Abstract
In this paper, a new modified version of the flower pollination algorithm based on the crossover for solving the multidimensional knapsack problems called (MFPA) is proposed. MFPA uses the sigmoid function as a discretization method to deal with the discrete search space. The penalty function is added to the evaluation function to recognize the infeasible solutions and assess them. A two-stage procedure is called FRIO is used to treat the infeasible solutions. MFPA uses an elimination procedure to decrease any duplication in the population in order to increase the diversity. The proposed algorithm is verified on a set of benchmark instances, and a comparison with other algorithms available in literature is shown. Several statistical and descriptive analysis was done such as recoding the results of the best, mean, worst, standard deviation, success rate, and time to prove the effectiveness and robustness of MFPA. The empirical results show that the proposed algorithm can be an effective algorithm as human-centric decision-making model for solving the multidimensional knapsack problems.
Similar content being viewed by others
References
Azad M, Abul K, Ana M, Rocha AC, Fernandes P, Edite MG (2014) Improved binary artificial fish swarm algorithm for the 0–1 multidimensional knapsack problems. Swarm Evolut Comput 14:66–75
Azad M, Abul K, Ana M, Rocha AC, Fernandes P, Edite MG (2015) Solving large 0–1 multidimensional knapsack problems by a new simplified binary artificial fish swarm algorithm. J Math Model Algorithms Oper Res 14(3):313–330
Beasley JE (2005) ORLib—operations research library. http://people.brunel.ac.uk/_mastjjb/jeb/orlib/mknapinfo.html
Beheshti Z, Shamsuddin SM, Yuhaniz SS (2013) Binary accelerated particle swarm algorithm (BAPSA) for discrete optimization problems. J Global Optim 57(2):549–573
Beheshti Z, Shamsuddin SM, Hasan S (2015) Memetic binary particle swarm optimization for discrete optimization problems. Inf Sci 299:58–84
Carlos BP et al (2010) A solution to multidimensional knapsack problem using a parallel genetic algorithm. Int J Intell Inf Process 1(2):47–54
Chih M (2015) Self-adaptive check and repair operator-based particle swarm optimization for the multidimensional knapsack problem. Appl Soft Comput 26:378–389
Chih M et al (2014) Particle swarm optimization with time-varying acceleration coefficients for the multidimensional knapsack problem. Appl Math Model 38(4):1338–1350
Chu PC, Beasley JE (1998) A genetic algorithm for the multidimensional knapsack problem. J Heurist 4(1):63–86
De Vries S, Vohra RV (2003) Combinatorial auctions: a survey. INFORMS J Comput 15(3):284–309
Fingler H et al (2014) A CUDA based solution to the multidimensional knapsack problem using the ant colony optimization. Proc Comput Sci 29:84–94
Gherboudj A, Labed S, Chikhi S (2012) A new hybrid binary particle swarm optimization algorithm for multidimensional knapsack problem. In: Wyld D, Zizka J, Nagamalai D (eds) Advances in computer science, engineering and applications. Springer, Berlin, pp 489–498
Gilmore P, Gomory R (1966) The theory and computation of knapsack functions. Oper Res 14:1045–1074
Güler A, Berberler ME, Nuriyev U (2016) A new genetic algorithm for the 0–1 knapsack problem. Acad Platf J Eng Sci 4(3):9–14
Haddar B et al (2016) A hybrid quantum particle swarm optimization for the multidimensional knapsack problem. Eng Appl Artif Intell 55:1–13
Hembecker F, Lopes HS, Godoy W Jr (2007) Particle swarm optimization for the multidimensional knapsack problem. In: International conference on adaptive and natural computing algorithms. Springer, Berlin
Horng M-H (2012) Vector quantization using the firefly algorithm for image compression. Exp Syst Appl 39(1):1078–1091
Kong M, Tian P (2006) Apply the particle swarm optimization to the multidimensional knapsack problem. In: International conference on artificial intelligence and soft computing. Springer, Berlin
