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Erschienen in: Soft Computing 8/2015

01.08.2015 | Methodologies and Application

A novel optimization hardness indicator based on the relationship between optimization hardness and frequency features of real-parameter problems

verfasst von: Kun Li, Ming Li, Hao Chen

Erschienen in: Soft Computing | Ausgabe 8/2015

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Abstract

For evolutionary algorithms with the ability to self-adapt, linking the algorithmic operators and the problem features is one of the most interesting topics. One of the best ways to begin a study of this topic is to explore the relationship between the optimization hardness and the problem features. This paper attempts to interpret the relationship between optimization hardness and frequency features of real-parameter problems through a qualitative analysis based on an idealized model. Based on the results of a theoretically qualitative analysis, the effective high-frequency ratio (EHFR) is subsequently proposed to measure the optimization hardness of real-parameter problems. Finally, three aspects to the performance of EHFR are evaluated: stability, precision and ability to distinguish. Test results show that the EHFR is relevant not only for the results of theoretical analysis, but also for the other features related to the optimization hardness.

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Literatur
Zurück zum Zitat Auger A, Teytaud O (2007) Continuous Lunches are Free! Gecco 2007: genetic and evolutionary computation conference, vol 1 and 2, pp 916–922 Auger A, Teytaud O (2007) Continuous Lunches are Free! Gecco 2007: genetic and evolutionary computation conference, vol 1 and 2, pp 916–922
Zurück zum Zitat Bao Y, Hu Z, Xiong T (2013) A PSO and pattern search based memetic algorithm for SVMs parameters optimization. Neurocomputing 117:98–106CrossRef Bao Y, Hu Z, Xiong T (2013) A PSO and pattern search based memetic algorithm for SVMs parameters optimization. Neurocomputing 117:98–106CrossRef
Zurück zum Zitat Beyer H-G (2000) Evolutionary algorithms in noisy environments: theoretical issues and guidelines for practice. Computer Methods Appl Mech Eng 186(2–4):239–267CrossRef Beyer H-G (2000) Evolutionary algorithms in noisy environments: theoretical issues and guidelines for practice. Computer Methods Appl Mech Eng 186(2–4):239–267CrossRef
Zurück zum Zitat Borenstein Y, Poli R (2005) Information landscapes. In: Proceedings of the 2005 conference on genetic and evolutionary computation. ACM, Washington, DC, pp 1515–1522 Borenstein Y, Poli R (2005) Information landscapes. In: Proceedings of the 2005 conference on genetic and evolutionary computation. ACM, Washington, DC, pp 1515–1522
Zurück zum Zitat Caraffini F, Neri F, Picinali L (2014) An analysis on separability for memetic computing automatic design. Inf Sci 265:1–22MathSciNetCrossRef Caraffini F, Neri F, Picinali L (2014) An analysis on separability for memetic computing automatic design. Inf Sci 265:1–22MathSciNetCrossRef
Zurück zum Zitat Chan KY, Aydin ME, Fogarty TC (2003) An epistasis measure based on the analysis of variance for the realcoded representation in genetic algorithms. In: Cec: 2003 Congress on evolutionary computation, vol 1–4, proceedings, pp 297–304 Chan KY, Aydin ME, Fogarty TC (2003) An epistasis measure based on the analysis of variance for the realcoded representation in genetic algorithms. In: Cec: 2003 Congress on evolutionary computation, vol 1–4, proceedings, pp 297–304
