thumb|Meta-optimization concept. '''Meta-optimization''' from numerical optimization is the use of one optimization method to tune another optimization method. Meta-optimization is reported to have been used as early as in the late 1970s by Mercer and Sampson<ref name="mercer78adaptive"/> for finding optimal parameter settings of a genetic algorithm.
Meta-optimization and related concepts are also known in the literature as meta-evolution, super-optimization, automated parameter calibration, hyper-heuristics, etc.
== Motivation == [[Image:DE Meta-Fitness Landscape (12 benchmark problems).JPG|thumb|Performance landscape for differential evolution.]] Optimization methods such as genetic algorithm and differential evolution have several parameters that govern their behaviour and efficiency in optimizing a given problem and these parameters must be chosen by the practitioner to achieve satisfactory results. Selecting the behavioural parameters by hand is a laborious task that is susceptible to human misconceptions of what makes the optimizer perform well.
The behavioural parameters of an optimizer can be varied and the optimization performance plotted as a landscape. This is computationally feasible for optimizers with few behavioural parameters and optimization problems that are fast to compute, but when the number of behavioural parameters increases the time usage for computing such a performance landscape increases exponentially. This is the curse of dimensionality for the search-space consisting of an optimizer's behavioural parameters. An efficient method is therefore needed to search the space of behavioural parameters.
== Methods == [[Image:DE Meta-Optimization Progress (12 benchmark problems).JPG|thumb|Meta-optimization of differential evolution.]] A simple way of finding good behavioural parameters for an optimizer is to employ another overlaying optimizer, called the meta-optimizer. There are different ways of doing this depending on whether the behavioural parameters to be tuned are real-valued or discrete-valued, and depending on what performance measure is being used, etc.
Meta-optimizing the parameters of a genetic algorithm was done by Grefenstette <ref name=grefenstette86optimization/> and Keane,<ref name=keane95genetic/> amongst others, and experiments with meta-optimizing both the parameters and the genetic operators were reported by Bäck.<ref name=back94parallel/> Meta-optimization of the COMPLEX-RF algorithm was done by Krus and Andersson,<ref name=Krus03optimizing/> and,<ref name=Krus13optimizing/> where performance index of optimization based on information theory was introduced and further developed. Meta-optimization of particle swarm optimization was done by Meissner et al.,<ref name=meissner06optimized/> Pedersen and Chipperfield,<ref name=pedersen08simplifying/> and Mason et al.<ref name=mason2017meta/> Pedersen and Chipperfield applied meta-optimization to differential evolution.<ref name=pedersen08thesis/> Birattari et al.<ref name=birattari02racing/><ref name=birattari04thesis/> meta-optimized ant colony optimization. Statistical models have also been used to reveal more about the relationship between choices of behavioural parameters and optimization performance, see for example Francois and Lavergne,<ref name=francois01design/> and Nannen and Eiben.<ref name=nannen06method/> A comparison of various meta-optimization techniques was done by Smit and Eiben.<ref name=smit09comparing/>
== See also == * Automated machine learning (AutoML) * Hyper-heuristics
== References == <references>
<ref name=mercer78adaptive> {{cite journal |last=Mercer |first=R.E. |author2=Sampson, J.R. |title=Adaptive search using a reproductive metaplan |journal=Kybernetes |year=1978 |volume=7 |pages=215–228 |doi=10.1108/eb005486 |issue=3 }} </ref>
<ref name=grefenstette86optimization> {{cite journal |doi=10.1109/TSMC.1986.289288 |last=Grefenstette |first=J.J. |title=Optimization of control parameters for genetic algorithms |journal=IEEE Transactions on Systems, Man, and Cybernetics |year=1986 |volume=16 |pages=122–128 |issue=1 |s2cid=23313487 }} </ref>
<ref name=keane95genetic> {{cite journal |doi=10.1016/0954-1810(95)95751-Q |last=Keane |first=A.J. |title=Genetic algorithm optimization in multi-peak problems: studies in convergence and robustness |journal=Artificial Intelligence in Engineering |year=1995 |volume=9 |pages=75–83 |issue=2 }} </ref>
