Skip to main content
SpringerLink
Log in

A survey on metaheuristics for stochastic combinatorial optimization

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

Metaheuristics are general algorithmic frameworks, often nature-inspired, designed to solve complex optimization problems, and they are a growing research area since a few decades. In recent years, metaheuristics are emerging as successful alternatives to more classical approaches also for solving optimization problems that include in their mathematical formulation uncertain, stochastic, and dynamic information. In this paper metaheuristics such as Ant Colony Optimization, Evolutionary Computation, Simulated Annealing, Tabu Search and others are introduced, and their applications to the class of Stochastic Combinatorial Optimization Problems (SCOPs) is thoroughly reviewed. Issues common to all metaheuristics, open problems, and possible directions of research are proposed and discussed. In this survey, the reader familiar to metaheuristics finds also pointers to classical algorithmic approaches to optimization under uncertainty, and useful informations to start working on this problem domain, while the reader new to metaheuristics should find a good tutorial in those metaheuristics that are currently being applied to optimization under uncertainty, and motivations for interest in this field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. Nevertheless, a solution algorithm may use a ‘dynamic’ or ‘stochastic’ mechanism also in these cases, as, for example, the dynamic programming algorithm applied to (deterministic, static) shortest path problems, or algorithms that involve some random choice such as virtually all metaheuristics and local search procedures.

References

  • Aarts E, Korst J (1990) Simulated annealing and the Boltzmann machine. Wiley, New York, NY, USA

    Google Scholar 

  • Albers S (2003) Online algorithms: a survey. Math Program 97(1–2):3–26

    MATH  MathSciNet  Google Scholar 

  • Alkhamis TM, Ahmed MA (2004) Simulation-based optimization using simulated annealing with confidence intervals. In: Ingalls RG, Rossetti MD, Smith JS, Peters BA (eds) Proceedings of the 2004 winter simulation conference (WSC04). IEEE Press, Piscataway, NJ, USA, pp 514–518

    Google Scholar 

  • Alkhamis TM, Ahmed MA, Kim Tuan W (1999) Simulated annealing for discrete optimization with estimation. Eur J Oper Res 116:530–544

    Article  MATH  Google Scholar 

  • Alrefaei MH, Andradóttir S (1999) A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Manag Sci 45:748–764

    Article  Google Scholar 

  • Andradóttir S (1998) A review of simulation optimization techniques. In: Medeiros DJ, Watson EF, Carson JS, Manivannan MS (eds) Proceedings of the 1998 winter simulation conference (WSC98). IEEE Press, Piscataway, NJ, USA, pp 151–158

    Google Scholar 

  • Aringhieri R (2004) Solving chance-constrained programs combining Tabu Search and simulation. In: Ribeiro CC, Martins SL (eds) Proceedings of the 3rd international workshop on experimental and efficient algorithms (WEA04), vol 3059: Lecture notes in computer science. Springer, Berlin, Germany, pp 30–41

  • Arnold D (2002) In Noisy optimization with evolutionary strategies, vol 8: Genetic algorithms and evolutionary computation series. Kluwer Academic Publishers, Boston, MA, USA

  • Bäck T, Fogel D, Michalewicz Z (eds) (1997) Handbook of evolutionary computation. Oxford University Press, Oxford, UK, and Institute of Physics Publishing, Bristol, UK

  • Balaprakash P, Birattari M, Stützle T, Dorigo M (2007a) Adaptive sample size and importance sampling in estimation-based local search for stochastic combinatorial optimization: a complete analysis. Technical Report TR/IRIDIA/2007-015, IRIDIA, Université Libre de Bruxelles, Brussels, Belgium, September

  • Balaprakash P, Birattari M, Stützle T, Dorigo M (2007b) An experimental study of estimation-based metaheuristics for the probabilistic traveling salesman problem. Technical Report TR/IRIDIA/2007-021, IRIDIA, Université Libre de Bruxelles, Brussels, Belgium

  • Banks A, Vincent J, Anyakoha C (2007) A review of particle swarm optimization, part i: background and development. Nat Comput 6(4):467–484

    Article  MATH  MathSciNet  Google Scholar 

  • Banks A, Vincent J, Anyakoha C (2008) A review of particle swarm optimization, part ii: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Nat Comput 7(1):109–124

    Article  MATH  MathSciNet  Google Scholar 

  • Barthelemy J-FM, Haftka RT (1993) Approximation concepts for optimum structural design—a review. Struct Optim 5:129–144

    Article  Google Scholar 

  • Bellman R, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17:141–161

    Article  MathSciNet  Google Scholar 

  • Beraldi P, Ruszczyński A (2005) Beam Search heuristic to solve stochastic integer problems under probabilistic constraints. Eur J Oper Res 167(1):35–47