Zurück zum Zitat Chen J, Xin B, Peng Z, Dou L, Zhang J (2009) Optimal contraction theorem for exploration–exploitation tradeoff in search and optimization. IEEE Trans Syst Man Cybernet Part A—Syst Hum 39(3):680–691CrossRef Chen J, Xin B, Peng Z, Dou L, Zhang J (2009) Optimal contraction theorem for exploration–exploitation tradeoff in search and optimization. IEEE Trans Syst Man Cybernet Part A—Syst Hum 39(3):680–691CrossRef
Zurück zum Zitat Cook Z, Franks DW, Robinson EJH (2013) Exploration versus exploitation in polydomous ant colonies. J Theor Biol 323:49–56CrossRef Cook Z, Franks DW, Robinson EJH (2013) Exploration versus exploitation in polydomous ant colonies. J Theor Biol 323:49–56CrossRef
Zurück zum Zitat Corne D, Oates M, Kell D (2003) Landscape state machines: tools for evolutionary algorithm performance analyses and landscape/algorithm mapping. In: Raidl G, Coimbra CS (eds) Applications of evolutionary computing, vol 2611. Springer, Portugal, pp 187–198 Corne D, Oates M, Kell D (2003) Landscape state machines: tools for evolutionary algorithm performance analyses and landscape/algorithm mapping. In: Raidl G, Coimbra CS (eds) Applications of evolutionary computing, vol 2611. Springer, Portugal, pp 187–198
Zurück zum Zitat Crepinsek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3):1–33CrossRef Crepinsek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3):1–33CrossRef
Zurück zum Zitat Davidor Y, Schwefel HP, Manner R (1991) Epistasis variance: a viewpoint on GA-hardness In foundations of genetic algorithms. Morgan Kauffman, San Mateo Davidor Y, Schwefel HP, Manner R (1991) Epistasis variance: a viewpoint on GA-hardness In foundations of genetic algorithms. Morgan Kauffman, San Mateo
Zurück zum Zitat Gibbs MS, Maier HR, Dandy GC (2011) Relationship between problem characteristics and the optimal number of genetic algorithm generations. Eng Optim 43(4):349–376CrossRef Gibbs MS, Maier HR, Dandy GC (2011) Relationship between problem characteristics and the optimal number of genetic algorithm generations. Eng Optim 43(4):349–376CrossRef
Zurück zum Zitat González RC, Woods RE (2002) Digital image processing, 2nd edn. Prentice Hall, Upper Saddle River González RC, Woods RE (2002) Digital image processing, 2nd edn. Prentice Hall, Upper Saddle River
Zurück zum Zitat He J, Yao X (2001) Drift analysis and average time complexity of evolutionary algorithms. Artif Intell 127(1):57–85MathSciNetCrossRef He J, Yao X (2001) Drift analysis and average time complexity of evolutionary algorithms. Artif Intell 127(1):57–85MathSciNetCrossRef
Zurück zum Zitat He J, Yao X (2003) An analysis of evolutionary algorithms for finding approximation solutions to hard optimisation problems. In: Cec: 2003 Congress on evolutionary computation, vol 1–4, proceedings, pp 2004–2010 He J, Yao X (2003) An analysis of evolutionary algorithms for finding approximation solutions to hard optimisation problems. In: Cec: 2003 Congress on evolutionary computation, vol 1–4, proceedings, pp 2004–2010
Zurück zum Zitat He J, Yao X (2003) Towards an analytic framework for analysing the computation time of evolutionary algorithms. Artif Intell 145(1–2):59–97MathSciNetCrossRef He J, Yao X (2003) Towards an analytic framework for analysing the computation time of evolutionary algorithms. Artif Intell 145(1–2):59–97MathSciNetCrossRef
Zurück zum Zitat Hofmann K, Whiteson S, De Rijke M (2013) Balancing exploration and exploitation in listwise and pairwise online learning to rank for information retrieval. Inf Retrieval 16(1):63–90CrossRef Hofmann K, Whiteson S, De Rijke M (2013) Balancing exploration and exploitation in listwise and pairwise online learning to rank for information retrieval. Inf Retrieval 16(1):63–90CrossRef
