Abstract
In this paper, a novel global firefly algorithm (GFA) is proposed for solving randomized time-varying knapsack problems (RTVKP). The RTVKP is an extension from the generalized time-varying knapsack problems (TVKP), by dynamically changing the profit and weight of items as well as the capacity of knapsack. In GFA, two-tuples which consists of real vector and binary vector is used to represent the individual in a population, and two principal search processes are developed: the current global best-based search process and the trust region-based search process. Moreover, a novel and effective two-stage repair operator is adopted to modify infeasible solutions and optimize feasible solutions as well. The performance of GFA is verified by comparison with five state-of-the-art classical algorithms over three RTVKP instances. The results indicate that the proposed GFA outperform the other five methods in most cases and that GFA is an efficient algorithm for solving randomized time-varying knapsack problems.
Similar content being viewed by others
References
Jin Y, Branke J (2005) Evolutionary optimization in uncertain environments—a survey. IEEE Trans Evol Comput 9(3):303–317
Weicker K (2003) Evolutionary algorithms and dynamic optimization problems. Verlag, Der Andere
Morrison RW (2004) Designing evolutionary algorithms for dynamic environments. Springer, Berlin
Krishnakumar K (1990) Micro-genetic algorithms for stationary and non-stationary function optimization//1989 Advances in Intelligent Robotics Systems Conference. In: International Society for Optics Photonics pp 289–296
Dréo J, Siarry P (2006) An ant colony algorithm aimed at dynamic continuous optimization. Appl Math Comput 181(1):457–467
Lepagnot J, Nakib A, Oulhadj H et al (2012) A new multi-agent algorithm for dynamic continuous optimization. Modeling, analysis, and applications in Metaheuristic Computing: advancements and trends: advancements and trends, p 131
Li C, Yang M, Kang L (2006) A new approach to solving dynamic traveling salesman problems. In: Simulated evolution and learning, lecture notes in computer science 4247: pp 236–243
Uyar AS, Harmanci AE (2005) A new population based adaptive domination change mechanism for diploid genetic algorithms in dynamic environments. Soft Comput 9(11):803–814
Goldberg DE, Smith RE (1987) Nonstationary function optimization using genetic algorithms with dominance and diploidy. In: International conference on genetic algorithms. L. Erlbaum Associates Inc, Hillsdale, pp 59–68
He Y, Zhang X, Li W et al (2016) Algorithms for randomized time-varying knapsack problems. J Comb Optim 31(1):95–117
He YC, Wang XZ, Li WB et al (2017) Exact algorithms and evolutionary algorithms for randomized time-varying knapsack problems. J Softw 28(2):185–202
Yang XS, Cui Z, Xiao R et al (2013) Swarm intelligence and bio-inspired computation: theory and applications. Elsevier insights
Eusuff M, Lansey K, Pasha F (2006) Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization. Eng Optim 38(2):129–154
Bhattacharjee KK, Sarmah SP (2014) Shuffled frog leaping algorithm and its application to 0/1 knapsack problem. ApplSoft Comput J 19:252–263
Li X, Zhang J, Yin M (2013) Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput Appl 1–11
Gandomi AH, Yang XS, Alavi AH, Talatahari S (2013) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255
Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483
Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: Proceeding of World Congress on Nature and Biologically Inspired Computing (NaBIC 2009), IEEE Publications, pp 210–214
Wang GG, Guo LH, Wang HQ et al (2014) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl 24(3–4):853–871
Wang GG, Guo LH, Gandomi AH et al (2014) Chaotic krill herd algorithm. Inf Sci 274:17–34
Wang GG, Gandomi AH, Alavi AH (2014) Stud krill herd algorithm. Neurocomputing 128:363–370
Cui ZH, Fan S, Zeng J et al (2013) Artificial plant optimization algorithm with three-period photosynthesis. Int J Bio Inspired Comput 5(2):133–139
Wang GG, Deb S, Cui ZH (2015) Monarch butterfly optimization. Neural Comput Appl. https://doi.org/10.1007/s00521-015-1923-y
Feng YH, Wang G-G, Deb S, Lu M, Zhao XJ (2017) Solving 0–1 knapsack problem by a novel binary monarch butterfly optimization. Neural Comput Appl 28(7):1619–1634
