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Constraint-guided evolutionary algorithm for solving the winner determination problem


Combinatorial Auctions (CAs) allow the participants to bid on a bundle of items and can result in more cost-effective deals than traditional auctions if the goods are complementary. However, solving the Winner Determination Problem (WDP) in CAs is an NP-hard problem. Since Evolutionary Algorithms (EAs) can find good solutions in polynomial time within a huge search space, the use of EAs has become quite suitable for solving this type of problem. In this paper, we introduce a new Constraint-Guided Evolutionary Algorithm (CGEA) for the WDP. It employs a penalty component to represent each constraint in the fitness function and introduces new variation operators that consider each package value and each type of violated constraint to induce the generation of feasible solutions. CGEA also presents a survivor selection operator that maintains the exploration versus exploitation balance in the evolutionary process. The performance of CGEA is compared with that of three other evolutionary algorithms to solve a WDP in a Combinatorial Reverse Auction (CRA) of electricity generation and transmission line assets. Each of the algorithms compared employs different methods to deal with constraints. They are tested and compared on several problem instances. The results show that CGEA is competitive and results in better performance in most cases.

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  1. 1.

  2. 2.

  3. 3.


  1. Andrade, C.E., Toso, R.F., Resende, M.G.C., Miyazawa, F.K.: Biased random-key genetic algorithms for the winner determination problem in combinatorial auctions. Evol. Comput. 23(2), 279–307 (2015)

    Article  Google Scholar 

  2. Arcuri, A., Briand, L.: A practical guide for using statistical tests to assess randomized algorithms in software engineering. In: 2011 33rd International Conference on Software Engineering (ICSE), IEEE, pp. 1–10 (2011)

  3. Ausubel, L.M., Cramton, P., et al.: Activity Rules for the Combinatorial Clock Auction. Department of Economics, University of Maryland, College Park (2011)

    Google Scholar 

  4. Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 6(2), 154–160 (1994)

    Article  Google Scholar 

  5. Boughaci, D., Benhamou, B., Drias, H.: A memetic algorithm for the optimal winner determination problem. Soft Comput. 13(8–9), 905 (2009)

    Article  Google Scholar 

  6. Buer, T., Pankratz, G.: Solving a bi-objective winner determination problem in a transportation procurement auction. Logist. Res. 2(2), 65–78 (2010)

    Article  Google Scholar 

  7. Cantillon, E., Pesendorfer, M.: Auctioning bus routes: the London experience. In: Cramton, P., Shoham, Y., Steinberg, R. (eds.) Combinatorial Auctions (2006)

  8. Chao, H., Wilson, R.: Coordination of electricity transmission and generation investments. Energy Econ. 86, 104623 (2020)

    Article  Google Scholar 

  9. Chaurasia, S.N., Kim, J.H.: An evolutionary algorithm based hyper-heuristic framework for the set packing problem. Inf. Sci. 505, 1–31 (2019)

    MathSciNet  Article  Google Scholar 

  10. Cheng, C.B., Lo, C.Y.: Multi-project scheduling by fuzzy combinatorial auction. In: 2017 3rd IEEE International Conference on Cybernetics (CYBCONF), IEEE, pp. 1–6 (2017)

  11. Coello, C.A.C.: A survey of constraint handling techniques used with evolutionary algorithms. Lania-RI-99-04, Laboratorio Nacional de Informática Avanzada (1999)

  12. Coello, C.A.C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191(11–12), 1245–1287 (2002)

    MathSciNet  Article  Google Scholar 

  13. Craenen, B., Eiben, A., Marchiori, E.: How to handle constraints with evolutionary algorithms. In: Applications, Practical Handbook Of Genetic Algorithms, pp. 341–361 (2001)

  14. Cramton, P., Shoham, Y., Steinberg, R., et al.: Combinatorial Auctions. Technical Report. University of Maryland, Department of Economics-Peter Cramton, College Park (2004)

    Google Scholar 

  15. De Vries, S., Vohra, R.V.: Combinatorial auctions: a survey. INFORMS J. Comput. 15(3), 284–309 (2003)

    MathSciNet  Article  Google Scholar 

  16. Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2–4), 311–338 (2000)

    Article  Google Scholar 

  17. de Castro, R.M., Guimarães, S., de Lima, B.S.L.P.: E-brm: a constraint handling technique to solve optimization problems with evolutionary algorithms. Appl. Soft Comput. 72, 14–29 (2018)

    Article  Google Scholar 

  18. Gen, M., Cheng, R.: A survey of penalty techniques in genetic algorithms. In: Proceedings of IEEE International Conference on Evolutionary Computation, IEEE, pp. 804–809

