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2016 | OriginalPaper | Buchkapitel

Ant-Based System Analysis on the Traveling Salesman Problem Under Real-World Settings

verfasst von : Gloria Cerasela Crişan, Elena Nechita, Vasile Palade

Erschienen in: Combinations of Intelligent Methods and Applications

Verlag: Springer International Publishing

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Abstract

Many optimization problems have huge solution spaces, deep restrictions, highly correlated parameters, and operate with uncertain or inconsistent data. Such problems sometimes elude the usual solving methods we are familiar with, forcing us to continuously improve these methods or to even completely reconsider the solving methodologies. When decision makers need faster and better results to more difficult problems, the quality of a decision support system is crucial. To estimate the quality of a decision support system when approaching difficult problems is not easy, but is very important when designing and conducting vital industrial processes or logistic operations. This paper studies the resilience of a solving method, initially designed for the static and deterministic TSP (Traveling Salesman Problem) variant, when applied to an uncertain and dynamic TSP version. This investigation shows how a supplementary level of complexity can be successfully handled. The traditional ant-based system under investigation is infused with a technique which allows the evaluation of its performances when uncertain input data are present. Like the real ant colonies do, the system rapidly adapts to repeated environmental changes. A comparison with the performance of another heuristic optimization method is also done.

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Literatur
4.
Zurück zum Zitat Soyster, A.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21, 1154–1157 (1973)CrossRefMathSciNetMATH Soyster, A.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21, 1154–1157 (1973)CrossRefMathSciNetMATH
5.
Zurück zum Zitat Gould, F.J.: Proximate linear programming: an experimental study of a modified simplex algorithm for solving programs with inexact data, University of North Carolina at Chapel Hill, Institute of Statistics Mimeo Series No. 789 (1971) Gould, F.J.: Proximate linear programming: an experimental study of a modified simplex algorithm for solving programs with inexact data, University of North Carolina at Chapel Hill, Institute of Statistics Mimeo Series No. 789 (1971)
6.
Zurück zum Zitat Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Program. 88, 411–424 (2000)CrossRefMathSciNetMATH Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Program. 88, 411–424 (2000)CrossRefMathSciNetMATH
8.
Zurück zum Zitat El-Ghaoui, L., Lebret, H.: Robust solutions to least-square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl. 18, 1035–1064 (1997)CrossRefMathSciNetMATH El-Ghaoui, L., Lebret, H.: Robust solutions to least-square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl. 18, 1035–1064 (1997)CrossRefMathSciNetMATH
9.
Zurück zum Zitat Crişan, G.C., Pintea, C.M., Chira, C.: Risk assessment for incoherent data. Environ. Eng. Manag. J. 11(12), 2169–2174 (2012) Crişan, G.C., Pintea, C.M., Chira, C.: Risk assessment for incoherent data. Environ. Eng. Manag. J. 11(12), 2169–2174 (2012)
10.
Zurück zum Zitat Crainic, T.G., Crişan, G.C., Gendreau, M., Lahrichi, N., Rei, W.: A concurrent evolutionary approach for rich combinatorial optimization. In: Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers 2017–2022 (2009) Crainic, T.G., Crişan, G.C., Gendreau, M., Lahrichi, N., Rei, W.: A concurrent evolutionary approach for rich combinatorial optimization. In: Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers 2017–2022 (2009)
11.
Zurück zum Zitat Tlili, T., Krichen, S., Faiz, S.: Simulated annealing-based decision support system for routing problems. In: 2014 IEEE International Conference on Systems, Man and Cybernetics (SMC), pp. 2954–2958 (2014) Tlili, T., Krichen, S., Faiz, S.: Simulated annealing-based decision support system for routing problems. In: 2014 IEEE International Conference on Systems, Man and Cybernetics (SMC), pp. 2954–2958 (2014)
13.
Zurück zum Zitat Applegate, D., Cook, W.J., Rohe, S.: Chained Lin-Kernighan for large traveling salesman problems. INFORMS J. Comput. 15(1), 82–92 (2003)CrossRefMathSciNetMATH Applegate, D., Cook, W.J., Rohe, S.: Chained Lin-Kernighan for large traveling salesman problems. INFORMS J. Comput. 15(1), 82–92 (2003)CrossRefMathSciNetMATH
16.
