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Majority voting for discrete population-based optimization algorithms

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Abstract

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.

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References

  • Alkoot FM, Kittler J (1999) Experimental evaluation of expert fusion strategies. Pattern Recognit Lett 20(11):1361–1369

    Article  Google Scholar 

  • Beheshti Z, Shamsuddin SM, Hasan S (2015) Memetic binary particle swarm optimization for discrete optimization problems. Inf Sci 299:58–84

    Article  Google Scholar 

  • Bengoetxea E (2002) Inexact graph matching using estimation of distribution algorithms. Ecole Natl Supér Télécommun Paris 2:4

    Google Scholar 

  • Blanche EE (1946) The mathematics of gambling. School Sci Math 46(3):217–227

    Article  Google Scholar 

  • Boiangiu C-A, Ioanitescu R (2013) Voting-based image segmentation. J Inf Syst Oper Manag 7:211–220

    Google Scholar 

  • Boiangiu C-A, Boglis P, Simion G, Ioanitescu R (2014) Voting-based layout analysis. J Inf Syst Oper Manag 8:39–47

    Google Scholar 

  • BoussaiD I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237:82–117

    Article  MathSciNet  MATH  Google Scholar 

  • Burman R, Chakrabarti S, Das S (2016) Democracy-inspired particle swarm optimizer with the concept of peer groups. Soft Comput 21:3267–3286

    Article  Google Scholar 

  • Cho S-B, Kim JH (1995a) Combining multiple neural networks by fuzzy integral for robust classification. IEEE Trans Syst Man Cybern 25(2):380–384

    Article  Google Scholar 

  • Cho S-B, Kim JH (1995b) Multiple network fusion using fuzzy logic. IEEE Trans Neural Netw 6(2):497–501

    Article  Google Scholar 

  • Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Tran Evolut Comput 15(1):4–31

    Article  Google Scholar 

  • Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution—an updated survey. Swarm Evolut Comput 27:1–30

    Article  Google Scholar 

  • Datta D, Figueira JR (2013) A real–integer–discrete-coded differential evolution. Appl Soft Comput 13(9):3884–3893

    Article  Google Scholar 

  • Dorigo M, Stützle T (1999) Ant colony optimization: a new meta-heuristic. In: Proceedings of the congress on evolutionary computation, IEEE Press, p 1470–1477

  • Forestier G, Gançarski P, Wemmert C (2010) Collaborative clustering with background knowledge. Data Knowl Eng 69(2):211–228

    Article  MATH  Google Scholar 

  • Gantovnik VB, Anderson-Cook CM, Gürdal Z, Watson LT (2003) A genetic algorithm with memory for mixed discrete-continuous design optimization. Comput Struct 81(20):2003–2009

    Article  MathSciNet  Google Scholar 

  • Gao J, Li H, Jiao Y-C (2009) Modified differential evolution for the integer programming problems. In: International conference on artificial intelligence and computational intelligence, 2009. AICI’09. IEEE, vol 1, pp 213–219

  • Ghaemi R, Sulaiman Md N, Ibrahim H, Mustapha N et al (2009) A survey: clustering ensembles techniques. World Acad Sci Eng Technol 50:636–645

    Google Scholar 

  • Grabisch M, Nicolas J-M (1994) Classification by fuzzy integral: performance and tests. Fuzzy Sets Syst 65(2–3):255–271

    Article  MathSciNet  Google Scholar 

  • Grim J, Kittler J, Pudil P, Somol P (2001) Information analysis of multiple classifier fusion? In: International workshop on multiple classifier systems, Springer, pp 168–177

  • Ho TK, Hull JJ, Srihari SN (1994) Decision combination in multiple classifier systems. IEEE Trans Pattern Anal Mach Intell 16(1):66–75

    Article  Google Scholar 

  • Inza I, Larrañaga P, Sierra B (2001) Feature subset selection by bayesian networks: a comparison with genetic and sequential algorithms. Int J Approx Reason 27(2):143–164

    Article  MATH  Google Scholar 

  • Kaveh A, Zolghadr A (2014) Democratic pso for truss layout and size optimization with frequency constraints. Comput Struct 130:10–21

    Article  Google Scholar 

  • Kennedy J, Eberhart R C (1997) A discrete binary version of the particle swarm algorithm. In: Systems, man, and cybernetics, 1997. IEEE international conference on computational cybernetics and simulation. IEEE, vol 5, pp 4104–4108

  • Kittler J, Hatef M, Duin RBW, Matas J (1998) On combining classifiers. IEEE Trans Pattern Anal Mach Intell 20(3):226–239

    Article  Google Scholar 

  • Krause J, Cordeiro J, Parpinelli R S, Lopes H S (2013) A survey of swarm algorithms applied to discrete optimization problems. Swarm intelligence and bio-inspired computation: theory and applications. Elsevier, Amsterdam, pp 169–191

    Chapter  Google Scholar 

  • Kuncheva LI (2001) Using measures of similarity and inclusion for multiple classifier fusion by decision templates. Fuzzy Sets Syst 122(3):401–407

