Abstract
The paper incorporates new extensional strategies into the traditional multi-objective optimization algorithms to proficiently obtain the Pareto-optimal solutions in the presence of noise in the fitness landscapes. The first strategy, referred to as adaptive selection of sample size, is employed to assess the trade-off between accuracy in fitness estimation and the associated run-time complexity. The second strategy is concerned with determining statistical expectation of fitness samples, instead of their conventional averaging, as the fitness measure of the trial solutions. The third strategy aims at improving Goldberg’s approach to examine possible accommodation of a seemingly inferior solution in the optimal Pareto front using a more statistically viable comparator. The traditional Non-dominated Sorting Bee Colony algorithm has been ameliorated by extending its selection step with the proposed strategies. Experiments undertaken to study the performance of the proposed algorithm reveal that the extended algorithm outperforms its contenders with respect to four performance metrics, when examined on a test suite of 23 standard benchmarks with additive noise of three statistical distributions.
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Aizawa AN, Wah BW (1993) Dynamic control of genetic algorithms in a noisy environment. In: Proceedings of the fifth international conference on genetic algorithms, pp 48–55
Ayache N (1991) Artificial vision for mobile robots. The MIT Press, Massachusetts
Babbar M, Lakshmikantha A, Goldberg DE (2003) A modified NSGA-II to solve noisy multi-objective problems. In: Proceedings of conference on genetic evolutionary computation
Boonma P, Suzuki J (2009) A confidence-based dominance operator in evolutionary algorithms for noisy multiobjective optimization problems. In: Proceedings of international conference on tools with artificial intelligence, pp 387–394
Box GEP, Muller ME (1958) A note on the generation of random deviates. Ann Math Stat 29:610–611
Branke J, Schmidt C (2003) Selection in the presence of noise. Lecture notes in computer science, vol 2723. In: Cantu-Paz E (ed) Proceedings of genetic and evolutionary computation, pp 766–777
Buche D, Stall P, Dornberger R, Koumoutsakos P (2002) Multiobjective evolutionary algorithm for the optimization of noisy combustion processes. IEEE Trans Syst Man Cybern Part C Appl Rev 32(4):460–473
Bui LT, Abbass HA, Essam D (2005) Fitness inheritance for noisy evolutionary multi-objective optimization. In: Proceedings of the 2005 conference on genetic and evolutionary computation. ACM, pp 779–785
Cáceres LP, Báñez ML, Stützle T (2014) Ant colony optimization on a budget of 1000. In: Swarm intelligence. Lecture Notes in Computer Science, vol 8667, pp 50–61
Coello CAC, Lechuga M (2002) MOPSO: a proposal for multiple objective particle swarm optimization. In: Proceedings of IEEE Congress of evolutionary computation, vol 2, pp 1051–1056
Coello CAC, Veldhuizen DAV, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, New York
Das S, Konar A, Chakraborty UK (2005) Improved differential evolution algorithms for handling noisy optimization problems. In: Proceedings of IEEE Congress of evolutionary computation, vol 2, pp 1691–1698
Deb K, Agrawal S, Pratap A, Meyarivan T (1917) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Lecture notes in computer science, vol 2000, pp 849–858
Fitzpatrick JM, Greffenstette JJ (1994) Genetic algorithms in noisy environments. Mach Learn 3:101–120
Fleischer M (2003) The measure of Pareto optima. Applications to multi-objective metaheuristics. In: Proceedings of second international conference on evolutionary multi-criterion optimization. Lecture Notes in Computer Science. Springer, vol 2632, pp 519–533
Flury B (1997) A first course in multivariate statistics, vol 28. Springer, New York
Hansen N, Niederberger AS, Guzzella L, Koumoutsakos P (2009) A method for handling uncertainty in evolutionary optimization with an application to feedback control of combustion. IEEE Trans Evol Comput 13(1):180–197
Hughes EJ (2001) Evolutionary multi-objective ranking with uncertainty and noise. In: Proceedings of evolutionary multi-criterion optimization, vol 1993