Zurück zum Zitat Horn J, Goldberg DE (1994) Genetic algorithm difficulty and the modality of fitness landscapes. In: Foundations of genetic algorithms. Morgan Kaufmann, pp 243–269 Horn J, Goldberg DE (1994) Genetic algorithm difficulty and the modality of fitness landscapes. In: Foundations of genetic algorithms. Morgan Kaufmann, pp 243–269
Zurück zum Zitat Igel C, Toussaint M (2004) A No-Free-Lunch theorem for non-uniform distributions of target functions. J Math Model Alg 3:313– 322 Igel C, Toussaint M (2004) A No-Free-Lunch theorem for non-uniform distributions of target functions. J Math Model Alg 3:313– 322
Zurück zum Zitat Jin Y, Branke H (2005) Evolutionary optimization in uncertain environments—a survey. IEEE Trans Evol Comput 9(3):303– 317 Jin Y, Branke H (2005) Evolutionary optimization in uncertain environments—a survey. IEEE Trans Evol Comput 9(3):303– 317
Zurück zum Zitat Jones T (1996) One Operator one landscape, vol 15. Technical Reports 95-02-025, Santa Fe Institute Jones T (1996) One Operator one landscape, vol 15. Technical Reports 95-02-025, Santa Fe Institute
Zurück zum Zitat Jones T, Forrest S (1995) Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of the 6th International Conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp 184–192 Jones T, Forrest S (1995) Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of the 6th International Conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp 184–192
Zurück zum Zitat Kallel L, Naudts B, Reeves CR (2001) Properties of fitness functions and search landscapes. In: Kallel L, Naudts B, Rogers A (eds) Theoretical aspects of evolutionary computing. Springer, Berlin, pp 175– 206 Kallel L, Naudts B, Reeves CR (2001) Properties of fitness functions and search landscapes. In: Kallel L, Naudts B, Rogers A (eds) Theoretical aspects of evolutionary computing. Springer, Berlin, pp 175– 206
Zurück zum Zitat Kauffman S, Levin S (1987) Towards a general theory of adaptive walks on rugged landscapes. J Theor Biol 128(1):11–45MathSciNetCrossRef Kauffman S, Levin S (1987) Towards a general theory of adaptive walks on rugged landscapes. J Theor Biol 128(1):11–45MathSciNetCrossRef
Zurück zum Zitat Khor S (2009) Exploring the influence of problem structural characteristics on evolutionary algorithm performance. In: 2009 IEEE Congress on evolutionary computation, vol 1–5. IEEE, Trondheim, pp 3345–3352 Khor S (2009) Exploring the influence of problem structural characteristics on evolutionary algorithm performance. In: 2009 IEEE Congress on evolutionary computation, vol 1–5. IEEE, Trondheim, pp 3345–3352
Zurück zum Zitat Levitan B, Kauffman S (1995) Adaptive walks with noisy fitness measurements. Mol Divers 1(1):53–68CrossRef Levitan B, Kauffman S (1995) Adaptive walks with noisy fitness measurements. Mol Divers 1(1):53–68CrossRef
Zurück zum Zitat Li J (2003) Research on fitness landscapes of genetic algorithms and GA-hardness. Tianjin University, Tian Jin Li J (2003) Research on fitness landscapes of genetic algorithms and GA-hardness. Tianjin University, Tian Jin
Zurück zum Zitat Li K, Li M, Chen H (2013) An estimation method of optimal feature factor based on the balance of exploration and exploitation. In: Information and automation (ICIA), IEEE International Conference on 2013 Li K, Li M, Chen H (2013) An estimation method of optimal feature factor based on the balance of exploration and exploitation. In: Information and automation (ICIA), IEEE International Conference on 2013
