2,864 research outputs found
Scalarizing Functions in Bayesian Multiobjective Optimization
Scalarizing functions have been widely used to convert a multiobjective
optimization problem into a single objective optimization problem. However,
their use in solving (computationally) expensive multi- and many-objective
optimization problems in Bayesian multiobjective optimization is scarce.
Scalarizing functions can play a crucial role on the quality and number of
evaluations required when doing the optimization. In this article, we study and
review 15 different scalarizing functions in the framework of Bayesian
multiobjective optimization and build Gaussian process models (as surrogates,
metamodels or emulators) on them. We use expected improvement as infill
criterion (or acquisition function) to update the models. In particular, we
compare different scalarizing functions and analyze their performance on
several benchmark problems with different number of objectives to be optimized.
The review and experiments on different functions provide useful insights when
using and selecting a scalarizing function when using a Bayesian multiobjective
optimization method
Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)
Recently, increasing works have proposed to drive evolutionary algorithms
using machine learning models. Usually, the performance of such model based
evolutionary algorithms is highly dependent on the training qualities of the
adopted models. Since it usually requires a certain amount of data (i.e. the
candidate solutions generated by the algorithms) for model training, the
performance deteriorates rapidly with the increase of the problem scales, due
to the curse of dimensionality. To address this issue, we propose a
multi-objective evolutionary algorithm driven by the generative adversarial
networks (GANs). At each generation of the proposed algorithm, the parent
solutions are first classified into real and fake samples to train the GANs;
then the offspring solutions are sampled by the trained GANs. Thanks to the
powerful generative ability of the GANs, our proposed algorithm is capable of
generating promising offspring solutions in high-dimensional decision space
with limited training data. The proposed algorithm is tested on 10 benchmark
problems with up to 200 decision variables. Experimental results on these test
problems demonstrate the effectiveness of the proposed algorithm
Rank-Based Learning and Local Model Based Evolutionary Algorithm for High-Dimensional Expensive Multi-Objective Problems
Surrogate-assisted evolutionary algorithms have been widely developed to
solve complex and computationally expensive multi-objective optimization
problems in recent years. However, when dealing with high-dimensional
optimization problems, the performance of these surrogate-assisted
multi-objective evolutionary algorithms deteriorate drastically. In this work,
a novel Classifier-assisted rank-based learning and Local Model based
multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional
expensive multi-objective optimization problems. The proposed algorithm
consists of three parts: classifier-assisted rank-based learning,
hypervolume-based non-dominated search, and local search in the relatively
sparse objective space. Specifically, a probabilistic neural network is built
as classifier to divide the offspring into a number of ranks. The offspring in
different ranks uses rank-based learning strategy to generate more promising
and informative candidates for real function evaluations. Then, radial basis
function networks are built as surrogates to approximate the objective
functions. After searching non-dominated solutions assisted by the surrogate
model, the candidates with higher hypervolume improvement are selected for real
evaluations. Subsequently, in order to maintain the diversity of solutions, the
most uncertain sample point from the non-dominated solutions measured by the
crowding distance is selected as the guided parent to further infill in the
uncertain region of the front. The experimental results of benchmark problems
and a real-world application on geothermal reservoir heat extraction
optimization demonstrate that the proposed algorithm shows superior performance
compared with the state-of-the-art surrogate-assisted multi-objective
evolutionary algorithms. The source code for this work is available at
https://github.com/JellyChen7/CLMEA
A Random Forest Assisted Evolutionary Algorithm for Data-Driven Constrained Multi-Objective Combinatorial Optimization of Trauma Systems for publication
Many real-world optimization problems can be
solved by using the data-driven approach only, simply because no
analytic objective functions are available for evaluating candidate
solutions. In this work, we address a class of expensive datadriven
constrained multi-objective combinatorial optimization
problems, where the objectives and constraints can be calculated
only on the basis of large amount of data. To solve this class
of problems, we propose to use random forests and radial basis
function networks as surrogates to approximate both objective
and constraint functions. In addition, logistic regression models
are introduced to rectify the surrogate-assisted fitness evaluations
and a stochastic ranking selection is adopted to further reduce
the influences of the approximated constraint functions. Three
variants of the proposed algorithm are empirically evaluated on
multi-objective knapsack benchmark problems and two realworld
trauma system design problems. Experimental results
demonstrate that the variant using random forest models as
the surrogates are effective and efficient in solving data-driven
constrained multi-objective combinatorial optimization problems
Which Surrogate Works for Empirical Performance Modelling? A Case Study with Differential Evolution
It is not uncommon that meta-heuristic algorithms contain some intrinsic
parameters, the optimal configuration of which is crucial for achieving their
peak performance. However, evaluating the effectiveness of a configuration is
expensive, as it involves many costly runs of the target algorithm. Perhaps
surprisingly, it is possible to build a cheap-to-evaluate surrogate that models
the algorithm's empirical performance as a function of its parameters. Such
surrogates constitute an important building block for understanding algorithm
performance, algorithm portfolio/selection, and the automatic algorithm
configuration. In principle, many off-the-shelf machine learning techniques can
be used to build surrogates. In this paper, we take the differential evolution
(DE) as the baseline algorithm for proof-of-concept study. Regression models
are trained to model the DE's empirical performance given a parameter
configuration. In particular, we evaluate and compare four popular regression
algorithms both in terms of how well they predict the empirical performance
with respect to a particular parameter configuration, and also how well they
approximate the parameter versus the empirical performance landscapes
A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms
This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.The research of Tinkle Chugh was funded by the COMAS Doctoral Program (at the University of Jyväskylä) and FiDiPro Project DeCoMo (funded by Tekes, the Finnish Funding Agency for Innovation), and the research of Dr. Karthik Sindhya was funded by SIMPRO project funded by Tekes as well as DeCoMo
Enhancing SAEAs with Unevaluated Solutions: A Case Study of Relation Model for Expensive Optimization
Surrogate-assisted evolutionary algorithms (SAEAs) hold significant
importance in resolving expensive optimization problems~(EOPs). Extensive
efforts have been devoted to improving the efficacy of SAEAs through the
development of proficient model-assisted selection methods. However, generating
high-quality solutions is a prerequisite for selection. The fundamental
paradigm of evaluating a limited number of solutions in each generation within
SAEAs reduces the variance of adjacent populations, thus impacting the quality
of offspring solutions. This is a frequently encountered issue, yet it has not
gained widespread attention. This paper presents a framework using unevaluated
solutions to enhance the efficiency of SAEAs. The surrogate model is employed
to identify high-quality solutions for direct generation of new solutions
without evaluation. To ensure dependable selection, we have introduced two
tailored relation models for the selection of the optimal solution and the
unevaluated population. A comprehensive experimental analysis is performed on
two test suites, which showcases the superiority of the relation model over
regression and classification models in the selection phase. Furthermore, the
surrogate-selected unevaluated solutions with high potential have been shown to
significantly enhance the efficiency of the algorithm.Comment: 18 pages, 9 figure
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