  19. Goeree, J.K., Lindsay, L.: The exposure problem and market design. Rev. Econ. Stud. 87(5), 2230–2255 (2020)

    Article  Google Scholar 

  20. Gonçalves, J.F., Resende, M.G.: Biased random-key genetic algorithms for combinatorial optimization. J. Heuristics 17(5), 487–525 (2011)

    Article  Google Scholar 

  21. Gorbanzadeh, F., Kazem, A.A.P.: Hybrid genetic algorithms for solving winner determination problem in combinatorial double auction in grid. IAES Int. J. Artif. Intell 1(2), 53 (2012)

    Google Scholar 

  22. Guerrero-Peña, E., Kazama, F.N., Correia, Pd.B., Araújo, A.F.R.: Solving constrained combinatorial reverse auctions using moeas: a comparative study. In: Proceedings of the 2020 Genetic and Evolutionary Computation Conference, pp. 193–200 (2020)

  23. Hamida, S.B., Schoenauer, M.: Aschea: new results using adaptive segregational constraint handling. In: Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No. 02TH8600), IEEE, vol. 1, pp. 884–889 (2002)

  24. Hogan, W., Rosellón, J., Vogelsang, I.: Toward a combined merchant-regulatory mechanism for electricity transmission expansion. J. Regul. Econ. 38(2), 113–143 (2010)

    Article  Google Scholar 

  25. Hsieh, F.S., Guo, Y.H.: Winner determination in combinatorial double auctions based on differential evolution algorithms. In: 2018 IEEE 42nd Annual Computer Software and Applications Conference (COMPSAC), IEEE, vol. 1, pp. 888–893 (2018)

  26. Hsieh, F.S., Guo, Y.H.: A discrete cooperatively coevolving particle swarm optimization algorithm for combinatorial double auctions. Appl. Intell. 49(11), 3845–3863 (2019)

    Article  Google Scholar 

  27. Joskow, P., Tirole, J.: Merchant transmission investment. J. Ind. Econ. 53(2), 233–264 (2005)

    Article  Google Scholar 

  28. Kramer, O.: A review of constraint-handling techniques for evolution strategies. Appl. Comput. Intell. Soft Comput. (2010)

  29. Li, Z., Liang, J.J., He, X., Shang, Z.: Differential evolution with dynamic constraint-handling mechanism. In: IEEE Congress on Evolutionary Computation, IEEE, pp. 1–8 (2010)

  30. Malan, K.M., Moser, I.: Constraint handling guided by landscape analysis in combinatorial and continuous search spaces. Evol. Comput. 27(2), 267–289 (2019)

    Article  Google Scholar 

  31. McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1), 55–61 (2000)

    Article  Google Scholar 

  32. Michalewicz, Z., Schmidt, M.: Evolutionary algorithms and constrained optimization. In: Evolutionary Optimization, pp. 57–86. Springer, Berlin (2003)

  33. Mochon, A., Saez, Y.: A review of radio spectrum combinatorial clock auctions. Telecommun. Policy 41(5–6), 303–324 (2017)

    Article  Google Scholar 

  34. Munoz, F.D., Sauma, E.E., Hobbs, B.F.: Approximations in power transmission planning: implications for the cost and performance of renewable portfolio standards. J. Regul. Econ. 43(3), 305–338 (2013)

    Article  Google Scholar 

  35. Orvosh, D., Davis, L.: Using a genetic algorithm to optimize problems with feasibility constraints. In: Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence, IEEE, pp. 548–553 (1994)

  36. Padhye, N., Mittal, P., Deb, K.: Feasibility preserving constraint-handling strategies for real parameter evolutionary optimization. Comput. Optim. Appl. 62(3), 851–890 (2015)

    MathSciNet  Article  Google Scholar 

  37. Patodi, P., Ray, A.K., Jenamani, M.: Ga based winner determination in combinatorial reverse auction. In: 2011 Second International Conference on Emerging Applications of Information Technology, IEEE, pp. 361–364 (2011)

  38. Pozo, D., Sauma, E., Contreras, J.: When doing nothing may be the best investment action: pessimistic anticipative power transmission planning. Appl. Energy 200, 383–398 (2017)

    Article  Google Scholar 

  39. Rassenti, S.J., Smith, V.L., Bulfin, R.L.: A combinatorial auction mechanism for airport time slot allocation. Bell J. Econ. 13, 402–417 (1982)