Zurück zum Zitat Lipsitch M (1991) Adaptation on rugged landscapes generated by local interactions of neighboring genes. In: Belew RK, Booker LB (eds) Proceedings of the 4th International Conference on genetic algorithms. Morgan Kaufmann, San Diego, pp 128–135 Lipsitch M (1991) Adaptation on rugged landscapes generated by local interactions of neighboring genes. In: Belew RK, Booker LB (eds) Proceedings of the 4th International Conference on genetic algorithms. Morgan Kaufmann, San Diego, pp 128–135
Zurück zum Zitat Malan KM, Engelbrecht AP (2009) Quantifying ruggedness of continuous landscapes using entropy. In: 2009 IEEE Congress on evolutionary computation, vol 1–5. Trondheim, Norway, pp 1440– 1447 Malan KM, Engelbrecht AP (2009) Quantifying ruggedness of continuous landscapes using entropy. In: 2009 IEEE Congress on evolutionary computation, vol 1–5. Trondheim, Norway, pp 1440– 1447
Zurück zum Zitat Malan KM, Engelbrecht AP (2013) A survey of techniques for characterising fitness landscapes and some possible ways forward. Inf Sci 241:148–163CrossRef Malan KM, Engelbrecht AP (2013) A survey of techniques for characterising fitness landscapes and some possible ways forward. Inf Sci 241:148–163CrossRef
Zurück zum Zitat Merz P, Freisleben B (2000) Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans Evol Comput 4(4):337–352CrossRef Merz P, Freisleben B (2000) Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans Evol Comput 4(4):337–352CrossRef
Zurück zum Zitat Merz P, Freisleben B (2000) Fitness landscapes, memetic algorithms, and Greedy operators for graph bipartitioning. Evol Comput 8(1):61–91CrossRef Merz P, Freisleben B (2000) Fitness landscapes, memetic algorithms, and Greedy operators for graph bipartitioning. Evol Comput 8(1):61–91CrossRef
Zurück zum Zitat Merz P, Freisleben B (2001) Memetic algorithms for the traveling salesman problem. Complex Syst 13(4):279–345 Merz P, Freisleben B (2001) Memetic algorithms for the traveling salesman problem. Complex Syst 13(4):279–345
Zurück zum Zitat Molina D, Herrera F, Lozano M (2005) Adaptive local search parameters for real-coded memetic algorithms. In: Evolutionary computation, 2005. The 2005 IEEE Congress Molina D, Herrera F, Lozano M (2005) Adaptive local search parameters for real-coded memetic algorithms. In: Evolutionary computation, 2005. The 2005 IEEE Congress
Zurück zum Zitat Naudts B, Kallel L (2000) A comparison of predictive measures of problem difficulty in evolutionary algorithms. IEEE Trans Evol Comput 4(1):1–15CrossRef Naudts B, Kallel L (2000) A comparison of predictive measures of problem difficulty in evolutionary algorithms. IEEE Trans Evol Comput 4(1):1–15CrossRef
Zurück zum Zitat Naudts B, Suys D, Verschoren A (1997) Epistasis as a basic concept in formal landscape analysis. In: Proceedings of the 7th International Conference on genetic algorithms. Morgan Kaufmann, pp 65–72 Naudts B, Suys D, Verschoren A (1997) Epistasis as a basic concept in formal landscape analysis. In: Proceedings of the 7th International Conference on genetic algorithms. Morgan Kaufmann, pp 65–72
Zurück zum Zitat Neri F, Cotta C (2012) Memetic algorithms and memetic computing optimization: a literature review. Swarm Evol Comput 2:1–14CrossRef Neri F, Cotta C (2012) Memetic algorithms and memetic computing optimization: a literature review. Swarm Evol Comput 2:1–14CrossRef
Zurück zum Zitat Neri F, Cotta C, Moscato P (2012) Handbook of memetic algorithm. Springer, Berlin, HeidelbergCrossRef Neri F, Cotta C, Moscato P (2012) Handbook of memetic algorithm. Springer, Berlin, HeidelbergCrossRef
Zurück zum Zitat Neri F, Mininno E, Lacca G (2013) Compact particle swarm optimization. Inf Sci 239:96–121CrossRef Neri F, Mininno E, Lacca G (2013) Compact particle swarm optimization. Inf Sci 239:96–121CrossRef
