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2014 | OriginalPaper | Buchkapitel

10. An Evolutionary Algorithm with Path Relinking for a Bi-objective Multiple Traveling Salesman Problem with Profits

verfasst von : N. Labadie, J. Melechovsky, C. Prins

Erschienen in: Applications of Multi-Criteria and Game Theory Approaches

Verlag: Springer London

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Abstract

This chapter deals with a bi-objective multiple traveling salesman problem with profits (BOMTSPP), generalizing the classical TSP with profits (TSPP). The TSPP is in fact a generic name for TSP problems taking into account the length of the tour and profits collected at customers. However, all these problems are not really bi-objective: the two criteria are aggregated into a single objective or one of them is replaced by a constraint. Our BOMTSPP aims at building m cycles covering a subset of potential customers so that the total collected profit is maximized and the overall traveling distance is minimized. This new problem generalizes the TSPP in two directions: a true bi-objective treatment and the construction of multiple tours. The proposed solution method is an effective evolutionary algorithm, reinforced by a post-optimization procedure based on path-relinking (PR).

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Literatur
Zurück zum Zitat Archetti C, Hertz A, Speranza MG (2007) Metaheuristics for the team orienteering problem. J Heur 13(1):49–76CrossRef Archetti C, Hertz A, Speranza MG (2007) Metaheuristics for the team orienteering problem. J Heur 13(1):49–76CrossRef
Zurück zum Zitat Basseur M, Seynhaeve F, Talbi EG (2005) Path relinking in pareto multi-objective genetic algorithms. In: Coello Coello CA, Hernndez Aguirre A, Zitzler E (eds) Evolutionary multi-criterion optimization. Thrid international conference, EMO 2005. Lecture notes in computer science, vol 3410. Springer Mexico, Guanajuato, pp 120–134. Basseur M, Seynhaeve F, Talbi EG (2005) Path relinking in pareto multi-objective genetic algorithms. In: Coello Coello CA, Hernndez Aguirre A, Zitzler E (eds) Evolutionary multi-criterion optimization. Thrid international conference, EMO 2005. Lecture notes in computer science, vol 3410. Springer Mexico, Guanajuato, pp 120–134.
Zurück zum Zitat Beausoleil R, Baldoquin G, Montejo R (2008) Multi-start and path relinking methods to deal with multi-objective knapsack problems. Ann Oper Res 157:105–133MathSciNetCrossRefMATH Beausoleil R, Baldoquin G, Montejo R (2008) Multi-start and path relinking methods to deal with multi-objective knapsack problems. Ann Oper Res 157:105–133MathSciNetCrossRefMATH
Zurück zum Zitat Bérubé JF, Gendreau M, Potvin JY (2009a) An exact \( \varepsilon \)-constraint method for bi-objective combinatorial optimization problems: application to the traveling salesman problem with profits. Eur J Oper Res 194(1):39–50 Bérubé JF, Gendreau M, Potvin JY (2009a) An exact \( \varepsilon \)-constraint method for bi-objective combinatorial optimization problems: application to the traveling salesman problem with profits. Eur J Oper Res 194(1):39–50
Zurück zum Zitat Bérubé JF, Gendreau M, Potvin JY (2009b) A branch-and-cut algorithm for the undirected prize collecting traveling salesman problem. Networks 54:56–67MathSciNetCrossRefMATH Bérubé JF, Gendreau M, Potvin JY (2009b) A branch-and-cut algorithm for the undirected prize collecting traveling salesman problem. Networks 54:56–67MathSciNetCrossRefMATH
Zurück zum Zitat Bouly H, Dang DC, Moukrim A (2010) A memetic algorithm for the team orienteering problem. 4OR: Q J Oper Res 8(1):49–70CrossRefMATH Bouly H, Dang DC, Moukrim A (2010) A memetic algorithm for the team orienteering problem. 4OR: Q J Oper Res 8(1):49–70CrossRefMATH
Zurück zum Zitat Chao IM, Golden BL, Wasil EA (1996) The team orienteering problem. Eur J Oper Res 88(3):464–474CrossRefMATH Chao IM, Golden BL, Wasil EA (1996) The team orienteering problem. Eur J Oper Res 88(3):464–474CrossRefMATH
Zurück zum Zitat Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evo Comput 6(2):182–197CrossRef Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evo Comput 6(2):182–197CrossRef
Zurück zum Zitat Feillet D, Dejax P, Gendreau M (2005) Traveling salesman problems with profits. Transp Sci 39(2):188–205CrossRef Feillet D, Dejax P, Gendreau M (2005) Traveling salesman problems with profits. Transp Sci 39(2):188–205CrossRef
Zurück zum Zitat Glover F, Laguna M, Marti R (2000) Fundamentals of scatter search and path relinking. Cont Cyber 39:653–684MathSciNet Glover F, Laguna M, Marti R (2000) Fundamentals of scatter search and path relinking. Cont Cyber 39:653–684MathSciNet