Zurück zum Zitat Cook, W.J.: In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation. Princeton University Press, Princeton (2012) Cook, W.J.: In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation. Princeton University Press, Princeton (2012)
17.
Zurück zum Zitat Dantzig, G.B., Fulkerson, R., Johnson, S.M.: Solution of a large-scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)MathSciNet Dantzig, G.B., Fulkerson, R., Johnson, S.M.: Solution of a large-scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)MathSciNet
18.
Zurück zum Zitat Laporte, G.: A short history of the traveling salesman problem. Canada Research Chair in Distribution Management,Centre for Research on Transportation (CRT) and GERAD HEC Montréal, Canada (2006) Laporte, G.: A short history of the traveling salesman problem. Canada Research Chair in Distribution Management,Centre for Research on Transportation (CRT) and GERAD HEC Montréal, Canada (2006)
19.
Zurück zum Zitat Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2011) Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2011)
20.
Zurück zum Zitat Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher J.W. (eds.) Complexity of Computer Computations. The IBM Research Symposia, pp. 85–103. Plenum. Press, New York (1972) Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher J.W. (eds.) Complexity of Computer Computations. The IBM Research Symposia, pp. 85–103. Plenum. Press, New York (1972)
21.
Zurück zum Zitat Applegate, D., Bixby, R., Chvátal, V., Cook, W.: On the solution of traveling salesman problems. Documenta Mathematica, Extra volume ICM 1998(III), 645–656 (1998) Applegate, D., Bixby, R., Chvátal, V., Cook, W.: On the solution of traveling salesman problems. Documenta Mathematica, Extra volume ICM 1998(III), 645–656 (1998)
22.
Zurück zum Zitat Sangalli, A.: Why sales reps pose a hard problem. New Sci. 24–28 (1992) Sangalli, A.: Why sales reps pose a hard problem. New Sci. 24–28 (1992)
23.
Zurück zum Zitat Moscato, P., Buriol, L., Cotta, C.: On the analysis of data derived from mitochondrial DNA distance matrices: Kolmogorov and a traveling salesman give their opinion. In: Pedal, C.D. (ed.) Advances in Nature Inspired Computation: The PPSN VII Workshops, University of Reading, pp. 37–38 (2002) Moscato, P., Buriol, L., Cotta, C.: On the analysis of data derived from mitochondrial DNA distance matrices: Kolmogorov and a traveling salesman give their opinion. In: Pedal, C.D. (ed.) Advances in Nature Inspired Computation: The PPSN VII Workshops, University of Reading, pp. 37–38 (2002)
24.
Zurück zum Zitat Climer, S., Zhang, W.: Take a walk and cluster genes: a TSP-based approach to optimal rearrangement clustering. In: 21st International Conference on Machine Learning (ICML’04), pp. 169–176, Banff, Canada (2004) Climer, S., Zhang, W.: Take a walk and cluster genes: a TSP-based approach to optimal rearrangement clustering. In: 21st International Conference on Machine Learning (ICML’04), pp. 169–176, Banff, Canada (2004)
25.
Zurück zum Zitat Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024 (1994)CrossRef Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024 (1994)CrossRef
26.
Zurück zum Zitat Adleman L.M.: Steering the future of computing. Nature 440(7083), 383 (2006) Adleman L.M.: Steering the future of computing. Nature 440(7083), 383 (2006)
27.
28.
32.
Zurück zum Zitat Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report 388, Graduate School of Industrial Administration, Carnegie Mellon University (1976) Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report 388, Graduate School of Industrial Administration, Carnegie Mellon University (1976)
33.
Zurück zum Zitat Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)CrossRefMathSciNetMATH Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)CrossRefMathSciNetMATH
34.
Zurück zum Zitat Gamboa, D., Rego, C., Glover, F.: Data structures and ejection chains for solving large scale traveling salesman problems. Eur. J. Oper. Res. 160(1), 154–171 (2005)CrossRefMATH Gamboa, D., Rego, C., Glover, F.: Data structures and ejection chains for solving large scale traveling salesman problems. Eur. J. Oper. Res. 160(1), 154–171 (2005)CrossRefMATH
35.
Zurück zum Zitat Braschi, B.: Solving the traveling salesman problem using the simulated annealing on a hypercube. In: Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers and Applications, pp. 765–768 (1989) Braschi, B.: Solving the traveling salesman problem using the simulated annealing on a hypercube. In: Proceedings of the Fourth Conference on Hypercubes, Concurrent Computers and Applications, pp. 765–768 (1989)
36.