    Article  MATH  Google Scholar 

  • Bertsekas DP (1995) Dynamic programming and optimal control, vol 1, 2. Athena Scientific, Belmont, MA, USA

  • Bertsekas DP (1998) Network optimization: continuous and discrete models. Athena Scientific, Belmont, MA, USA

    MATH  Google Scholar 

  • Bertsekas DP, Castañon DA (1998) Rollout algorithms for stochastic scheduling problems. J Heuristics 5:89–108

    Article  Google Scholar 

  • Bertsekas DP, Tsitsiklis JN, Wu C (1997) Rollout algorithms for combinatorial optimization. J Heuristics 3(3):245–262

    Article  MATH  Google Scholar 

  • Beyer H-G (2000) Evolutionary algorithms in noisy environments: theoretical issues and guidelines for practice. Comput Meth Appl Mech Eng 186(2–4):239–267

    Article  MATH  Google Scholar 

  • Bianchi L (2006) Ant colony optimization and local search for the probabilistic traveling salesman problem: a case study in stochastic combinatorial optimization. PhD thesis, Université Libre de Bruxelles, Brussels, Belgium

  • Bianchi L, Campbell AM (2007) Extension of the 2-p-opt and 1-shift algorithms to the heterogeneous probabilistic traveling salesman problem. Eur J Oper Res 176(1):131–144

    Article  MATH  MathSciNet  Google Scholar 

  • Bianchi L, Gambardella LM, Dorigo M (2002a) An ant colony optimization approach to the probabilistic traveling salesman problem. In: Merelo Guervós JJ, Adamidis P, Beyer H-G, Fernández-Villacañas J-L, Schwefel H-P (eds) Proceedings of the 7th international conference on parallel problem solving from nature (PPSN VII), vol 2439: Lecture notes in computer science. Springer, London, UK, pp 883–892

  • Bianchi L, Gambardella LM, Dorigo M (2002b) Solving the homogeneous probabilistic traveling salesman problem by the ACO metaheuristic. In: Dorigo M, Di Caro G, Sampels M (eds) Proceedings of the 3rd international workshop on ant algorithms (ANTS 2002), vol 2463: Lecture notes in computer science. Springer, London, UK, pp 176–187

  • Bianchi L, Birattari M, Chiarandini M, Manfrin M, Mastrolilli M, Paquete L, Rossi-Doria O, Schiavinotto T (2004) Metaheuristics for the vehicle routing problem with stochastic demands. In: Yao X, Burke E, Lozano JA, Smith J, Merelo Guervós JJ, Bullinaria JA, Rowe J, Tiňo P, Kabán A, Schwefel H-P (eds) Proceedings of the 8th international conference on parallel problem solving from nature (PPSN VIII), vol 3242: Lecture notes in computer science. Springer, Berlin, Germany, pp 450–460

  • Bianchi L, Knowles J, Bowler N (2005) Local search for the probabilistic traveling salesman problem: correction to the 2-p-opt and 1-shift algorithms. Eur J Oper Res 162(1):206–219

    Article  MATH  MathSciNet  Google Scholar 

  • Bianchi L, Birattari M, Manfrin M, Mastrolilli M, Paquete L, Rossi-Doria O, Schiavinotto T (2006) Hybrid metaheuristics for the vehicle routing problem with stochastic demands. J Math Model Algorithms 5(1):91–110

    Article  MATH  MathSciNet  Google Scholar 

  • Birattari M, Balaprakash P, Dorigo M (2005) ACO/F-Race: ant colony optimization and racing techniques for combinatorial optimization under uncertainty. In: Doerner KF, Gendreau M, Greistorfer P, Gutjahr WJ, Hartl RF, Reimann M (eds) Proceedings of the 6th metaheuristics international conference (MIC 2005), pp 107–112

  • Birattari M, Balaprakash P, Dorigo M (2006) The ACO/F-RACE algorithm for combinatorial optimization under uncertainty. In: Doerner KF, Gendreau M, Greistorfer P, Gutjahr WJ, Hartl RF, Reimann M (eds) Metaheuristics—progress in complex systems optimization. Operations research/computer science interfaces series. Springer, Berlin, Germany

    Google Scholar 

  • Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, New York, NY, USA

    MATH  Google Scholar 

  • Birnbaum ZW (1948) On random variables with comparable peakedness. Ann Math Stat 19:76–81

    Article  MATH  MathSciNet  Google Scholar 

  • Blum C (2005) Ant colony optimization: introduction and recent trends. Phys Life Rev 2(4):353–373