Zurück zum Zitat Nguyen QH, Ong YS, Krasnogor N (2007) A study on the design issues of memetic algorithm. In: Evolutionary computation, 2007. CEC 2007. IEEE Congress Nguyen QH, Ong YS, Krasnogor N (2007) A study on the design issues of memetic algorithm. In: Evolutionary computation, 2007. CEC 2007. IEEE Congress
Zurück zum Zitat Ong Y-S, Lim M-H, Chen X (2010) Memetic computation: past, present and future (Research Frontier). Comput Intell Mag IEEE 5(2):24–31CrossRef Ong Y-S, Lim M-H, Chen X (2010) Memetic computation: past, present and future (Research Frontier). Comput Intell Mag IEEE 5(2):24–31CrossRef
Zurück zum Zitat Ong Y-S, Lim M-H, Zhu N, Wong K-W (2006) Classification of adaptive memetic algorithms: a comparative study. Syst Man Cybernet Part B: Cybernet IEEE Trans 36(1):141–152CrossRef Ong Y-S, Lim M-H, Zhu N, Wong K-W (2006) Classification of adaptive memetic algorithms: a comparative study. Syst Man Cybernet Part B: Cybernet IEEE Trans 36(1):141–152CrossRef
Zurück zum Zitat Oppenheim AV, Willsky AS, Hamid S (1996) Signals and systems. Prentice Hall, Upper Saddle River, New Jersey, US Oppenheim AV, Willsky AS, Hamid S (1996) Signals and systems. Prentice Hall, Upper Saddle River, New Jersey, US
Zurück zum Zitat Piotrowski AP (2013) Adaptive memetic differential evolution with global and local neighborhood-based mutation operators. Inf Sci 241:164–194CrossRef Piotrowski AP (2013) Adaptive memetic differential evolution with global and local neighborhood-based mutation operators. Inf Sci 241:164–194CrossRef
Zurück zum Zitat Reeves CR, Wright CC (1995) Epistasis in genetic algorithms: an experimental design perspective. In: Proceedings of the 6th International Conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp 217–224 Reeves CR, Wright CC (1995) Epistasis in genetic algorithms: an experimental design perspective. In: Proceedings of the 6th International Conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp 217–224
Zurück zum Zitat Rowe W, Corne D, Knowles J (2006) Predicting stochastic search algorithm performance using landscape state machines. In: 2006 IEEE Congress on evolutionary computation, vol 1–6, pp 2929–2936 Rowe W, Corne D, Knowles J (2006) Predicting stochastic search algorithm performance using landscape state machines. In: 2006 IEEE Congress on evolutionary computation, vol 1–6, pp 2929–2936
Zurück zum Zitat Seo DI, Choi SS, Moon BR (2004) New epistasis measures for detecting independently optimizable partitions of variables. In: Kalyanmoy D, Harman M, Holland O (eds) Genetic and evolutionary computation Conference 2004. Seattle, pp 26–30 Seo DI, Choi SS, Moon BR (2004) New epistasis measures for detecting independently optimizable partitions of variables. In: Kalyanmoy D, Harman M, Holland O (eds) Genetic and evolutionary computation Conference 2004. Seattle, pp 26–30
Zurück zum Zitat Seo DI, Kim Y-H, Moon B-R (2003) New entropy-based measures of gene significance and epistasis. Genetic Evol Comput—Gecco 2003 Pt Ii Proc E CantuPaz FJA 2724:1345–1356CrossRef Seo DI, Kim Y-H, Moon B-R (2003) New entropy-based measures of gene significance and epistasis. Genetic Evol Comput—Gecco 2003 Pt Ii Proc E CantuPaz FJA 2724:1345–1356CrossRef
Zurück zum Zitat Seo DI, Moon BR (2005) Computing the epistasis variance of large-scale traveling salesman problems. In: Beyer HG (ed) Gecco 2005: genetic and evolutionary computation Conference, vols 1 and 2. Assoc Computing Machinery, New York, pp 1169–1176 Seo DI, Moon BR (2005) Computing the epistasis variance of large-scale traveling salesman problems. In: Beyer HG (ed) Gecco 2005: genetic and evolutionary computation Conference, vols 1 and 2. Assoc Computing Machinery, New York, pp 1169–1176