Zurück zum Zitat Dorigo, M., Gambardella, L.M.: Ant colonies for the traveling salesman problem. Technical Report TR/IRIDIA/1996-3 Université Libre de Bruxelles (1996) Dorigo, M., Gambardella, L.M.: Ant colonies for the traveling salesman problem. Technical Report TR/IRIDIA/1996-3 Université Libre de Bruxelles (1996)
41.
Zurück zum Zitat Jaillet, P.: A priori solution of a traveling salesman problem in which a random set of the customers are visited. Oper. Res. 36(6), 929–936 (1988)CrossRefMathSciNetMATH Jaillet, P.: A priori solution of a traveling salesman problem in which a random set of the customers are visited. Oper. Res. 36(6), 929–936 (1988)CrossRefMathSciNetMATH
42.
Zurück zum Zitat Berman, O., Simchi-Levi, D.: Finding the optimal a priori tour and location of traveling salesman with nonhomogeneous customers. Transp. Sci. 22(2), 148–154 (1988)CrossRefMathSciNetMATH Berman, O., Simchi-Levi, D.: Finding the optimal a priori tour and location of traveling salesman with nonhomogeneous customers. Transp. Sci. 22(2), 148–154 (1988)CrossRefMathSciNetMATH
43.
Zurück zum Zitat Laporte, G., Louveaux, F., Mercure, H.: A priori optimization of the traveling salesman problem. Oper. Res. 42(3), 543–549 (1994)CrossRefMathSciNetMATH Laporte, G., Louveaux, F., Mercure, H.: A priori optimization of the traveling salesman problem. Oper. Res. 42(3), 543–549 (1994)CrossRefMathSciNetMATH
44.
Zurück zum Zitat Rossi, F.A., Gavioli, I.: Aspects of heuristic methods in traveling salesman problem. In: Andreatta, G., Mason, F., Serafini, P. (eds.) Advanced School on Statistics in Combinatorial Optimization, pp. 214–227. World Scientific Publication, Singapore (1987) Rossi, F.A., Gavioli, I.: Aspects of heuristic methods in traveling salesman problem. In: Andreatta, G., Mason, F., Serafini, P. (eds.) Advanced School on Statistics in Combinatorial Optimization, pp. 214–227. World Scientific Publication, Singapore (1987)
45.
Zurück zum Zitat Bianchi, L., Knowles, J., Bowler, N.: Local search for the traveling salesman problem: correction of the 2-p-opt and 1-shift algorithms. Eur. J. Oper. Res. 162(1), 206–219 (2005)CrossRefMathSciNetMATH Bianchi, L., Knowles, J., Bowler, N.: Local search for the traveling salesman problem: correction of the 2-p-opt and 1-shift algorithms. Eur. J. Oper. Res. 162(1), 206–219 (2005)CrossRefMathSciNetMATH
46.
Zurück zum Zitat Bianchi, L., Gambardella, L.M., Dorigo, M.: An ant colony optimization approach to the probabilistic traveling salesman problem. In: 7th International Conference on Parallel Problem Solving from Nature I, vol. 2439, pp. 883–892 (2002) Bianchi, L., Gambardella, L.M., Dorigo, M.: An ant colony optimization approach to the probabilistic traveling salesman problem. In: 7th International Conference on Parallel Problem Solving from Nature I, vol. 2439, pp. 883–892 (2002)
47.
Zurück zum Zitat Marinakis, Y., Marinaki, M.: A hybrid honey bees mating optimization algorithm for the probabilistic traveling salesman problem. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1762–1769 (2010) Marinakis, Y., Marinaki, M.: A hybrid honey bees mating optimization algorithm for the probabilistic traveling salesman problem. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1762–1769 (2010)
48.
Zurück zum Zitat Henchiri, A., Bellalouna, M., Khaznaji, W.: Probabilistic traveling salesman problem: a survey. In: Position papers of the 2014 Federated Conference on Computer Science and Information Systems, Annals of Computer Science and Information Systems, vol. 2, pp. 55–60 (2014) Henchiri, A., Bellalouna, M., Khaznaji, W.: Probabilistic traveling salesman problem: a survey. In: Position papers of the 2014 Federated Conference on Computer Science and Information Systems, Annals of Computer Science and Information Systems, vol. 2, pp. 55–60 (2014)
49.