    Article  MathSciNet  Google Scholar 

  • Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35(3):268–308

    Article  Google Scholar 

  • Borodin A, El-Yaniv R (1998) Online computation and competitive analysis. Cambridge University Press, Cambridge, MA, USA

    MATH  Google Scholar 

  • Bowler NE, Fink TMA, Ball RC (2003) Characterization of the probabilistic traveling salesman problem. Phys Rev E 68(036703)

  • Branke J (2001) Evolutionary approaches to dynamic optimization problems—updated survey. In: Beyer H-G, Cantú-Paz E, Goldberg D, Parmee IC, Spector L, Whitley D (eds) Proceedings of the genetic and evolutionary computation conference (GECCO 2001). Morgan Kaufmann, San Francisco, CA, USA, pp 27–30

    Google Scholar 

  • Branke J (2002) Evolutionary optimization in dynamic environments. Springer, Berlin, Germany

    MATH  Google Scholar 

  • Branke J, Guntsch M (2003) New ideas for applying ant colony optimization to the probabilistic TSP. In Proceedings of the 3rd European workshop on evolutionary computation in combinatorial optimization (EvoCOP 2003), vol 2611: Lecture notes in computer science. Springer, Berlin, Germany, pp 165–175

  • Branke J, Guntsch M (2004) Solving the probabilistic TSP with ant colony optimization. J Math Model Algorithms 3(4):403–425

    Article  MATH  MathSciNet  Google Scholar 

  • Brodersen O, Schumann M (2007) Optimizing a stochastic warehouse using particle swarm optimization. In Second international conference on innovative computing (ICICIC). IEEE Press, Piscataway, NJ, USA, pp 449–452

  • Brusco M, Jacobs L (1993a) A simulated annealing approach to the cyclic staff-scheduling problem. Nav Res Logist 40(1):69–84

    Article  MATH  Google Scholar 

  • Brusco M, Jacobs L (1993b) A simulated annealing approach to the solution of flexible labour scheduling problems. J Oper Res Soc 44(12):1191–1200

    Article  MATH  Google Scholar 

  • Bulgak AA, Sanders JL (1988) Integrating a modified simulated annealing algorithm with the simulation of a manufacturing system to optimize buffer sizes in automatic assembly systems. In: Abrams M, Haigh P, Comfort J (eds) Proceedings of the 1988 winter simulation conference (WSC98). IEEE Press, Piscataway, NJ, USA, pp 684–690

    Chapter  Google Scholar 

  • Calégari P, Coray G, Hertz A, Kobler D, Kuonen P (1999) A taxonomy of evolutionary algorithms in combinatorial optimization. J Heuristics 5:145–158

    Article  MATH  Google Scholar 

  • Chang HS (2004) An ant system based exploration-exploitation for reinforcement learning. In Proceedings of the IEEE conference on systems, man, and cybernetics. IEEE Press, Piscataway, NJ, USA, pp 3805–3810

  • Chang HS, Gutjahr WJ, Yang J, Park S (2004) An ant system approach to Markov decision processes. In Proceedings of the 23rd American control conference (ACC04), vol 4. IEEE Press, Piscataway, NJ, USA, pp 3820–3825

  • Chang HS, Lee H-G, Fu MC, Marcus SI (2005) Evolutionary policy iteration for solving Markov decision processes. IEEE T Automat Contr 50(11):1804–1808

    Article  MathSciNet  Google Scholar 

  • Cheung RK, Dongsheng X, Yongpei G (2007) A solution method for a two-dispatch delivery problem with stochastic customers. J Math Model Algorithms 6:87–107

    Article  MATH  MathSciNet  Google Scholar 

  • Costa D, Silver EA (1998) Tabu Search when noise is present: an illustration in the context of cause and effect analysis. J Heuristics 4:5–23

    Article  MATH  Google Scholar 

  • Dengiz B, Alabas C (2000) Simulation optimization using Tabu Search. In: Joines JA, Barton RR, Kang K, Fishwick PA (eds) Proceedings of the 2000 winter simulation conference (WSC00). IEEE Press, Piscataway, NJ, USA, pp 805–810

    Google Scholar 

  • Doerner K, Gutjahr WJ, Kotsis G, Polaschek M, Strauss C (2006) Enriched workflow modelling and stochastic branch-and-bound. Eur J Oper Res 175:1798–1817

    Article  MATH  MathSciNet  Google Scholar 

  • Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theor Comput Sci 344(2–3):243–278

    Article  MATH  MathSciNet  Google Scholar 

  • Dorigo M, Gambardella LM (1997) Ant Colony System: A cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1:53–66