Knowles J, Hughes EJ (2005) Multiobjective optimization on a budget of 250 evaluations. Evolutionary multi-criterion optimization. Springer, Berlin, pp 176–190
Knowles J, Corne D, Reynolds A (2009) Noisy multiobjective optimization on a budget of 250 evaluations. Evolutionary multi-criterion optimization. Springer, Berlin, pp 36–50
Knuth DE (1981) Seminumerical algorithms: The art of computer programming, vol 2. Addison Wesley
Markon S, Arnold D, Back T, Beislstein T, Beyer HG (2001) Thresholding—A selection operator for noisy ES. In: Proceedings of Congress on evolutionary computation, vol 1, pp 465–472
Miller BL, Goldberg DE (1996) Genetic algorithms, selection schemes, and the varying effects of noise. Evol Comput 4(2):113–131
Miller BL (1997) Noise, sampling, and efficient genetic algorithms. Ph. D. dissertation, Dept. of Computer Science, Univ. Illinois at Urbana-Champaign, Urbana. Available as TR 97001
Picek S, Golub M, Jakobovic D (2011) Evaluation of crossover operator performance in genetic algorithms with binary representation. In: Proceedings of the seventh international conference on intelligent computing: bio-inspired computing and applications. Springer, Berlin, pp 223–230
Rakshit P, Konar A, Das S, Jain LC, Nagar AK (2014) Uncertainty management in differential evolution induced multi-objective optimization in presence of measurement noise. IEEE Trans Syst Man Cybern Syst 44(7):922–937
Rakshit P, Sadhu AK, Bhattacharya P, Konar A, Janarthanan R (2011) Multi-robot box-pushing using non-dominated Sorting Bee Colony Optimization Algorithm. In: Proceedings of swarm. Evolutionary and Memetic Computing, Lecture Notes in Computer Science, vol 7076, pp 601–609
Robic T, Philipic B (2005) DEMO: differential evolution for multiobjective optimization. In: Coello Coello CA, Aguirre AH, Zitzler E (eds) Proceedings of the third international conference on evolutionary multi-criterion optimization. Springer Lecture Notes in Computer Science, vol 3410. Guanajuato, pp 520–533
Schott JR (1995) Fault tolerant design using single and multi-criteria genetic algorithm optimization. ME thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts
Sheskin D (2007) Handbook of parametric and nonparametric statistical procedures, 4th edn. Chapman and Hall/CRC
Singh A (2003) Uncertainty based multi-objective optimization of groundwater remediation design. M.S. thesis, Univ. Illinois at Urbana-Champaign, Urbana
Siwik L, Natanek S (2008) Elitist evolutionary multi-agent system in solving noisy multi-objective optimization problems. In: Proceedings of IEEE Congress on evolutionary computation, pp 3319–3326
Stagge P (1998) Averaging efficiently in the presence of noise. In: Eiben AE et al (eds) Proceedings of the fifth international conference on parallel problem solving from nature, LNCS, vol 1498. Springer, Berlin, pp 188–197
Tezuka S (1995) Linear congruential generators. Unif Random Numbers. Springer, US, pp 57–82
Veldhuizen DAV (1999) Multiobjective evolutionary algorithms: classification, analysis, and new innovations. PhD thesis, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, Ohio
Wheeler DJ (1995) Advanced topics in statistical process control, vol 470. SPC Press, Knoxville
Zhang Q, Zhou A, Zhao S, Suganthan PN, Liu W, Tiwari S (2008) Multi-objective optimization test instances for the CEC 2009 special session and competition, Working Report, CES-887. University of Essex, School of Computer Science and Electrical Engineering
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Funding by Council of Scientific and Industrial Research (CSIR) (for awarding Senior Research Fellowship to the first author) and funding by UGC for UPE-II program are gratefully acknowledged for the present work.
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Communicated by V. Loia.
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Rakshit, P., Konar, A. Non-dominated Sorting Bee Colony optimization in the presence of noise. Soft Comput 20, 1139–1159 (2016). https://doi.org/10.1007/s00500-014-1579-z
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DOI: https://doi.org/10.1007/s00500-014-1579-z