Zurück zum Zitat Jaszkiewicz A, Zielniewicz P (2009) Pareto memetic algorithm with path relinking for bi-objective traveling salesperson problem. Eur J Oper Res 193(3):885–890MathSciNetCrossRefMATH Jaszkiewicz A, Zielniewicz P (2009) Pareto memetic algorithm with path relinking for bi-objective traveling salesperson problem. Eur J Oper Res 193(3):885–890MathSciNetCrossRefMATH
Zurück zum Zitat Jozefowiez N, Glover F, Laguna M (2008) Multi-objective meta-heuristics for the traveling salesman problem with profits. J Math Mod Alg 7(2):177–195MathSciNetCrossRefMATH Jozefowiez N, Glover F, Laguna M (2008) Multi-objective meta-heuristics for the traveling salesman problem with profits. J Math Mod Alg 7(2):177–195MathSciNetCrossRefMATH
Zurück zum Zitat Ke L, Archetti C, Feng Z (2008) Ants can solve the team orienteering problem. Comput Ind Eng 54(3):648–665CrossRef Ke L, Archetti C, Feng Z (2008) Ants can solve the team orienteering problem. Comput Ind Eng 54(3):648–665CrossRef
Zurück zum Zitat Keller CP, Goodchild M (1988) The multi-objective vending problem: a generalization of the travelling salesman problem. Environ Plan B: Plan Des 15:447–460CrossRef Keller CP, Goodchild M (1988) The multi-objective vending problem: a generalization of the travelling salesman problem. Environ Plan B: Plan Des 15:447–460CrossRef
Zurück zum Zitat Konak A, Coit DW, Smith AE (2006) Multi-objective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91(9):992–1007CrossRef Konak A, Coit DW, Smith AE (2006) Multi-objective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91(9):992–1007CrossRef
Zurück zum Zitat Labadi N, Prins C, Reghioui M (2008) Grasp with path relinking for the capacitated arc routing problem with time windows. In Fink A and Rothlauf F (eds) Advances in computational intelligence in transport, logistics, and supply chain management. Studies in computational intelligence, vol 144. Springer, Berlin, pp 111–135 Labadi N, Prins C, Reghioui M (2008) Grasp with path relinking for the capacitated arc routing problem with time windows. In Fink A and Rothlauf F (eds) Advances in computational intelligence in transport, logistics, and supply chain management. Studies in computational intelligence, vol 144. Springer, Berlin, pp 111–135
Zurück zum Zitat Labadie N, Melechovsky J, Wolfler Calvo R (2010) An effective hybrid evolutionary local search for orienteering and team orienteering problem with time windows. In: Schaefer R et al (eds) Lecture Notes in Computer Science, vol 6239. Springer Berlin, Heidelberg, pp 219–228 Labadie N, Melechovsky J, Wolfler Calvo R (2010) An effective hybrid evolutionary local search for orienteering and team orienteering problem with time windows. In: Schaefer R et al (eds) Lecture Notes in Computer Science, vol 6239. Springer Berlin, Heidelberg, pp 219–228
Zurück zum Zitat Labadie N, Melechovsky J, Wolfler Calvo R (2011) Hybridized evolutionary local search algorithm for the team orienteering problem with time windows. J Heur 17(6):729–753CrossRefMATH Labadie N, Melechovsky J, Wolfler Calvo R (2011) Hybridized evolutionary local search algorithm for the team orienteering problem with time windows. J Heur 17(6):729–753CrossRefMATH
Zurück zum Zitat Labadie N, Mansini R, Melechovský J, Wolfler-Calvo R (2012) The team orienteering problem with time windows: an LP-based granular variable neighborhood search. Eur J Oper Res 220(1):15–27CrossRefMATH Labadie N, Mansini R, Melechovský J, Wolfler-Calvo R (2012) The team orienteering problem with time windows: an LP-based granular variable neighborhood search. Eur J Oper Res 220(1):15–27CrossRefMATH
Zurück zum Zitat Martí R, Laguna M, Campos V (2005) Scatter search vs. genetic algorithms. In: Ramesh Sharda, Stefan Vo, Csar Rego, Bahram Alidaee, Ramesh Sharda, and Stefan Voss (eds) Metaheuristic optimization via memory and evolution. Operations Research/Computer Science Interfaces Series, vol 30. Springer, New York, pp 263–282 Martí R, Laguna M, Campos V (2005) Scatter search vs. genetic algorithms. In: Ramesh Sharda, Stefan Vo, Csar Rego, Bahram Alidaee, Ramesh Sharda, and Stefan Voss (eds) Metaheuristic optimization via memory and evolution. Operations Research/Computer Science Interfaces Series, vol 30. Springer, New York, pp 263–282
Zurück zum Zitat Martí R, Campos V, Resende MGC, Duarte A (2011) Multi-objective grasp with path-relinking. Technical report, AT and T Labs Research Martí R, Campos V, Resende MGC, Duarte A (2011) Multi-objective grasp with path-relinking. Technical report, AT and T Labs Research