    Article  Google Scholar 

  • Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, Cambridge, MA, USA

    MATH  Google Scholar 

  • Dorigo M, Maniezzo V, Colorni A (1991) The ant system: an autocatalytic optimization process. Technical Report 91-016, Department of Electronics. Politecnico di Milano, Milan, Italy

    Google Scholar 

  • Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern—Part B 26(1):29–41

    Article  Google Scholar 

  • Dorigo M, Di Caro G, Gambardella LM (1999) Ant algorithms for discrete optimization. Artif Life 5(2):137–172

    Article  Google Scholar 

  • Dyer M, Stougie L (2003) Computational complexity of stochastic programming problems. Technical Report SPOR-report 2003-20. Department of Mathematics and Computer Science. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

  • Easton F, Mansour N (1999) A distributed genetic algorithm for deterministic and stochastic labor scheduling problems. Eur J Oper Res 118(3):505–523

    Article  MATH  Google Scholar 

  • Easton F, Rossin D (1996) A stochastic goal program for employee scheduling. Dec Sci 27(3):541–568

    Article  Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the IEEE international symposium on micro machine and human science (MHS’95). IEEE Press, Piscataway, NJ, USA, pp 39–43

  • Erel E, Sabuncuoglu I, Sekerci H (2005) Stochastic assembly line balancing using Beam Search. Int J Prod Res 43(7):1411–1426

    Article  MATH  Google Scholar 

  • Finke DA, Medeiros DJ, Traband M (2002) Shop scheduling using Tabu Search and simulation. In: Yücesan E, Chen CH, Snowdon JL, Charnes JM (eds) Proceedings of the 2002 winter simulation conference (WSC02). IEEE Press, Piscataway, NJ, USA, pp 1013–1017

    Chapter  Google Scholar 

  • Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution. Wiley, New York, NY, USA

    MATH  Google Scholar 

  • Fox BL, Heine GW (1995) Probabilistic search with overrides. Ann Appl Probab 4:1087–1094

    Article  MathSciNet  Google Scholar 

  • Fu MC (2002) Optimization for simulation: theory vs. practice. INFORMS J Comput 14(3):192–215

    Article  MathSciNet  Google Scholar 

  • Fu MC (2003) Guest editorial of the ACM TOMACS special issue on “simulation optimization”. ACM Trans Model Comput Simul 13(2):105–107

    Article  Google Scholar 

  • Gambardella LM, Dorigo M (1996) Solving symmetric and asymmetric TSPs by ant colonies. In: Proceedings of the 1996 IEEE international conference on evolutionary computation (ICEC’96). IEEE Press, Piscataway, NJ, USA, pp 622–627

  • Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman & Co., New York, NY, USA

    MATH  Google Scholar 

  • Gelfand SB, Mitter SK (1985) Analysis of simulated annealing for optimization. In: Proceedings of the 24th IEEE conference on decision and control (CDC’85), vol 2. IEEE Press, Piscataway, NJ, USA, pp 779–786

  • Gelfand SB, Mitter SK (1989) Simulated annealing with noisy or imprecise measurements. J Optim Theory Appl 69:49–62

    Article  MathSciNet  Google Scholar 

  • Geman D, Geman S (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. In: IEEE transactions of pattern analysis and machine intelligence, vol 6, pp 721–741

  • Gendreau M, Laporte G, Séguin R (1995) An exact algorithm for the vehicle routing problem with stochastic demands and customers. Transp Sci 29(2):143–155

    Article  MATH  Google Scholar 

  • Gendreau M, Laporte G, Séguin R (1996) A Tabu Search heuristic for the vehicle routing problem with stochastic demands and customers. Oper Res 44(3):469–477

    Article  MATH  Google Scholar 

  • Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13:533–549

    Article  MATH  MathSciNet  Google Scholar 

  • Glover F (1998) A template for scatter search and path relinking. In: Hao J-K, Lutton E, Ronald E, Schoenaurer M, Snyers D (eds) Artificial evolution, vol 1363: Lecture notes in computer science. Springer, Berlin, Germany

  • Glover F (2002) Tabu Search and finite convergence. Discret Appl Math 119:3–36

    Article  MATH  MathSciNet  Google Scholar 

  • Glover F, Laguna M (1997) Tabu Search. Kluwer Academic Publishers, Norwell, MA, USA

    MATH  Google Scholar 

  • Grimmett GR, Stirzaker DR (2001) Probability and random processes, 3rd edn. Oxford University Press, New York, NY, USA

    Google Scholar 

  • Gutin G, Punnen A (eds) (2002) The traveling salesman problem and its variations. Kluwer Academic Publishers, Dordrecht, The Netherlands