<ref name=meissner06optimized> {{cite journal |last1=Meissner |first1=M. |last2=Schmuker |first2=M. |last3=Schneider |first3=G. |title=Optimized Particle Swarm Optimization (OPSO) and its application to artificial neural network training |journal=BMC Bioinformatics |year=2006 |volume=7 |doi=10.1186/1471-2105-7-125 |pmid=16529661 |pmc=1464136 |issue=1 |pages=125 |doi-access=free }} </ref>
<ref name=pedersen08simplifying> {{cite journal |doi=10.1016/j.asoc.2009.08.029 |last=Pedersen |first=M.E.H. |author2=Chipperfield, A.J. |title=Simplifying particle swarm optimization |journal=Applied Soft Computing |year=2010 |volume=10 |pages=618–628 |issue=2 |citeseerx=10.1.1.149.8300 }} </ref>
<ref name=mason2017meta> {{cite journal |last=Mason |first=Karl |author2=Duggan, Jim |author3=Howley, Enda |title=A Meta Optimisation Analysis of Particle Swarm Optimisation Velocity Update Equations for Watershed Management Learning |journal=Applied Soft Computing |year=2018 |volume=62 |pages=148–161 |doi =10.1016/j.asoc.2017.10.018 }} </ref>
<ref name=pedersen08thesis> {{cite book |type=PhD thesis |title=Tuning & Simplifying Heuristical Optimization |url=https://pdfs.semanticscholar.org/a5d2/8c26a2e2824170d67b69f14120cf67cabe26.pdf |archive-url=https://web.archive.org/web/20200213130101/https://pdfs.semanticscholar.org/a5d2/8c26a2e2824170d67b69f14120cf67cabe26.pdf |url-status=dead |archive-date=2020-02-13 |last=Pedersen |first=M.E.H. |year=2010 |publisher=University of Southampton, School of Engineering Sciences, Computational Engineering and Design Group |s2cid=107805461 }} </ref>
<ref name=francois01design> {{cite journal |last1=Francois |first1=O. |last2=Lavergne |first2=C. |title=Design of evolutionary algorithms - a statistical perspective |journal=IEEE Transactions on Evolutionary Computation |year=2001 |volume=5 |pages=129–148 |issue=2 |doi=10.1109/4235.918434 }} </ref>
<ref name=birattari02racing> {{cite conference |last1=Birattari |first1=M. |last2=Stützle |first2=T. |last3=Paquete |first3=L. |last4=Varrentrapp |first4=K. |title=A racing algorithm for configuring metaheuristics |book-title=Proceedings of the Genetic and Evolutionary Computation Conference (GECCO) |year=2002 |pages=11–18 |url=https://www.researchgate.net/publication/220740639 }} </ref>
<ref name=Krus03optimizing> {{cite conference |last1=Krus |first1=PK. |last2=Andersson (Ölvander) |first2=J. |title=Optimizing optimization for design optimization |book-title=Proceedings of DETC’03 2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference Chicago, Illinois, USA |year=2003 }} </ref>
<ref name=Krus13optimizing> {{cite journal |last1=Krus |first1=PK. |last2=Ölvander(Andersson) |first2=J. |url=https://liu.diva-portal.org/smash/get/diva2:572570/FULLTEXT01.pdf |title=Performance index and meta-optimization of a direct search optimization method |journal=Engineering Optimization |year=2013 |volume=45 |pages=1167–1185 |issue=10 |doi=10.1080/0305215X.2012.725052 |bibcode=2013EnOp...45.1167K |s2cid=62731978 }} </ref>
<ref name=birattari04thesis> {{cite book |type=PhD thesis |title=The Problem of Tuning Metaheuristics as Seen from a Machine Learning Perspective |url=https://iridia.ulb.ac.be/~mbiro/paperi/BirattariPhD.pdf |last=Birattari |first=M. |year=2004 |publisher=Université Libre de Bruxelles }} </ref>
<ref name=smit09comparing> {{cite conference |last1=Smit |first1=S.K. |last2=Eiben |first2=A.E. |title=Comparing parameter tuning methods for evolutionary algorithms |book-title=Proceedings of the IEEE Congress on Evolutionary Computation (CEC) |year=2009 |pages=399–406 |url=https://www.few.vu.nl/~gusz/papers/2009-CEC-tuning-methods.pdf }} </ref>
<ref name=back94parallel> {{cite conference |last1=Bäck |first1=T. |title=Parallel optimization of evolutionary algorithms |book-title=Proceedings of the International Conference on Evolutionary Computation |year=1994 |pages=418–427 }} </ref>
<ref name=nannen06method> {{cite conference |last1=Nannen |first1=V. |last2=Eiben |first2=A.E. |title=A method for parameter calibration and relevance estimation in evolutionary algorithms |book-title=Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation (GECCO) |year=2006 |pages=183–190 |url=http://srv.uib.es/pub/1012.pdf }} </ref>
</references> {{Optimization algorithms}} Category:Evolutionary computation Category:Heuristics