Zurück zum Zitat Smith T, Husbands P, Layzell P, O’shea M (2002) Fitness landscapes and evolvability. Evol Comput 10(1):1–34CrossRef Smith T, Husbands P, Layzell P, O’shea M (2002) Fitness landscapes and evolvability. Evol Comput 10(1):1–34CrossRef
Zurück zum Zitat Stadler P, Institute S (1995) Towards a theory of landscapes. In: López-Peña R, Waelbroeck H, Capovilla R, García-Pelayo R, Zertuche F (eds) Complex systems and binary networks, vol 461–461. Springer, Berlin, Heidelberg, pp 78–163 Stadler P, Institute S (1995) Towards a theory of landscapes. In: López-Peña R, Waelbroeck H, Capovilla R, García-Pelayo R, Zertuche F (eds) Complex systems and binary networks, vol 461–461. Springer, Berlin, Heidelberg, pp 78–163
Zurück zum Zitat Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Singapore Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Singapore
Zurück zum Zitat Sutton AM, Whitley D, Lunacek M, Howe A (2006) PSO and multi-funnel landscapes: how cooperation might limit exploration. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation. ACM, Seattle, Washington, pp 75–82 Sutton AM, Whitley D, Lunacek M, Howe A (2006) PSO and multi-funnel landscapes: how cooperation might limit exploration. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation. ACM, Seattle, Washington, pp 75–82
Zurück zum Zitat Vassilev V, Fogarty T, Miller J (2003) Smoothness, ruggedness and neutrality of fitness landscapes: from theory to application. In: Ghosh A, Tsutsui S (eds) Advances in evolutionary computing. Springer, Berlin, Heidelberg, pp 3–44 Vassilev V, Fogarty T, Miller J (2003) Smoothness, ruggedness and neutrality of fitness landscapes: from theory to application. In: Ghosh A, Tsutsui S (eds) Advances in evolutionary computing. Springer, Berlin, Heidelberg, pp 3–44
Zurück zum Zitat Vassilev VK, Fogarty TC, Miller JF (2000) Information characteristics and the structure of landscapes. Evol Comput 8(1):31–60CrossRef Vassilev VK, Fogarty TC, Miller JF (2000) Information characteristics and the structure of landscapes. Evol Comput 8(1):31–60CrossRef
Zurück zum Zitat Volchenkov D, Helbach J, Tscherepanow M, Kuehnel S (2013) Exploration–exploitation trade-off features a saltatory search behaviour. J R Soc Interface 10(85):1–12CrossRef Volchenkov D, Helbach J, Tscherepanow M, Kuehnel S (2013) Exploration–exploitation trade-off features a saltatory search behaviour. J R Soc Interface 10(85):1–12CrossRef
Zurück zum Zitat Weinberger E (1990) Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol Cybernet 63(5):325–336CrossRef Weinberger E (1990) Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol Cybernet 63(5):325–336CrossRef
Zurück zum Zitat Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRef Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRef
Zurück zum Zitat Yang H, Li J, Li M (2012) Evolutionary algorithms: schema, emergence and hardness. Science Press, Beijing Yang H, Li J, Li M (2012) Evolutionary algorithms: schema, emergence and hardness. Science Press, Beijing
Metadaten
Titel
A novel optimization hardness indicator based on the relationship between optimization hardness and frequency features of real-parameter problems
verfasst von
Kun Li
Ming Li
Hao Chen
Publikationsdatum
01.08.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 8/2015
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-014-1419-1

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