Zurück zum Zitat Bianchi, L.: Ant colony optimization and local search for the probabilistic traveling salesman problem: a case study in stochastic combinatorial optimization. Ph.D. Thesis, Université Libre de Bruxelles (2006) Bianchi, L.: Ant colony optimization and local search for the probabilistic traveling salesman problem: a case study in stochastic combinatorial optimization. Ph.D. Thesis, Université Libre de Bruxelles (2006)
50.
Zurück zum Zitat Montemanni, R., Barta, J., Gambardella, L.M.: The robust traveling salesman problem with interval data, Technical Report IDSIA 20–05 (2005) Montemanni, R., Barta, J., Gambardella, L.M.: The robust traveling salesman problem with interval data, Technical Report IDSIA 20–05 (2005)
51.
Zurück zum Zitat Crişan, G.C., Nechita, E.: Solving fuzzy TSP with Ant algorithms. Int. J. Comput., Commun. Control III, suppl. issue, 228–231 (2008) Crişan, G.C., Nechita, E.: Solving fuzzy TSP with Ant algorithms. Int. J. Comput., Commun. Control III, suppl. issue, 228–231 (2008)
52.
Zurück zum Zitat Toriello, A., Haskell, W.B., Poremba, M.: A dynamic traveling salesman problem with stochastic arc costs. Oper. Res. 62, 1107–1125 (2014)CrossRefMathSciNet Toriello, A., Haskell, W.B., Poremba, M.: A dynamic traveling salesman problem with stochastic arc costs. Oper. Res. 62, 1107–1125 (2014)CrossRefMathSciNet
53.
54.
Zurück zum Zitat de Farias, D.P., van Roy, B.: The linear programming approach to approximate dynamic programming. Oper. Res. 51, 850–865 (2003)CrossRefMathSciNetMATH de Farias, D.P., van Roy, B.: The linear programming approach to approximate dynamic programming. Oper. Res. 51, 850–865 (2003)CrossRefMathSciNetMATH
56.
Zurück zum Zitat Secomandi, N.: Analysis of a rollout approach to sequencing problems with stochastic routing applications. J. Heuristics 9, 321–352 (2003)CrossRefMATH Secomandi, N.: Analysis of a rollout approach to sequencing problems with stochastic routing applications. J. Heuristics 9, 321–352 (2003)CrossRefMATH
57.
Zurück zum Zitat Cheong, T., White, C.C.: Dynamic traveling salesman problem: value of real-time traffic information. IEEE Trans. Intell. Transp. Syst. 13, 619–630 (2012)CrossRef Cheong, T., White, C.C.: Dynamic traveling salesman problem: value of real-time traffic information. IEEE Trans. Intell. Transp. Syst. 13, 619–630 (2012)CrossRef
58.
Zurück zum Zitat Buhmann, J.M., Mihalák, M., Šrámek, R., Widmayer, P.: Robust optimization in the presence of uncertainty. In: Proceedings of the 4th conference on Innovations in Theoretical Computer Science (ITCS ’13), pp. 505–514. ACM, New York, USA (2013) Buhmann, J.M., Mihalák, M., Šrámek, R., Widmayer, P.: Robust optimization in the presence of uncertainty. In: Proceedings of the 4th conference on Innovations in Theoretical Computer Science (ITCS ’13), pp. 505–514. ACM, New York, USA (2013)
59.
Zurück zum Zitat Jaillet, P., Lu, X.: Online traveling salesman problems with service flexibility. Networks 58, 137–146 (2011)MathSciNetMATH Jaillet, P., Lu, X.: Online traveling salesman problems with service flexibility. Networks 58, 137–146 (2011)MathSciNetMATH
60.
Zurück zum Zitat Jaillet, P., Wagner, M.R.: Online vehicle routing problems: a survey. In: Golden, B.L., Raghavan, S., Wasil, E.A. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges. Springer (2008) Jaillet, P., Wagner, M.R.: Online vehicle routing problems: a survey. In: Golden, B.L., Raghavan, S., Wasil, E.A. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges. Springer (2008)
62.
Zurück zum Zitat Schultz, T.R.: In search of Ant ancestors. Proc. Nat. Acad. Sci. 97(26), 14028–14029 (2000) Schultz, T.R.: In search of Ant ancestors. Proc. Nat. Acad. Sci. 97(26), 14028–14029 (2000)
63.