    MATH  Google Scholar 

  • Gutjahr WJ (2000) A graph-based ant system and its convergence. Future Gener Comput Syst 16(8):873–888

    Article  Google Scholar 

  • Gutjahr WJ (2002) ACO algorithms with guaranteed convergence to the optimal solution. Inf Process Lett 82(3):145–153

    Article  MATH  MathSciNet  Google Scholar 

  • Gutjahr WJ (2003) A converging ACO algorithm for stochastic combinatorial optimization. In: Proceedings of the 2nd symposium on stochastic algorithms, foundations and applicaions (SAGA 2003), vol 2827: Lecture notes in computer science. Springer, Berlin, Germany, pp 10–25

  • Gutjahr WJ (2004) S-ACO: an ant-based approach to combinatorial optimization under uncertainty. In: Proceedings of the 4th international workshop on ant colony optimization and swarm intelligence (ANTS 2004), vol 3172: Lecture notes in computer science. Springer, Berlin, Germany, pp 238–249

  • Gutjahr WJ, Hellmayr A, Pflug GCh (1999) Optimal stochastic single-machine tardiness scheduling by stochastic branch-and-bound. Eur J Oper Res 117:396–413

    Article  MATH  Google Scholar 

  • Gutjahr WJ, Katzensteiner S, Reiter P (2007) A VNS algorithm for noisy problems and its application to project portfolio analysis. In: Hromkovič J, Královič R, Nunkesser M, Widmayer P (eds) Proceedings of the 4th symposium on stochastic algorithms, foundations and applications (SAGA 2007), vol 4665: Lecture notes in computer science, pp 93–104

  • Gutjahr WJ, Pflug GCh (1996) Simulated annealing for noisy cost functions. J Glob Optim 8:1–13

    Article  MATH  MathSciNet  Google Scholar 

  • Gutjahr WJ, Strauss C, Toth M (2000a) Crashing of stochastic activities by sampling and optimization. Bus Process Manag J 6:65–83

    Article  Google Scholar 

  • Gutjahr WJ, Strauss C, Wagner E (2000b) A stochastic branch-and-bound approach to activity crashing in project management. INFORMS J Comput 12:125–135

    Article  MATH  Google Scholar 

  • Haddock J, Mittenthal J (1992) Simulation optimization using simulated annealing. Comput Ind Eng 22:387–395

    Article  Google Scholar 

  • Hajek B (1988) Cooling schedules for optimal annealing. Math Oper Res 13:311–329

    Article  MATH  MathSciNet  Google Scholar 

  • Hanafi S (2000) On the convergence of Tabu Search. J Heuristics 7:47–58

    Article  Google Scholar 

  • Haneveld WKK, van der Vlerk MH (1999) Stochastic integer programming: state of the art. Ann Oper Res 85:39–57

    Article  MATH  MathSciNet  Google Scholar 

  • Hansen P (1986) The steepest ascent mildest descent heuristics for combinatorial programming. Talk presented at the congress on numerical methods in combinatorial optimization. Capri, Italy

  • Hansen P, Mladenović N (2001) Variable neighborhood search: Principles and applications. Eur J Oper Res 130:449–467

    Article  MATH  Google Scholar 

  • Haugen KK, Løkketangen A, Woodruff DL (2001) Progressive hedging as a meta-heuristic applied to stochastic lot-sizing. Eur J Oper Res 132:116–122

    Article  MATH  Google Scholar 

  • Haugland D, Ho SC, Laporte G (2007) Designing delivery districts for the vehicle routing problem with stochastic demands. Eur J Oper Res 180:997–1010

    Article  MATH  MathSciNet  Google Scholar 

  • Hertz A, Kobler D (2000) A framework for the description of evolutionary algorithms. Eur J Oper Res 126:1–12

    Article  MATH  MathSciNet  Google Scholar 

  • Hertz A, Taillard E, de Werra D (1997) Tabu Search. In: Aarts EHL, Lenstra JK (eds) Local search in combinatorial optimization. Wiley, New York, NY, USA, pp 121–136

    Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Ann Harbor, MI, USA

    Google Scholar 

  • Homem-de-Mello T (2000) Variable-sample methods and simulated annealing for discrete stochastic optimization. Stochastic Programming E-Print Series, http://hera.rz.hu-berlin.de/speps/

  • Homem-de-Mello T (2003) Variable-sample methods for stochastic optimization. ACM Trans Model Comput Simul 13:108–133

    Article  Google Scholar 

  • Hvattum LM, Løkketangen A (in press) Using scenario trees and progressive hedging for stochastic inventory routing problems. J Heuristics. doi:10.1007/s10732-008-9076-0