Wang GG, Deb S, Coelho LDS (2015) Earthworm optimization algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Int J Bio Inspired Comput. https://doi.org/10.1504/IJBIC.2015.10004283
Gandomi AH, Yang XS, Alavi AH (2011) Mixed variable structural optimization using Firefly Algorithm. Comput Struct 89(23–24):2325–2336
Karthikeyan S, Asokan P, Nickolas S, Page T (2015) A hybrid discrete firefly algorithm for solving multi-objective flexible job shop scheduling problems. Int J Bio Inspired Comput 7(6):386–401. https://doi.org/10.1504/IJBIC.2015.073165
Yang XS (2008) Nature-inspired metaheuristic algorithms. Luniver
Fister I, Fister I Jr, Yang XS et al (2013) A comprehensive review of firefly algorithms. Swarm Evolut Comput 13:34–46
Baykasoğlu A, Ozsoydan FB (2014) An improved firefly algorithm for solving dynamic multidimensional knapsack problems. Expert Syst Appl 41(8):3712–3725
Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Teoh BE, Ponnambalam SG, Kanagaraj G (2015) Differential evolution algorithm with local search for capacitated vehicle routing problem. Int J Bio Inspired Comput 7(5):321–342. https://doi.org/10.1504/IJBIC.2015.072260
Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs. Springer, Berlin
Dantzig GB (1957) Discrete variable extremum problems. Oper Res 5(2):266–288
Du DZ, Ko KI (2011) Theory of computational complexity. Wiley, Hoboken
Brassard G, Bratley P (1996) Fundamentals of algorithmics. Prentice Hall, Englewood Cliffs
Pisinger D (1995) Algorithms for knapsack problems. N-Holl Math Stud 132:213–257
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceeding of the IEEE International Conference on Neural Networks, pp 1942–1948
Zou D, Gao L, Li S et al (2011) Solving 0–1 knapsack problem by a novel global harmony search algorithm. Appl Soft Comput J 11(2):1556–1564
He YC, Wang XZ, Kou YZ (2007) A binary differential evolution algorithm with hybrid encoding. J Comput Res Dev 44(9):1476–1484
Feng Y, Jia K, He Y (2014) An improved hybrid encoding cuckoo search algorithm for 0–1 knapsack problems. Comput Intell Neurosci 2014(2):970456. https://doi.org/10.1155/2014/970456
Wilcoxon F (1945) Individual comparisons by ranking methods. Biom Bull 1(6):80–83
Wilcoxon F, Katti SK, Wilcox RA (1970) Critical values and probability levels for the Wilcoxon rank sum test and the Wilcoxon signed rank test. Sel Tables Math Stat 1:171–259
Bhattacharjee KK, Sarmah SP (2015) A binary firefly algorithm for knapsack problems// Industrial Engineering and Engineering Management (IEEM), 2015 IEEE International Conference on IEEE
Joines JA, Houck CR (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA’s//Evolutionary Computation, 1994. IEEE World Congress on Computational Intelligence. In: Proceedings of the First IEEE Conference on. IEEE, pp 579–584
Olsen AL (1994) Penalty functions and the knapsack problem//Evolutionary Computation, 1994. IEEE World Congress on Computational Intelligence. Proceedings of the First IEEE Conference on IEEE, pp 554–558
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Boston
Simon D (2013) Evolutionary optimization algorithms. Wiley, New York
He YC, Song JM, Zhang JM et al (2015) Research on genetic algorithms for solving static and dynamic knapsack problems. Appl Res Comput 32(4):1011–1015
He YC, Wang XZ, He YL et al (2016) Exact and approximate algorithms for discounted {0–1 knapsack problem. Inf Sci 369:634–647
Feng Y, Wang G-G, Li W, Li N (2017) Multi-strategy monarch butterfly optimization algorithm for discounted {0–1} knapsack problem. Neural Comput Appl. https://doi.org/10.1007/s00521-017-2903-1
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 61503165, No. 61402207, No. 61673196, No. 61772225), Natural Science Foundation of Jiangsu Province (No. BK20150239), and National Natural Science Fund for Distinguished Young Scholars of China (No. 61525304).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Feng, Y., Wang, GG. & Wang, L. Solving randomized time-varying knapsack problems by a novel global firefly algorithm. Engineering with Computers 34, 621–635 (2018). https://doi.org/10.1007/s00366-017-0562-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-017-0562-6