14 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
A Pareto-Compliant Surrogate Approach for Multiobjective Optimization
This paper discusses the idea of using a single Pareto-compliant surrogate model for multiobjective optimization. While most surrogate approaches to multi-objective optimization build a surrogate model for each objective, the recently proposed mono surrogate approach aims at building a global surrogate model defined on the decision space and tightly characterizing the current Pareto set and the dominated region, in order to speed up the evolution progress toward the true Pareto set. This surrogate model is specified by combining a One-class Support Vector Machine (SVMs) to characterize the dominated points, and a Regression SVM to clamp the Pareto front on a single value. The aims of this paper are to identify issues of the proposed approach demanding further study and to raise the question of how to efficiently incorporate quality indicators, such as the hypervolume into the surrogate model
Dominance-Based Pareto-Surrogate for Multi-Objective Optimization
Mainstream surrogate approaches for multi-objective problems build one approximation for each objective. Mono-surrogate approaches instead aim at characterizing the Pareto front with a single model. Such an approach has been recently introduced using a mixture of regression Support Vector Machine (SVM) to clamp the current Pareto front to a single value, and one-class SVM to ensure that all dominated points will be mapped on one side of this value. A new mono-surrogate EMO approach is introduced here, relaxing the previous approach and modelling Pareto dominance within the rank-SVM framework. The resulting surrogate model is then used as a filter for offspring generation in standard Evolutionary Multi-Objective Algorithms, and is comparatively validated on a set of benchmark problems
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 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