  • Irani S, Lu X, Regan A (2004) On-line algorithms for the dynamic traveling repair problem. J Sched 7(3):243–258

    Article  MATH  MathSciNet  Google Scholar 

  • Jellouli O, Châtelet E (2001) Monte Carlo simulation and genetic algorithm for optimising supply chain management in a stochastic environment. In: Proceedings of the 2001 IEEE conference on systems, man, and cybernetics, vol 3. IEEE Press, Piscataway, NJ, USA, pp 1835–1839

  • Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9(1):3–12

    Article  Google Scholar 

  • Jin Y, Branke J (2005) Evolutionary optimization in uncertain environments—a survey. IEEE Trans Evol Comput 9(3):303–317

    Article  Google Scholar 

  • Jönsson H, Silver EA (1996) Some insights regarding selecting sets of scenarios in combinatorial stochastic problems. J Prod Econ 45:463–472

    Article  Google Scholar 

  • Jovanović D, Mladenović M, Ognjanović Z (2007) Variable neighborhood search for the probabilistic satisfiability problem. In: Doerner KF, Gendreau M, Greistorfer P, Gutjahr WJ, Hartl RF, Reimann M (eds) Metaheuristics—progress in complex systems optimization, vol 39: Operations research/Computer Science Interfaces Series. Springer, New York, NY, USA, pp 173–188

  • Kall P, Wallace SW (1994) Stochastic programming. Wiley, Chichester, UK, 1994. Wiley has released the copyright on the book, and the authors made the text available to the scientific community: it can be downloaded for free at http://www.unizh.ch/ior/Pages/Deutsch/Mitglieder/Kall/bib/ka-wal-94.pdf

  • Kennedy J (1997) The particle swarm: social adaptation of knowledge. In: Proceedings of the IEEE international conference on evolutionary computation (CEC’97). IEEE Press, Piscataway, NJ, USA, pp 303–308

  • Kenyon A, Morton DP (2002) A survey on stochastic location and routing problems. Central Eur J Oper Res 9:277–328

    MathSciNet  Google Scholar 

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  MathSciNet  Google Scholar 

  • Kouvelis P, Yu G (1997) Robust discrete optimization and its applications, vol 14: Nonconvex optimization and its applications. Kluwer Academic Publishers, Dordrecht, The Netherlands

  • Laporte G, Louveaux F, Mercure H (1994) An exact solution for the a priori optimization of the probabilistic traveling salesman problem. Oper Res 42(3):543–549

    Article  MATH  MathSciNet  Google Scholar 

  • Liu Y-H (2007) A hybrid scatter search for the probabilistic traveling salesman problem. Comput Oper Res 34:2949–2963

    Article  MATH  Google Scholar 

  • Lin Z-Z, Bean JC, White CC III (2004) A hybrid genetic/optimization algorithm for finite-horizon, partially observed Markov decision processes. INFORMS J Comput 16(1):27–38

    Article  MathSciNet  Google Scholar 

  • Liu B, Wang L, Jin Y-H (2005) Hybrid particle swarm optimization for flow shop scheduling with stochastic processing time, vol 380: Lecture notes in computer science, pp 630–637

  • Liu Y-H, Jou R-C, Wang C-C, Chiu C-S (2007) An evolutionary algorithm with diversified crossover operator for the heterogeneous probabilistic TSP. In: Carbonell JG, Siekmann J (eds) Modeling decisions for artificial intelligence. 4th international conference, (MDAI 2007), vol 4617: Lecture notes in computer science. Springer, Berlin, Germany, pp 351–360

  • Løkketangen A, Woodruff DL (1996) Progressive hedging and Tabu Search applied to mixed integer (0,1) multistage stochastic programming. J Heuristics 2:111–128

    Article  Google Scholar 

  • Lu L, Tan Q-M (2006) Hybrid particle swarm optimization algorithm for stochastic vehicle routing problem. Xi Tong Gong Cheng Yu Dian Zi Ji Shu/Syst Eng Electron 28(2):244–247

    MathSciNet  Google Scholar 

  • Lu M, Wu D-P, Zhang J-P (2006) A particle swarm optimization-based approach to tackling simulation optimization of stochastic, large-scale and complex systems, vol 3930: Lecture notes in computer science, pp 528–537

  • Lutz CM, Davis KR, Sun M (1998) Determining buffer location and size in production lines using Tabu Search. Eur J Oper Res 106:301–316

