Applied Intelligence

, Volume 49, Issue 11, pp 3845–3863 | Cite as

A discrete cooperatively coevolving particle swarm optimization algorithm for combinatorial double auctions

  • Fu-Shiung HsiehEmail author
  • Yi-Hong Guo


A combinatorial double auction is a type of double-side auction which makes buyers and sellers trade goods more conveniently than multiple combinatorial auctions. In this paper, we consider the combinatorial double auction problem in which there are transaction costs, supply constraints and surplus constraints. We formulate the WDP of combinatorial double auction problem as an integer programming problem formulation. The winner determination problem (WDP) in combinatorial double auctions poses a challenge due to computational complexity. Particle swarm optimization (PSO) is a well-known approach to deal with complex optimization problems. In the existing literature, different variants of PSO algorithms have been proposed. However, there still lacks a comparative study on effectiveness of applying different variants of PSO algorithms in combinatorial double auctions. As standard discrete PSO (DPSO) algorithm suffers from premature convergence problem, we adopt a coevolution approach to develop a discrete cooperatively coevolving particle swarm optimization (DCCPSO) algorithm that can scale with the problem. The effectiveness of the proposed algorithm is verified by comparing the results with several variants of PSO algorithms and Differential Evolution algorithms through simulation. Simulation results indicate that the proposed DCCPSO algorithm significantly outperforms these variants of PSO algorithms and Differential Evolution algorithms in most test cases of combinatorial double auctions.


Particle swarm Coevolution Combinatorial double auction Integer programming 



This paper is currently supported in part by Ministry of Science and Technology, Taiwan under Grant MOST 106-2410-H-324-002-MY2.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringChaoyang University of TechnologyTaichungTaiwan

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