Labed S, Gherboudj A, Chikhi S (2011) A modified hybrid particle swarm optimization algorithm for multidimensional knapsack problem. Int J Comput Appl 34(2):1
Layeb A (2013) A hybrid quantum inspired harmony search algorithm for 0–1 optimization problems. J Comput Appl Math 253:14–25
Layeb A, Boussalia SR (2012) A novel quantum inspired cuckoo search algorithm for bin packing problem. Int J Inf Technol Comput Sci (IJITCS) 4(5):58
Liu J et al (2016) A Binary differential search algorithm for the 0–1 multidimensional knapsack problem. Appl Math Model 40(23):9788–9805
Mansini R, Speranza MG (1999) Heuristic algorithms for the portfolio selection problem with minimum transaction lots. Eur J Oper Res 114(2):219–233
Mantegna RN (1994) Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes. Phys Rev E 49(5):4677
Medhane DV, Sangaiah AK (2017) Search space-based multi-objective optimization evolutionary algorithm. Comput Electr Eng 58:126–143
Meng T, Pan Q-K (2017) An improved fruit fly optimization algorithm for solving the multidimensional knapsack problem. Appl Soft Comput 50:79–93
Nakbi W, Alaya I, Zouari W (2015) A Hybrid Lagrangian search ant colony optimization algorithm for the multidimensional knapsack problem. Proc Comput Sci 60:1109–1119
Pirkul H (1987) A heuristic solution procedure for the multiconstraint zero? one knapsack problem. Naval Res Log 34(2):161–172
Ratanavilisagul C, Kruatrachue AB (2014) A modified particle swarm optimization with mutation and reposition. Int J Innov Comput Inform Control 10(6):2127–2142
Sabba S, Chikhi S (2014) A discrete binary version of bat algorithm for multidimensional knapsack problem. Int J Bioinspir Comput 6(2):140–152
Salman AA, Ahmad I, Omran MGH (2016) Stochastic diffusion binary differential evolution to solve multidimensional knapsack problem. Int J Mach Learn Comput 6(2):130
Samuel OW, Asogbon GM, Sangaiah AK, Fang P, Li G (2017) An integrated decision support system based on ANN and fuzzy_AHP for heart failure risk prediction. Exp Syst Appl 68:163–172
Sangaiah AK, Thangavelu AK, Gao XZ, Anbazhagan N, Durai MS (2015) An ANFIS approach for evaluation of team-level service climate in GSD projects using Taguchi-genetic learning algorithm. Appl Soft Comput 30:628–635
Wang L et al (2008) A novel probability binary particle swarm optimization algorithm and its application. J Softw 3(9):28–35
Weingartner HM (1966) Capital budgeting of interrelated projects: survey and synthesis. Manag Sci 12(7):485–516
Yang, X-S (2012) Flower pollination algorithm for global optimization. In: International conference on unconventional computing and natural computation. Springer, Berlin
Zan D, Jaros J (2014) Solving the multidimensional knapsack problem using a CUDA accelerated PSO. In: 2014 IEEE congress on evolutionary computation (CEC). IEEE
Zhang B et al (2015) An effective hybrid harmony search-based algorithm for solving multidimensional knapsack problems. Appl Soft Comput 29:288–297
Zhang X et al (2016) Binary artificial algae algorithm for multidimensional knapsack problems. Appl Soft Comput 43:583–595
Zouache D, Nouioua F, Moussaoui A (2016) Quantum-inspired firefly algorithm with particle swarm optimization for discrete optimization problems. Soft Comput 20(7):2781–2799
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All authors declare that they have no conflict of interest.
Human participants or animals
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent
Informed consent was obtained from all individual participants included in the study.
Additional information
Communicated by J. Park.
Rights and permissions
About this article
Cite this article
Abdel-Basset, M., El-Shahat, D., El-Henawy, I. et al. A modified flower pollination algorithm for the multidimensional knapsack problem: human-centric decision making. Soft Comput 22, 4221–4239 (2018). https://doi.org/10.1007/s00500-017-2744-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-017-2744-y