    Article  MATH  Google Scholar 

  • Mak KL, Guo ZG (2004) A genetic algorithm for vehicle routing problems with stochastic demand and soft time windows. In: Jones MH, Patek SD, Tawney BE (eds) Proceedings of the 2004 IEEE systems and information engineering design symposium (SIEDS04). IEEE Press, Piscataway, NJ, USA, pp 183–190

    Google Scholar 

  • Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Article  Google Scholar 

  • Miller BL, Goldberg DE (1997) Genetic algorithms, selection schemes, and the varying effects of noise. Evol Comput 4(2):113–131

    Article  Google Scholar 

  • Morrison RW (2004) Designing evolutionary algorithms for dynamic environments. Springer, Berlin, Germany

    MATH  Google Scholar 

  • Metaheuristics Network web site. http://www.metaheuristics.org/

  • Norkin VI, Ermoliev YM, Ruszczyński A (1998a) On optimal allocation of indivisibles under uncertainty. Oper Res 46(3):381–395

    Article  MATH  Google Scholar 

  • Norkin VI, Pflug GCh, Ruszczyński A (1998b) A Branch and Bound method for stochastic global optimization. Math Program 83:425–450

    MATH  Google Scholar 

  • Ólafsson S, Kim J (2002) Simulation optimization. In: Yücesan E, Chen CH, Snowdown JL, Charnes JM (eds) Proceedings of the 2002 winter simulation conference (WSC02). IEEE Press, Piscataway, NJ, USA, pp 89–84

  • Papadimitriou CH, Steiglitz K (1982) Combinatorial optimization. Dover Publications, Mineola, NY, USA

    MATH  Google Scholar 

  • Pappala VS, Erlich I (2007) Management of distributed generation units under stochastic load demands using particle swarm optimization. In: Power engineering society general meeting (PES), IEEE Press, Piscataway, NJ, USA, pp 24–28

  • Pichitlamken J (2002) A combined procedure for optimization via simulation. PhD thesis, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA

  • Pichitlamken J, Nelson LB (2001) Selection-of-the-best procedures for optimization via simulation. In: Peters BA, Smith JS, Medeiros DJ, Rohrer MW (eds) Proceedings of the 2001 winter simulation conference (WSC01). IEEE Press, Piscataway, NJ, USA, pp 401–407

    Google Scholar 

  • Pichitlamken J, Nelson LB (2003) A combined procedure for optimization via simulation. ACM Trans Model Comput Simul 13(2):155–179

    Article  Google Scholar 

  • Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization: an overview. Swarm Intell 1:33–57

    Article  Google Scholar 

  • Rauner M, Brailsford SC, Gutjahr WJ, Zeppelzauer W (2005) Optimal screening policies for diabetic retinopathy using a combined discrete event simulation and ant colony optimization approach. In: Andersen JG, Katzper M (eds) Proceedings of the 15th international conference on health sciences simulation, western multiconference 2005. SCS—Society of Computer Simulation International, San Diego, CA, USA, pp 147–152

    Google Scholar 

  • Rechenberg RI (1973) Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, Stuttgart, Germany

    Google Scholar 

  • Reeves CR, Rowe JE (2003) Genetic algorithms: principles and perspectives—a guide to GA theory. Operaations Research/Computer Science Interfaces Series. Kluwer Academic Publishers, Boston, MA, USA

  • Resende MGC, Ribeiro CC (2003) In: Glover F, Kochenberger G (eds) Handbook of metaheuristics. vol 57: International series in operations research & management, chapter Greedy randomized adaptive search procedures. Kluwer Academic Publishers, Boston, USA, pp 219–249

  • Rockafellar RT, Wets RJ-B (1991) Scenarios and policy aggregation in optimization under uncertainty. Math Oper Res 16:119–147

    Article  MATH  MathSciNet  Google Scholar 

  • Roenko N (1990) Simulated annealing under uncertainty. Technical report, Institute for Operations Research, University of Zurich, Switzerland

  • Rosen SL, Harmonosky CM (2005) An improved simulated annealing simulation optimization method for discrete parameter stochastic systems. Comput Oper Res 32(2):343–358

    MATH  MathSciNet  Google Scholar 

  • Rubinstein RY (1981) Simulation and the Monte Carlo method. Wiley, New York, NY, USA

    Book  MATH  Google Scholar 

  • Rudolph G (1996) Convergence of evolutionary algorithms in general search spaces. In: Proceedings of the IEEE international conference on evolutionary computation (ICEC’96). IEEE Press, Piscataway, NJ, USA, pp 50–54

  • Secomandi N (2000) Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands. Comput Oper Res 27(5):1171–1200

    Google Scholar 

  • Secomandi N (2001) A rollout policy for the vehicle routing problem with stochastic demands. Oper Res 49(5):796–802

