89 research outputs found
Improved sampling of the pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm
Previous work on multiobjective genetic algorithms has been focused on preventing genetic drift and the issue of convergence has been given little attention. In this paper, we present a simple steady-state strategy, Pareto Converging Genetic Algorithm (PCGA), which naturally samples the solution space and ensures population advancement towards the Pareto-front. PCGA eliminates the need for sharing/niching and thus minimizes heuristically chosen parameters and procedures. A systematic approach based on histograms of rank is introduced for assessing convergence to the Pareto-front, which, by definition, is unknown in most real search problems.
We argue that there is always a certain inheritance of genetic material belonging to a population, and there is unlikely to be any significant gain beyond some point; a stopping criterion where terminating the computation is suggested. For further encouraging diversity and competition, a nonmigrating island model may optionally be used; this approach is particularly suited to many difficult (real-world) problems, which have a tendency to get stuck at (unknown) local minima. Results on three benchmark problems are presented and compared with those of earlier approaches. PCGA is found to produce diverse sampling of the Pareto-front without niching and with significantly less computational effort
Sub-structural Niching in Estimation of Distribution Algorithms
We propose a sub-structural niching method that fully exploits the problem
decomposition capability of linkage-learning methods such as the estimation of
distribution algorithms and concentrate on maintaining diversity at the
sub-structural level. The proposed method consists of three key components: (1)
Problem decomposition and sub-structure identification, (2) sub-structure
fitness estimation, and (3) sub-structural niche preservation. The
sub-structural niching method is compared to restricted tournament selection
(RTS)--a niching method used in hierarchical Bayesian optimization
algorithm--with special emphasis on sustained preservation of multiple global
solutions of a class of boundedly-difficult, additively-separable multimodal
problems. The results show that sub-structural niching successfully maintains
multiple global optima over large number of generations and does so with
significantly less population than RTS. Additionally, the market share of each
of the niche is much closer to the expected level in sub-structural niching
when compared to RTS
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
Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms
In the field of multi-objective optimization algorithms, multi-objective
Bayesian Global Optimization (MOBGO) is an important branch, in addition to
evolutionary multi-objective optimization algorithms (EMOAs). MOBGO utilizes
Gaussian Process models learned from previous objective function evaluations to
decide the next evaluation site by maximizing or minimizing an infill
criterion. A common criterion in MOBGO is the Expected Hypervolume Improvement
(EHVI), which shows a good performance on a wide range of problems, with
respect to exploration and exploitation. However, so far it has been a
challenge to calculate exact EHVI values efficiently. In this paper, an
efficient algorithm for the computation of the exact EHVI for a generic case is
proposed. This efficient algorithm is based on partitioning the integration
volume into a set of axis-parallel slices. Theoretically, the upper bound time
complexities are improved from previously and , for two- and
three-objective problems respectively, to , which is
asymptotically optimal. This article generalizes the scheme in higher
dimensional case by utilizing a new hyperbox decomposition technique, which was
proposed by D{\"a}chert et al, EJOR, 2017. It also utilizes a generalization of
the multilayered integration scheme that scales linearly in the number of
hyperboxes of the decomposition. The speed comparison shows that the proposed
algorithm in this paper significantly reduces computation time. Finally, this
decomposition technique is applied in the calculation of the Probability of
Improvement (PoI)
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
Multi-Guide Particle Swarm Optimization for Large-Scale Multi-Objective Optimization Problems
Multi-guide particle swarm optimization (MGPSO) is a novel metaheuristic for multi-objective optimization based on particle swarm optimization (PSO). MGPSO has been shown to be competitive when compared with other state-of-the-art multi-objective optimization algorithms for low-dimensional problems. However, to the best of the author’s knowledge, the suitability of MGPSO for high-dimensional multi-objective optimization problems has not been studied. One goal of this thesis is to provide a scalability study of MGPSO in order to evaluate its efficacy for high-dimensional multi-objective optimization problems. It is observed that while MGPSO has comparable performance to state-of-the-art multi-objective optimization algorithms, it experiences a performance drop with the increase in the problem dimensionality. Therefore, a main contribution of this work is a new scalable MGPSO-based algorithm, termed cooperative co-evolutionary multi-guide particle swarm optimization (CCMGPSO), that incorporates ideas from cooperative PSOs. A detailed empirical study on well-known benchmark problems comparing the proposed improved approach with various state-of-the-art multi-objective optimization algorithms is done. Results show that the proposed CCMGPSO is highly competitive for high-dimensional problems
Portfolio Optimization Using Evolutionary Algorithms
Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced AnalyticsPortfolio optimization is a widely studied field in modern finance. It involves finding
the optimal balance between two contradictory objectives, the risk and the return.
As the number of assets rises, the complexity in portfolios increases considerably,
making it a computational challenge. This report explores the application of the
Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) and
Genetic Algorithm (GA) in the field of portfolio optimization.
MOEA/D and GA have proven to be effective at finding portfolios. However, it
remains unclear how they perform when compared to traditional approaches used
in finance. To achieve this, a framework for portfolio optimization is proposed, using
MOEA/D, and GA separately as optimization algorithms and Capital Asset Pricing
Model (CAPM) and Mean-Variance Model as methods to evaluate portfolios.
The proposed framework is able to produce weighted portfolios successfully. These
generated portfolios were evaluated using a simulation with subsequent (unseen)
prices of the assets included in the portfolio. The simulation was compared with
well known portfolios in the same market and other market benchmarks (Security
Market Line and Market Portfolio).
The results obtained in this investigation exceeded expectation by creating
portfolios that perform better than the market. CAPM and Mean-Variance Model,
although they fail to model all the variables that affect the stock market, provide a
simple valuation for assets and portfolios. MOEA/D using Differential Evolution
operators and the CAPM model produced the best portfolios in this research.
Work can still be done to accommodate more variables that can affect markets and
portfolios, such as taxes, investment horizon and costs for transactions
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