about computational complexity for multiobjective combinatorial problems. In Lecture notes in economics and mathematical systems : Vol. 294. Recent advances and historical development of vector optimization (pp. 222-231). Berlin: Springer.
31. Talbi, E. G. (2003). A hybrid evolutionary approach for multicriteria optimization problems: application to the flow shop. In C. Fonseca, P. Fleming, E. Zitzler K. Deb & L. Thiele (Eds.), Lecture notes in computer science : Vol. 2632. Evolutionary multi-criterion optimization (EMO 2003) (pp. 416-428). Berlin: Springer.
32. Warburton, A. (1987). Approximation of Pareto optima in multi-objective shortest-path problems. Operations Research, 35(1), 70-79.
33. Zitzler, E., Deb, K., Thiele, L., Coello, C. A., & Corne, D. (Eds.). (2001). In Lecture notes in computer science: Vol. 1993. Evolutionary multi-criterion optimization (EMO 2001). Berlin: Springer.
34. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C. M., & Fonseca, V. G. (2003). Performance assessment of multiobjective optimizers: an analysis and review. IEEE Transactions on Evolutionary Computation, 7(2), 117-132.