    Article  Google Scholar 

  • Secomandi N (2003) Analysis of a rollout approach to sequencing problems with stochastic routing applications. J Heuristics 9:321–352

    Article  MATH  Google Scholar 

  • Shi L, Ólafsson S (2000) Nested partitions method for global optimization. Oper Res 48(3):390–407

    Article  MATH  MathSciNet  Google Scholar 

  • Stochastic Programming Community Homepage. http://stoprog.org/

  • Stützle T, Dorigo M (2002) A short convergence proof for a class of ACO algorithms. IEEE Trans Evol Comput 6(4):358–365

    Article  Google Scholar 

  • Sudhir Ryan Daniel J, Rajendran C (2005) A simulation-based genetic algorithm for inventory optimization in a serial supply chain. Int Trans Oper Res 12(1):101–127

    Article  Google Scholar 

  • Swisher JR, Jacobson SH, Yücesan E (2003) Discrete-event simulation optimization using ranking, selection, multiple comparison procedures: a survey. ACM Trans Model Comput Simul 13(2):134–154

    Article  Google Scholar 

  • Teodorović D, Pavković G (1992) A simulated annealing technique approach to the vehicle routing problem in the case of stochastic demand. Transp Plan Technol 16:261–273

    Article  Google Scholar 

  • Tesauro G, Galperin GR (1997) On-line policy improvement using monte carlo search. Adv Neural Inf Process Syst 9:1068–1074

    Google Scholar 

  • van Laarhoven PJM, Aarts EHL (1987) Simulated annealing: theory and applications. D. Reidel Publishing Company, Dordrecht, The Netherlands

  • Vose M (1999) The simple genetic algorithm: foundations and theory. The MIT Press, Cambridge, MA, USA

    MATH  Google Scholar 

  • Wang L, Singh C (2008) Stochastic economic emission load dispatch through a modified particle swarm optimization algorithm. Electr Pow Syst Res 78(8):1466–1476

    Article  Google Scholar 

  • Wang K-J, Wang S-M, Chen J-C (2008) A resource portfolio planning model using sampling-based stochastic programming and genetic algorithm. Eur J Oper Res 184:327–340

    Article  MATH  Google Scholar 

  • Watson JP, Rana S, Whitley LD, Howe AE (1999) The impact of approximate evaluation on the performance of search algorithms for warehouse scheduling. J Sched 2(2):79–98

    Article  MATH  MathSciNet  Google Scholar 

  • Yang W, Mathur K, Ballou RH (2000) Stochastic vehicle routing problem with restocking. Transp Sci 34(1):99–112

    Article  MATH  Google Scholar 

  • Yoshitomi Y (2002) A genetic algorithm approach to solving stochastic job-shop scheduling problems. Int Trans Oper Res 9(4):479–495

    Article  MATH  MathSciNet  Google Scholar 

  • Yoshitomi Y, Yamaguchi R (2003) A genetic algorithm and the Monte Carlo method for stochastic job-shop scheduling. Int Trans Oper Res 10(6):577–596

    Article  MATH  MathSciNet  Google Scholar 

  • Zhao P-X (2007) Improved particle swarm optimization algorithm for the stochastic loader problem. In: Second IEEE conference on industrial electronics and applications (ICIEA 2007). IEEE Press, Piscataway, NJ, USA, pp 773–776

  • Zimmermann HJ (1991) Fuzzy set theory and its application, 2nd edn. Kluwer Academic Publishers, Boston, MA, USA

Download references

Acknowledgments

Leonora Bianchi acknowledges the support of the FNS grant Nr. 200021-108007. She also would like to thank Nicola Secomandi for the useful suggestions and informations he provided during a preliminary writing phase of the paper, and the numerous researchers that kindly made available an electronic version of their paper.

Author information

Authors and Affiliations

  1. IDSIA—Dalle Molle Institute for Artificial Intelligence, Via Cantonale, Galleria 2, 6928, Manno, Switzerland

    Leonora Bianchi & Luca Maria Gambardella

  2. IRIDIA, Université Libre de Bruxelles, Brussels, Belgium

    Marco Dorigo

  3. Department of Statistics and Decision Support Systems, University of Vienna, Vienna, Austria

    Walter J. Gutjahr

Authors
  1. Leonora Bianchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Dorigo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luca Maria Gambardella
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Walter J. Gutjahr
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leonora Bianchi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bianchi, L., Dorigo, M., Gambardella, L.M. et al. A survey on metaheuristics for stochastic combinatorial optimization. Nat Comput 8, 239–287 (2009). https://doi.org/10.1007/s11047-008-9098-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-008-9098-4

Keywords

Search

Navigation