Fitness approximation
[Y. Jin]
A comprehensive survey of fitness approximation in evolutionary computation
''Soft Computing'', 9:3–12, 2005 aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based on data collected from numerical simulations or physical experiments. The machine learning models for fitness approximation are also known as meta-models or surrogates, and evolutionary optimization based on approximated fitness evaluations are also known as surrogate-assisted evolutionary approximation.
[Surrogate-assisted evolutionary computation: Recent advances and future challenges]
Swarm and Evolutionary Computation, 1(2):61–70, 2011 Fitness approximation in evolutionary optimization can be seen as a sub-area of data-driven evolutionary optimization.
Approximate models in function optimization
Motivation
In many real-world
optimization problem
In mathematics, engineering, computer science and economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goo ...
s including engineering problems, the number of
fitness function
A fitness function is a particular type of objective or cost function that is used to summarize, as a single figure of merit, how close a given candidate solution is to achieving the set aims. It is an important component of evolutionary algorit ...
evaluations needed to obtain a good solution dominates the
optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...
cost. In order to obtain efficient optimization algorithms, it is crucial to use prior information gained during the optimization process. Conceptually, a natural approach to utilizing the known prior information is building a model of the fitness function to assist in the selection of candidate solutions for evaluation. A variety of techniques for constructing such a model, often also referred to as surrogates, metamodels or
approximation
An approximation is anything that is intentionally similar but not exactly equal to something else.
Etymology and usage
The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ...
models – for computationally expensive optimization problems have been considered.
Approaches
Common approaches to constructing approximate models based on learning and interpolation from known fitness values of a small population include:
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Low-degree polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...
s and
regression models
*Fourier
surrogate modeling
[Manzoni, L.; Papetti, D.M.; Cazzaniga, P.; Spolaor, S.; Mauri, G.; Besozzi, D.; Nobile, M.S. Surfing on Fitness Landscapes: A Boost on Optimization by Fourier Surrogate Modeling. Entropy 2020, 22, 285.]
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Artificial neural networks
In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a computational model inspired by the structure and functions of biological neural networks.
A neural network consists of connected ...
including
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Multilayer perceptrons
**
Radial basis function network
In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination of radial basis functions of the in ...
s
**
Support vector machines
In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms that analyze data for classification and regression analysis. Developed at AT&T Bell Laborato ...
Due to the limited number of training samples and high dimensionality encountered in engineering design optimization, constructing a globally valid approximate model remains difficult. As a result, evolutionary algorithms using such approximate fitness functions may converge to
local optima. Therefore, it can be beneficial to selectively use the original
fitness function
A fitness function is a particular type of objective or cost function that is used to summarize, as a single figure of merit, how close a given candidate solution is to achieving the set aims. It is an important component of evolutionary algorit ...
together with the approximate model.
See also
A complete list of references on Fitness Approximation in Evolutionary Computation b
That is designed to accelerate the convergence rate of EAs.
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Inverse reinforcement learning
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Reinforcement learning from human feedback
References
{{Reflist
Evolutionary algorithms
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