    Article  MathSciNet  MATH  Google Scholar 

  • Kuncheva LI (2002) Switching between selection and fusion in combining classifiers: an experiment. IEEE Trans Syst Man Cybern Part B (Cybern) 32(2):146–156

    Article  Google Scholar 

  • Kuncheva LI (2002b) A theoretical study on six classifier fusion strategies. IEEE Trans Pattern Anal Mach Intell 24(2):281–286

    Article  Google Scholar 

  • Kuncheva LI, Bezdek JC, Duin RPW (2001) Decision templates for multiple classifier fusion: an experimental comparison. Pattern Recognit 34(2):299–314

    Article  MATH  Google Scholar 

  • Li H, Zhang L (2014) A discrete hybrid differential evolution algorithm for solving integer programming problems. Eng Optim 46(9):1238–1268

    Article  MathSciNet  Google Scholar 

  • Lu Y (1996) Knowledge integration in a multiple classifier system. Appl Intell 6(2):75–86

    Article  Google Scholar 

  • Moslah O, Hachaïchi Y, Lahbib Y (2016) Democratic inspired particle swarm optimization for multi-robot exploration task

  • Nearchou AC (2008) A differential evolution approach for the common due date early/tardy job scheduling problem. Comput Oper Res 35(4):1329–1343

    Article  MATH  Google Scholar 

  • Pan Q-K, Tasgetiren MF, Liang Y-C (2008) A discrete particle swarm optimization algorithm for the no-wait flowshop scheduling problem. Comput Oper Res 35(9):2807–2839

    Article  MathSciNet  MATH  Google Scholar 

  • Pugh J, Martinoli A (2006) Discrete multi-valued particle swarm optimization. In: Proceedings of IEEE swarm intelligence symposium, number SWIS-CONF-2006–2004, pp 103–110

  • Rahnamayan S, Tizhoosh H R, Salama M MA (2006) Weighted voting-based robust image thresholding. In: 2006 international conference on image processing. IEEE, pp 1129–1132

  • Rogova G (1994) Combining the results of several neural network classifiers. Neural Netw 7(5):777–781

    Article  Google Scholar 

  • Ruta D, Gabrys B (2005) Classifier selection for majority voting. Inf Fusion 6(1):63–81

    Article  MATH  Google Scholar 

  • Strehl A, Ghosh J (2002) Cluster ensembles—a knowledge reuse framework for combining multiple partitions. J Mach Learn Res 2(Dec):583–617

    MathSciNet  MATH  Google Scholar 

  • Tasgetiren M F, Liang Y-C, Sevkli M, Gencyilmaz G (2004) Differential evolution algorithm for permutation flowshop sequencing problem with makespan criterion. In: Proceedings of the 4th international symposium on intelligent manufacturing systems (IMS 2004), Citeseer, Sakarya, pp 442–452

  • Tax D MJ, Van Breukelen M, Duin R PW, Kittler J (2000) Combining multiple classifiers by averaging or by multiplying? Pattern Recognit 33(9):1475–1485

    Article  Google Scholar 

  • Thorp EO (1984) The mathematics of gambling. Gambling Times

  • Williams RJ, Connolly D (2006) Does learning about the mathematics of gambling change gambling behavior? Psychol Addict Behav 20(1):62

    Article  Google Scholar 

  • Wolpert D H, Macready W G (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  • Wu S-J, Pei-Tse C (1994) Genetic algorithms for solving mixed-discrete optimization problems. J Frankl Inst 331(4):381–401

    Article  MATH  Google Scholar 

  • Zaharie D (2003) Control of population diversity and adaptation in differential evolution algorithms. Proc MENDEL 9:41–46

    Google Scholar 

  • Zaheer H, Pant M (2015) A differential evolution approach for solving integer programming problems. In: Proceedings of fourth international conference on soft computing for problem solving, Springer, pp 413–424

  • Zheng LM, Zhang SX, Tang KS, Zheng SY (2017) Differential evolution powered by collective information. Inf Sci 399:13–29

    Article  Google Scholar 

  • Zou D, Gao L, Li S, Wu J (2011) Solving 0–1 knapsack problem by a novel global harmony search algorithm. Appl Soft Comput 11(2):1556–1564

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Electrical, Computer, and Software Engineering, University of Ontario Institute of Technology (UOIT), Oshawa, Canada

    Sedigheh Mahdavi & Shahryar Rahnamayan

  2. Department of Statistics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

    Abbas Mahdavi

Authors
  1. Sedigheh Mahdavi
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  2. Shahryar Rahnamayan
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  3. Abbas Mahdavi
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Correspondence to Shahryar Rahnamayan.

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Communicated by A. Di Nola.

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Mahdavi, S., Rahnamayan, S. & Mahdavi, A. Majority voting for discrete population-based optimization algorithms. Soft Comput 23, 1–18 (2019). https://doi.org/10.1007/s00500-018-3530-1

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