Zurück zum Zitat Wilson, E.O., Hölldobler, B.: Eusociality: origin and consequences. Proc. Nat. Acad. Sci. 102(38), 13367–13371 (2005)CrossRef Wilson, E.O., Hölldobler, B.: Eusociality: origin and consequences. Proc. Nat. Acad. Sci. 102(38), 13367–13371 (2005)CrossRef
64.
65.
Zurück zum Zitat Pintea, C.M.: Advances in Bio-inspired Computing for Combinatorial Optimization Problems. Springer (2014) Pintea, C.M.: Advances in Bio-inspired Computing for Combinatorial Optimization Problems. Springer (2014)
66.
Zurück zum Zitat Crişan, G.C., Pintea, C.M., Pop, P.: On the resilience of an ant-based system in fuzzy environments. An empirical study. In: Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, Beijing, China, pp. 2588–2593 (2014) Crişan, G.C., Pintea, C.M., Pop, P.: On the resilience of an ant-based system in fuzzy environments. An empirical study. In: Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, Beijing, China, pp. 2588–2593 (2014)
67.
Zurück zum Zitat Nechita, E.: On the Approaches of Classical AI and Embodied AI. Scientific Studies and Research, Series Mathematics and Informatics, vol. 21(1), pp. 175–178 (2011) Nechita, E.: On the Approaches of Classical AI and Embodied AI. Scientific Studies and Research, Series Mathematics and Informatics, vol. 21(1), pp. 175–178 (2011)
68.
Zurück zum Zitat Nechita, E.: Simulation of Discrete Events Systems (in Romanian). Tehnopress Publishing House, Iaşi (2005) Nechita, E.: Simulation of Discrete Events Systems (in Romanian). Tehnopress Publishing House, Iaşi (2005)
69.
Zurück zum Zitat Glover, F., Laguna M.: Tabu Search, Kluwer Academic Publishers (1997) Glover, F., Laguna M.: Tabu Search, Kluwer Academic Publishers (1997)
70.
71.
Zurück zum Zitat Černý, V.: Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J. Optim. Theory Appl. 45, 41–51 (1985)CrossRefMathSciNetMATH Černý, V.: Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J. Optim. Theory Appl. 45, 41–51 (1985)CrossRefMathSciNetMATH
72.
Zurück zum Zitat Birattari, M., Dorigo, M.: How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs? Optim. Lett. 1(3), 309–311 (2007)CrossRefMathSciNetMATH Birattari, M., Dorigo, M.: How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs? Optim. Lett. 1(3), 309–311 (2007)CrossRefMathSciNetMATH
73.
Zurück zum Zitat Crişan, G.C.: Ant algorithms in artificial intelligence. Ph.D. Thesis, A.I. Cuza University of Iaşi, Romania (2008) Crişan, G.C.: Ant algorithms in artificial intelligence. Ph.D. Thesis, A.I. Cuza University of Iaşi, Romania (2008)
74.
Zurück zum Zitat Jin, Y.: A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput. 9(1), 3–12 (2005)CrossRef Jin, Y.: A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput. 9(1), 3–12 (2005)CrossRef
75.
Zurück zum Zitat Hertz, A., Widmer, M.: Guidelines for the use of meta-heuristics in combinatorial optimization. Eur. J. Oper. Res. 151, 247–252 (2003)CrossRefMathSciNetMATH Hertz, A., Widmer, M.: Guidelines for the use of meta-heuristics in combinatorial optimization. Eur. J. Oper. Res. 151, 247–252 (2003)CrossRefMathSciNetMATH
76.
Zurück zum Zitat Matthews, D.C., Sutton, A.M., Hains, D., Whitley, L.D.: Improved Robustness through Population Variance in Ant Colony Optimization, Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics, Lecture Notes in Computer Science, vol. 5752, pp. 145–149 (2009) Matthews, D.C., Sutton, A.M., Hains, D., Whitley, L.D.: Improved Robustness through Population Variance in Ant Colony Optimization, Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics, Lecture Notes in Computer Science, vol. 5752, pp. 145–149 (2009)
Metadaten
Titel
Ant-Based System Analysis on the Traveling Salesman Problem Under Real-World Settings
verfasst von
Gloria Cerasela Crişan
Elena Nechita
Vasile Palade
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-26860-6_3