Speeding up many-objective optimization by Monte Carlo approximations

Many state-of-the-art evolutionary vector optimization algorithms compute the contributing hypervolume for ranking candidate solutions. However, with an increasing number of objectives, calculating the volumes becomes intractable. Therefore, although hypervolume-based algorithms are often the method...

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Vydáno v:Artificial intelligence Ročník 204; s. 22 - 29
Hlavní autoři: Bringmann, Karl, Friedrich, Tobias, Igel, Christian, Voß, Thomas
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Elsevier B.V 01.11.2013
Elsevier
Témata:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Decision theory. Utility theory
Evolutionary algorithm
Exact sciences and technology
Hypervolume indicator
Mathematical programming
Multi-objective optimization
Operational research and scientific management
Operational research. Management science
Pareto-front approximation
Theoretical computing
Pareto-front approximation
Multi-objective optimization
Hypervolume indicator
Evolutionary algorithm
Monte Carlo method
Dominating set
Pareto optimum
Hierarchical classification
Objective analysis
Multiobjective programming
Covariance matrix
Approximation algorithm
Vector method
Modeling
Function evaluation
Computation time
Budget
Objective function
Vector optimization
ISSN:0004-3702, 1872-7921
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Popis
Shrnutí:Many state-of-the-art evolutionary vector optimization algorithms compute the contributing hypervolume for ranking candidate solutions. However, with an increasing number of objectives, calculating the volumes becomes intractable. Therefore, although hypervolume-based algorithms are often the method of choice for bi-criteria optimization, they are regarded as not suitable for many-objective optimization. Recently, Monte Carlo methods have been derived and analyzed for approximating the contributing hypervolume. Turning theory into practice, we employ these results in the ranking procedure of the multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) as an example of a state-of-the-art method for vector optimization. It is empirically shown that the approximation does not impair the quality of the obtained solutions given a budget of objective function evaluations, while considerably reducing the computation time in the case of multiple objectives. These results are obtained on common benchmark functions as well as on two design optimization tasks. Thus, employing Monte Carlo approximations makes hypervolume-based algorithms applicable to many-objective optimization.
ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2013.08.001