Abstract
An important problem in the study of evolutionary algorithms is how to continuously predict promising solutions while simultaneously escaping from local optima. In this paper, we propose an elitist probability schema (EPS) for the first time, to the best of our knowledge. Our schema is an index of binary strings that expresses the similarity of an elitist population at every string position. EPS expresses the accumulative effect of fitness selection with respect to the coding similarity of the population. For each generation, EPS can quantify the coding similarity of the population objectively and quickly. One of our key innovations is that EPS can continuously predict promising solutions while simultaneously escaping from local optima in most cases. To demonstrate the abilities of the EPS, we designed an elitist probability schema genetic algorithm and an elitist probability schema compact genetic algorithm. These algorithms are estimations of distribution algorithms (EDAs). We provided a fair comparison with the persistent elitist compact genetic algorithm (PeCGA), quantum-inspired evolutionary algorithm (QEA), and particle swarm optimization (PSO) for the 0–1 knapsack problem. The proposed algorithms converged quicker than PeCGA, QEA, and PSO, especially for the large knapsack problem. Furthermore, the computation time of the proposed algorithms was less than some EDAs that are based on building explicit probability models, and was approximately the same as QEA and PSO. This is acceptable for evolutionary algorithms, and satisfactory for EDAs. The proposed algorithms are successful with respect to convergence performance and computation time, which implies that EPS is satisfactory.
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Holland JH (1975) Adaptation in natural and artificial systems. MIT Press, Cambridge
Goldberg DE, Korb B, Deb K (1989) Messy genetic algorithm: motivation, analysis, and first results. Complex Syst 3:493–530
Kenneth P (1997) Differential evolution vs. the functions of the 2nd ICEO. In: Proc ICEC’97, pp 153–157
Rainer S, Kenneth P (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 4:341–359
Fogel LJ (1964) On the organization of intellect. Dissertation, University of California
Alipouri Y, Poshtan J et al (2013) A modification to classical evolutionary programming by shifting strategy parameters. Appl Intell 38:175–192
Liang KH, Yao X, Newton CS (2001) Adapting self-adaptive parameters in evolutionary algorithms. Appl Intell 15:171–180
Glover F, Taillard E, Werra DD (1993) A user’s guide to tabu search. Ann Oper Res 41:1–28
Laguna M, Barnes JW, Glover F (1993) Intelligent scheduling with tabu search: an application to jobs with linear delay penalties and sequence-dependent setup costs and times. Appl Intell 3:159–172
Hedar AR, Ali AF (2012) Tabu search with multi-level neighborhood structures for high dimensional problems. Appl Intell 37:189–206
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proc IEEE int conf neural netw, pp 1942–1948
Kennedy J, Eberhart R (1997) A discrete binary version of the particle swarm algorithm. In: Proc IEEE int conf syst man cybern, pp 4104–4108
Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1:33–57
Hasanzadeh M, Meybodi MR, Ebadzadeh MM (2013) Adaptive cooperative particle swarm optimizer. Appl Intell 39:397–420
Birattari M, Pellegrini P, Dorigo M (2007) On the invariance of ant colony optimization. IEEE Trans Evol Comput 11:732–742
Dekkers A, Aarts E (1991) Global optimization and simulated annealing. Math Program 50:367–393
Han KH, Park KH, Lee CH, Kim JH (2001) Parallel quantum-inspired genetic algorithm for combinatorial optimization problem. In: Proc ICEC’01, pp 1422–1429
Han KH, Kim JH (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6:580–593
Han KH, Kim JH (2003) On setting the parameters of quantum-inspired evolutionary algorithm for practical application. In: Proc ICEC’03, pp 178–194
Han KH (2003) Quantum-inspired evolutionary algorithm. Dissertation, Korea Advanced Institute of Science and Technology
Glover F, Laguna M, Martí R (2000) Fundamentals of scatter search and path relinking. Control Cybern 29:653–684
Martí R, Laguna M, Glover F (2006) Principles of scatter search. Eur J Oper Res 169:359–372
Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 22:52–67
Lam AYS, Li VOK (2010) Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans Evol Comput 14:381–399
Lam AYS, Li VOK (2012) Chemical reaction optimization: a tutorial. Memetic Comp 4:3–17
Truong TK, Li KL, Xu YM (2013) Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem. Appl Soft Comput 13:1774–1780
Mühlenbein H, Paass G (1996) From recombination of genes to the estimation of distributions I. Binary parameters. In: Proc int conf evol comput parallel problem solving from nature—PPSN IV, pp 178–187
De Bonet JS, Lsbell CL, Viola JP (1997) MIMIC: finding optima by estimating probability densities. Adv Neural Inf Process Syst 9:424–431
Baluja S, Davies S (1997) Using optimal dependency-trees for combinatorial optimization: learning the structure of the search space. In: Proc int conf mach learn, pp 30–38
Baluja S, Davies S (1998) Fast probabilistic modeling for combinatorial optimization. In: Proc 15th national conf artif intell, pp 469–476
Pelikan M, Mühlenbein H (1999) The bivariate marginal distribution algorithm. In: Advances in soft computing—engineering design and manufacturing, pp 521–535
Mühlenbein H, Mahnig T, Rodriguez A (1999) Schemata, distributions and graphical models in evolutionary optimization. J Heuristics 5:215–247
Harik GR, Cantú-Paz E, Goldberg DE et al (1999) The gambler’s ruin problem, genetic algorithms, and the sizing of populations. Evol Comput 7:231–253
Harik GR, Lobo FG, Goldberg DE et al (1999) The compact genetic algorithm. IEEE Trans Evol Comput 3:287–297
Sastry K, Goldberg DE (2000) On extended compact genetic algorithm. IIIiGAL Report No. 2000026, Illinois Genetic Algorithms Lab
Ahn CW, Ramakrishna RS (2003) Elitism-based compact genetic algorithms. IEEE Trans Evol Comput 7:367–385
Lee JY, Kim MS, Lee JJ (2011) Compact genetic algorithms using belief vectors. Appl Soft Comput 11:3385–3401
Pelikan M, Goldberg DE, Cantú-paz EE (2000) Linkage problem, distribution estimation, and Bayesian networks. Evol Comput 8:311–340
Pelikan M, Goldberg DE, Lobo FG (2002) A survey of optimization by building and using probabilistic models. Comput Optim Appl 21:5–20
Kang MH, Choi HR, Kim HS, Park BJ (2012) Development of a maritime transportation planning support system for car carriers based on genetic algorithm. Appl Intell 36:585–604
Cho JH, Kim HS, Choi HR (2012) An intermodal transport network planning algorithm using dynamic programming—a case study: from Busan to Rotterdam in intermodal freight routing. Appl Intell 36:529–541
Brunel University website (2013). http://people.brunel.ac.uk/~mastjjb/jeb/info.html
Florida State University website (2013). http://people.sc.fsu.edu/~jburkardt/datasets/knapsack_01/knapsack_01.html
Kreher DL, Stinson DR (1998) Combinatorial algorithms: generation, enumeration and search. CRC Press, Boca Raton
Martello S, Toth P (1990) Knapsack problem: algorithms and computer implementations. Wiley, New York
University of Copenhagen website (2013). http://www.diku.dk/~pisinger/gen2.c
Martello S, Pisinger D, Toth P (1999) Dynamic programming and strong bounds for the 0–1 knapsack problem. Manag Sci 45:414–424
Pisinger D (1999) Core problems in knapsack algorithms. Oper Res 47:570–575
Kumar R, Singh PK (2010) Assessing solution quality of biobjective 0–1 knapsack problem using evolutionary and heuristic algorithms. Appl Soft Comput 10:711–718
Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Dissertation, Swiss Federal Institute of Technology Zurich
Acknowledgements
The authors would like to thank the anonymous reviewers for their careful reading and constructive comments. This work was supported by National Natural Science Foundation of China (Grant No. 61272518, 61272516, 61170275), National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2012ZX03001001-002), and Guangdong Provincial Science and Technology Project (Grant No. 2011B090400433).
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Zhang, HG., Liu, YA., Tang, BH. et al. An exploratory research of elitist probability schema and its applications in evolutionary algorithms. Appl Intell 40, 695–709 (2014). https://doi.org/10.1007/s10489-013-0494-9
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DOI: https://doi.org/10.1007/s10489-013-0494-9