Soft Computing

, Volume 23, Issue 1, pp 1–18 | Cite as

Majority voting for discrete population-based optimization algorithms

  • Sedigheh Mahdavi
  • Shahryar RahnamayanEmail author
  • Abbas Mahdavi


Population-based metaheuristic algorithms have been extensively applied to solve discrete optimization problems. Generally speaking, they work with a set of candidate solutions in the population which evolve during generations using variant reproduction and selection operations to find the optimal solution(s). The population is similar to a small society having several individuals which seek a common goal/solution. This study is motivated from the election systems of societies which can be applied in the population-based algorithms. We propose utilizing the majority voting for discrete population-based optimization algorithms which uses the information of all candidate solutions in the current generation to create a new trial candidate solution, called a president candidate solution. During optimization process, after applying the evolutionary operations, all candidate solutions vote collectively to determine the values of the president’s variables. In the proposed method, a majority voting is utilized to choose a value for each variable (gene) of the president candidate solution. This method keeps untouched all other steps of population-based algorithms; therefore, it can be used with any kind of population-based algorithm. As case studies, the discrete differential evolution (DDE) algorithm and the discrete particle swarm optimization (DPSO) are used as the parent algorithms to develop majority voting-based discrete DE (MVDDE) and majority voting-based discrete PSO (MVDPSO). These two algorithms are evaluated on the fifteen discrete benchmark functions with the dimensions of D = 10, 30, 50, 100, 200 and 500. Simulation results confirm that majority voting-based discrete optimization algorithms obtain a promising performance on the majority of the benchmark functions. In addition, we have conducted some tests on large-scale 0–1 knapsack problems with large scales as a real-world application.


Election Majority voting Evolutionary algorithms Differential evolution (DE) Population-based algorithms President Particle swarm optimization (PSO) Metaheuristics Discrete optimization Collective intelligence 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Sedigheh Mahdavi
    • 1
  • Shahryar Rahnamayan
    • 1
    Email author
  • Abbas Mahdavi
    • 2
  1. 1.Department of Electrical, Computer, and Software EngineeringUniversity of Ontario Institute of Technology (UOIT)OshawaCanada
  2. 2.Department of Statistics, Faculty of Mathematical SciencesVali-e-Asr University of RafsanjanRafsanjanIran

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