Zurück zum Zitat Montemanni R, Gambardella LM (2009) An ant colony system for team orienteering problem with time windows. Found Comput Dec Sci 34(4):287–306 Montemanni R, Gambardella LM (2009) An ant colony system for team orienteering problem with time windows. Found Comput Dec Sci 34(4):287–306
Zurück zum Zitat Prins C (2004) A simple and effective evolutionary algorithm for the vehicle routing problem. Comput Oper Res 31(12):1985–2002MathSciNetCrossRefMATH Prins C (2004) A simple and effective evolutionary algorithm for the vehicle routing problem. Comput Oper Res 31(12):1985–2002MathSciNetCrossRefMATH
Zurück zum Zitat Reinelt G (1991) TSPLIB—A traveling salesman problem library. ORSA J Comput 3(4):376–384CrossRefMATH Reinelt G (1991) TSPLIB—A traveling salesman problem library. ORSA J Comput 3(4):376–384CrossRefMATH
Zurück zum Zitat Riera-Ledesma J, Salazar-González JJ (2005) The biobjective travelling purchaser problem. Eur J Oper Res 160(3):599–613CrossRefMATH Riera-Ledesma J, Salazar-González JJ (2005) The biobjective travelling purchaser problem. Eur J Oper Res 160(3):599–613CrossRefMATH
Zurück zum Zitat Schilde M, Doerner KF, Hartl RF, Kiechle G (2009) Metaheuristics for the bi-objective orienteering problem. Swarm Intell 3(3):179–201CrossRef Schilde M, Doerner KF, Hartl RF, Kiechle G (2009) Metaheuristics for the bi-objective orienteering problem. Swarm Intell 3(3):179–201CrossRef
Zurück zum Zitat Tang H, Miller-Hooks E (2005) A tabu search heuristic for the team orienteering problem. Comput Oper Res 32(6):1379–1407CrossRef Tang H, Miller-Hooks E (2005) A tabu search heuristic for the team orienteering problem. Comput Oper Res 32(6):1379–1407CrossRef
Zurück zum Zitat Tricoire F, Romauch M, Doerner KF, Hartl RF (2010) Heuristics for the multi-period orienteering problem with multiple time windows. Comput Oper Res 37(2):351–367MathSciNetCrossRefMATH Tricoire F, Romauch M, Doerner KF, Hartl RF (2010) Heuristics for the multi-period orienteering problem with multiple time windows. Comput Oper Res 37(2):351–367MathSciNetCrossRefMATH
Zurück zum Zitat Tsiligirides T (1984) Heuristic methods applied to orienteering. J Oper Res Soc 35(9):797–809 Tsiligirides T (1984) Heuristic methods applied to orienteering. J Oper Res Soc 35(9):797–809
Zurück zum Zitat Vansteenwegen P, Souffriau W, Berghe GV, Oudheusden DV (2009a) In: Metaheuristics in the service industry. Lecture notes in economics and mathematical systems, chapter metaheuristics for tourist trip planning, vol 624. Springer Berlin, Heidelberg, pp 15–31 Vansteenwegen P, Souffriau W, Berghe GV, Oudheusden DV (2009a) In: Metaheuristics in the service industry. Lecture notes in economics and mathematical systems, chapter metaheuristics for tourist trip planning, vol 624. Springer Berlin, Heidelberg, pp 15–31
Zurück zum Zitat Vansteenwegen P, Souffriau W, Berghe GV, Oudheusden DV (2009b) Iterated local search for the team orienteering problem with time windows. Comput Oper Res 36(12):3281–3290 Vansteenwegen P, Souffriau W, Berghe GV, Oudheusden DV (2009b) Iterated local search for the team orienteering problem with time windows. Comput Oper Res 36(12):3281–3290
Zurück zum Zitat Vansteenwegen P, Souffriau W, Oudheusden DV (2011) The orienteering problem: a survey. Eur J Oper Res 209:1–10CrossRefMATH Vansteenwegen P, Souffriau W, Oudheusden DV (2011) The orienteering problem: a survey. Eur J Oper Res 209:1–10CrossRefMATH
Zurück zum Zitat Wang X, Golden BL, Wasil EA (2008) Using a genetic algorithm to solve the generalized orienteering problem. In: Golden B, Raghavan S, Wasil EA (eds) The vehicle routing problem: latest advances and new challenges. Springer, pp 263–274 Wang X, Golden BL, Wasil EA (2008) Using a genetic algorithm to solve the generalized orienteering problem. In: Golden B, Raghavan S, Wasil EA (eds) The vehicle routing problem: latest advances and new challenges. Springer, pp 263–274
Zurück zum Zitat Zitzler E (1999) Evolutionary algorithms for multi-objective optimization: methods and applications. Ph.D. thesis, Swiss Federal Institute of Technology, Zurich Zitzler E (1999) Evolutionary algorithms for multi-objective optimization: methods and applications. Ph.D. thesis, Swiss Federal Institute of Technology, Zurich
Metadaten
Titel
An Evolutionary Algorithm with Path Relinking for a Bi-objective Multiple Traveling Salesman Problem with Profits
verfasst von
N. Labadie
J. Melechovsky
C. Prins
Copyright-Jahr
2014
Verlag
Springer London
DOI
https://doi.org/10.1007/978-1-4471-5295-8_10

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