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Constraint-guided evolutionary algorithm for solving the winner determination problem

Abstract

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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Notes

  1. 1.

    http://www.fcc.gov/auctions/.

  2. 2.

    https://julialang.org/.

  3. 3.

    https://www.aneel.gov.br/.

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Acknowledgements

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). https://doi.org/10.1007/s10732-021-09485-x

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Keywords

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