Model-based Evolutionary Algorithms Research Articles

Neural Net-Enhanced Competitive Swarm Optimizer for Large-Scale Multiobjective Optimization.

The competitive swarm optimizer (CSO) classifies swarm particles into loser and winner particles and then uses the winner particles to efficiently guide the search of the loser particles. This approach has very promising performance in solving large-scale multiobjective optimization problems (LMOPs). However, most studies of CSOs ignore the evolution of the winner particles, although their quality is very important for the final optimization performance. Aiming to fill this research gap, this article proposes a new neural net-enhanced CSO for solving LMOPs, called NN-CSO, which not only guides the loser particles via the original CSO strategy, but also applies our trained neural network (NN) model to evolve winner particles. First, the swarm particles are classified into winner and loser particles by the pairwise competition. Then, the loser particles and winner particles are, respectively, treated as the input and desired output to train the NN model, which tries to learn promising evolutionary dynamics by driving the loser particles toward the winners. Finally, when model training is complete, the winner particles are evolved by the well-trained NN model, while the loser particles are still guided by the winner particles to maintain the search pattern of CSOs. To evaluate the performance of our designed NN-CSO, several LMOPs with up to ten objectives and 1000 decision variables are adopted, and the experimental results show that our designed NN model can significantly improve the performance of CSOs and shows some advantages over several state-of-the-art large-scale multiobjective evolutionary algorithms as well as over model-based evolutionary algorithms.

A dual-population multi-objective evolutionary algorithm driven by generative adversarial networks for benchmarking and protein-peptide docking

Multi-objective optimization problems (MOPs) are characterized as optimization problems in which multiple conflicting objective functions are optimized simultaneously. To solve MOPs, some algorithms used machine learning models to drive the evolutionary algorithms, leading to the design of a variety of model-based evolutionary algorithms. However, model collapse occurs during the generation of candidate solutions, which results in local optima and poor diversity in model-based evolutionary algorithms. To address this problem, we propose a dual-population multi-objective evolutionary algorithm driven by Wasserstein generative adversarial network with gradient penalty (DGMOEA), where the dual-populations coordinate and cooperate to generate high-quality solutions, thus improving the performance of the evolutionary algorithm. We compare the proposed algorithm with the 7 state-of-the-art algorithms on 20 multi-objective benchmark functions. Experimental results indicate that DGMOEA achieves significant results in solving MOPs, where the metrics IGD and HV outperform the other comparative algorithms on 15 and 18 out of 20 benchmarks, respectively. Our algorithm is evaluated on the LEADS-PEP dataset containing 53 protein-peptide complexes, and the experimental results on solving the protein-peptide docking problem indicated that DGMOEA can effectively reduce the RMSD between the generated and the original peptide's 3D poses and achieve more competitive results.

A Kriging model-based evolutionary algorithm with support vector machine for dynamic multimodal optimization

Dynamic multimodal optimization problems (DMMOPs) have to search multiple global optimal solutions with the objectives and constraints dynamically changing over time. In recent years, dynamic optimization problems and multimodal optimization problems have been extensively studied in the field of evolutionary computation. However, DMMOPs have not yet been paid significant attention and only a few studies have been designed for dynamic multimodal optimization. The key issue in optimizing DMMOPs is to address the challenges induced by both the multimodal nature and the dynamic nature. Existing works perform poorly in locating all global optima in static environments and tracking global optima with various change modes. Therefore, in this paper, a Kriging Model-based Evolutionary Algorithm with Support Vector Machine called KMEA-SVM is proposed for tackling DMMOPs. Two important operators are designed in this algorithm, including a Kriging-based preselection and a support vector machine (SVM)-based prediction. The aim of Kriging-based preselection is to search all global optimal solutions more efficiently by preselecting promising solutions with a trained Kriging model, while the purpose of SVM-based prediction is to predict more outstanding solutions as the initial population for new environment when the environment changes. The proposed KMEA-SVM is compared with several state-of-the-art evolutionary algorithms on twenty-four test DMMOPs and the experimental results validate the advantages of KMEA-SVM on seeking more multiple optima in dynamic environments.