    Article  Google Scholar 

  40. Rothkopf, M.H., Pekeč, A., Harstad, R.M.: Computationally manageable combinational auctions. Manag. Sci. 44(8), 1131–1147 (1998)

    Article  Google Scholar 

  41. Salcedo-Sanz, S.: A survey of repair methods used as constraint handling techniques in evolutionary algorithms. Comput. Sci. Rev. 3(3), 175–192 (2009)

    Article  Google Scholar 

  42. Sandholm, T.: Algorithm for optimal winner determination in combinatorial auctions. Artif. Intell. 135(1–2), 1–54 (2002)

    MathSciNet  Article  Google Scholar 

  43. Segura, C., Coello, C.A.C., Miranda, G., León, C.: Using multi-objective evolutionary algorithms for single-objective constrained and unconstrained optimization. Ann. Oper. Res. 240(1), 217–250 (2016)

    MathSciNet  Article  Google Scholar 

  44. Shil, S.K., Sadaoui, S.: Multi-objective optimization in multi-attribute and multi-unit combinatorial reverse auctions. Int. J. Artif. Intell. Tools 26(05), 1760016 (2017)

    Article  Google Scholar 

  45. Shil, S.K., Sadaoui, S.: Meeting peak electricity demand through combinatorial reverse auctioning of renewable energy. J. Mod. Power Syst. Clean Energy 6(1), 73–84 (2018)

    Article  Google Scholar 

  46. Shil, S.K., Mouhoub, M., Sadaoui, S.: Winner determination in combinatorial double auctions based on differential evolution algorithms. In: 2018 IEEE 42nd Annual Computer Software and Applications Conference (COMPSAC), IEEE, vol. 1, pp. 888–893 (2013a)

  47. Shil, S.K., Sadaoui, S., Mouhoub, M.: Evolutionary techniques for reverse auctions. Intell. Control. Autom. 4(4), 371 (2013)

    Article  Google Scholar 

  48. Stanovov, V., Akhmedova, S., Semenkin, E.: Combined fitness-violation epsilon constraint handling for differential evolution. Soft Comput. 1–17 (2020)

  49. Takahama, T., Sakai, S.: Constrained optimization by the \(\varepsilon \) constrained differential evolution with gradient-based mutation and feasible elites. In: 2006 IEEE international conference on evolutionary computation, IEEE, pp. 1–8 (2006)

  50. Tan, X., Leon-Garcia, A., Wu, Y., Tsang, D.H.: Online combinatorial auctions for resource allocation with supply costs and capacity limits. IEEE J. Sel. Areas Commun. 38(4), 655–668 (2020)

    Article  Google Scholar 

  51. Tessema, B., Yen, G.G.: A self adaptive penalty function based algorithm for constrained optimization. In: 2006 IEEE international conference on evolutionary computation, IEEE, pp. 246–253 (2006)

  52. Triki, C.: Location-based techniques for the synergy approximation in combinatorial transportation auctions. Optim. Lett. 10(5), 1125–1139 (2016)

    MathSciNet  Article  Google Scholar 

  53. Vemuganti R (1998) Applications of set covering, set packing and set partitioning models: a survey. In: Handbook of Combinatorial Optimization, pp. 573–746. Springer

  54. Vose, M.D.: The Simple Genetic Algorithm: Foundations and Theory. MIT Press, Cambridge (1999)

    MATH  Google Scholar 

  55. Ykhlef, M., Alqifari, R.: A new hybrid algorithm to solve winner determination problem in multiunit double internet auction. Math. Probl. Eng. (2015)

  56. Zaidi, B.H., Bhatti, D.M.S., Ullah, I.: Combinatorial auctions for energy storage sharing amongst the households. J. Energy Storage 19, 291–301 (2018)

    Article  Google Scholar 

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The authors acknowledge the financial support of the companies CPFL Paulista, Foz do Chapecó Energia, Campos Novos Energia and Transmissora Morro Agudo. This Project was developed through the ANEEL research and development program, with number PD 00063-3042. The author also thank Espaço da Escrita - Pró-Reitoria de Pesquisa - UNICAMP - for the language services provided.

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Correspondence to Fernanda Nakano Kazama.

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Kazama, F.N., Araujo, A.F.R., de Barros Correia, P. et al. Constraint-guided evolutionary algorithm for solving the winner determination problem. J Heuristics 27, 1111–1150 (2021).

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  • Evolutionary algorithm
  • Constraint-handling
  • Guided variation operator
  • Combinatorial reverse auction
  • Winner determination problem
  • Electricity and transmission line auction