A model-based evolutionary algorithm for home health care scheduling

In this paper, for the first time a model-based evolutionary algorithm is presented for a real-life Home Health Care Routing and Scheduling Problem (HHCRSP). The algorithm generates routes consisting of care activities jointly with the underlying shift schedule, while taking into account the qualification levels. The performance is optimized in terms of travel time, time window waiting time and shift overtime. The algorithm is a novel extension of the permutation Gene-Pool Optimal Mixing Evolutionary Algorithm. Numerical experiments, using real-life data, show that the algorithm performs close to optimal for small instances, and outperforms schedules from a case study, leading to efficiency gains of 41%. Furthermore, it is shown that the model-based evolutionary algorithm performs better than a more traditional evolutionary algorithm, which demonstrates the importance of learning and exploiting a model to guide the optimization in HHCRSP.

A random forest‐regression‐based inverse‐modeling evolutionary algorithm using uniform reference points

The model-based evolutionary algorithms are divided into three groups: estimation of distribution algorithms, inverse modeling, and surrogate modeling. Existing inverse modeling is mainly applied to solve multi-objective optimization problems and is not suitable for many-objective optimization problems. Some inversed-model techniques, such as the inversed-model of multi-objective evolutionary algorithm, constructed from the Pareto front (PF) to the Pareto solution on nondominated solutions using a random grouping method and Gaussian process, were introduced. However, some of the most efficient inverse models might be eliminated during this procedure. Also, there are challenges, such as the presence of many local PFs and developing poor solutions when the population has no evident regularity. This paper proposes inverse modeling using random forest regression and uniform reference points that map all nondominated solutions from the objective space to the decision space to solve many-objective optimization problems. The proposed algorithm is evaluated using the benchmark test suite for evolutionary algorithms. The results show an improvement in diversity and convergence performance (quality indicators).

An improved model‐based evolutionary algorithm for multi‐objective optimization

AbstractThe basic idea in the estimation of distribution algorithms is the replacement of heuristic operators with machine learning models such as regression models, clustering models, or classification models. So, recently, the model‐based evolutionary algorithms (MBEAs) have been suggested in three groups: The estimation of distribution algorithms (EDAs), surrogate assisted evolutionary algorithms, and the inversed models to map from the objective space to the decision space. In this article, a new approach, based on an inversed model of Gaussian process and random forest framework, is proposed. The main idea is applying the process of random forest variable importance with a random grouping that determines some of the best assignment of decision variables to objective functions in order to form a Gaussian process in inverse models that maps to decision space the rich solutions which are discovered from objective space. Then these inverse models through sampling the objective space generate offspring. The proposed algorithm has been tested on the benchmark test suite for evolutionary algorithms (modified Deb K, Thiele L, Laumanns M, Zitzler E (DTLZ), and Walking Fish Group (WFG)) and indicates that the proposed method is a competitive and promising approach.

Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs).

Recently, increasing works have been 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 multiobjective 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 ten benchmark problems with up to 200 decision variables. The experimental results on these test problems demonstrate the effectiveness of the proposed algorithm.

An Empirical Investigation on Evolutionary Algorithm Evolving Developmental Timings

Recently, evolutionary algorithms that can efficiently solve decomposable binary optimization problems have been developed. They are so-called model-based evolutionary algorithms, which build a model for generating solution candidates by applying a machine learning technique to a population. Their central procedure is linkage detection that reveals a problem structure, that is, how the entire problem consists of sub-problems. However, the model-based evolutionary algorithms have been shown to be ineffective for problems that do not have relevant structures or those whose structures are hard to identify. Therefore, evolutionary algorithms that can solve both types of problems quickly, reliably, and accurately are required. The objective of the paper is to investigate whether the evolutionary algorithm evolving developmental timings (EDT) that we previously proposed can be the desired one. The EDT makes some variables values more quickly converge than the remains for any problems, and then, decides values of the remains to obtain a higher fitness value under the fixation of the variables values. In addition, factors to decide which variable values converge more quickly, that is, developmental timings are evolution targets. Simulation results reveal that the EDT has worse performance than the linkage tree genetic algorithm (LTGA), which is one of the state-of-the-art model-based evolutionary algorithms, for decomposable problems and also that the difference in the performance between them becomes smaller for problems with overlaps among linkages and also that the EDT has better performance than the LTGA for problems whose structures are hard to identify. Those results suggest that an appropriate search strategy is different between decomposable problems and those hard to decompose.

Enhancing Gaussian Estimation of Distribution Algorithm by Exploiting Evolution Direction With Archive.

As a typical model-based evolutionary algorithm, estimation of distribution algorithm (EDA) possesses unique characteristics and has been widely applied in global optimization. However, the commonly used Gaussian EDA (GEDA) usually suffers from premature convergence, which severely limits its search efficiency. This paper first systematically analyzes the reasons for the deficiency of traditional GEDA, then tries to enhance its performance by exploiting the evolution direction, and finally develops a new GEDA variant named EDA2. Instead of only utilizing some good solutions produced in the current generation to estimate the Gaussian model, EDA2 preserves a certain number of high-quality solutions generated in the previous generations into an archive and employs these historical solutions to assist estimating the covariance matrix of Gaussian model. By this means, the evolution direction information hidden in the archive is naturally integrated into the estimated model, which in turn can guide EDA2 toward more promising solution regions. Moreover, the new estimation method significantly reduces the population size of EDA2 since it needs fewer individuals in the current population for model estimation. As a result, a fast convergence can be achieved. To verify the efficiency of EDA2, we tested it on a variety of benchmark functions and compared it with several state-of-the-art EAs. The experimental results demonstrate that EDA2 is efficient and competitive.

Model-based evolutionary algorithms: a short survey

The evolutionary algorithms (EAs) are a family of nature-inspired algorithms widely used for solving complex optimization problems. Since the operators (e.g. crossover, mutation, selection) in most traditional EAs are developed on the basis of fixed heuristic rules or strategies, they are unable to learn the structures or properties of the problems to be optimized. To equip the EAs with learning abilities, recently, various model-based evolutionary algorithms (MBEAs) have been proposed. This survey briefly reviews some representative MBEAs by considering three different motivations of using models. First, the most commonly seen motivation of using models is to estimate the distribution of the candidate solutions. Second, in evolutionary multi-objective optimization, one motivation of using models is to build the inverse models from the objective space to the decision space. Third, when solving computationally expensive problems, models can be used as surrogates of the fitness functions. Based on the review, some further discussions are also given.

Image-Guided Rendering with an Evolutionary Algorithm Based on Cloud Model.

The process of creating nonphotorealistic rendering images and animations can be enjoyable if a useful method is involved. We use an evolutionary algorithm to generate painterly styles of images. Given an input image as the reference target, a cloud model-based evolutionary algorithm that will rerender the target image with nonphotorealistic effects is evolved. The resulting animations have an interesting characteristic in which the target slowly emerges from a set of strokes. A number of experiments are performed, as well as visual comparisons, quantitative comparisons, and user studies. The average scores in normalized feature similarity of standard pixel-wise peak signal-to-noise ratio, mean structural similarity, feature similarity, and gradient similarity based metric are 0.486, 0.628, 0.579, and 0.640, respectively. The average scores in normalized aesthetic measures of Benford's law, fractal dimension, global contrast factor, and Shannon's entropy are 0.630, 0.397, 0.418, and 0.708, respectively. Compared with those of similar method, the average score of the proposed method, except peak signal-to-noise ratio, is higher by approximately 10%. The results suggest that the proposed method can generate appealing images and animations with different styles by choosing different strokes, and it would inspire graphic designers who may be interested in computer-based evolutionary art.

A Multifractal-Guided Multilevel Surrogate Model-Based Evolutionary Algorithm for Expensive Multiobjective Problems

In applied engineering, there are tremendous optimization problems which are multiobjective problems. Meanwhile, a number of them require large amount of time to evaluate their expensive cost function during optimization procedures. This kind of problems can be either financially expensive due to significant computational resources being required or time expensive due to numerous computational complexity. Aiming to this kind of problems, this paper proposed a multilevel surrogate model-based evolutionary algorithm. The proposed method employs DACE modeling method at the beginning to obtain a global trend in the decision domain. When more and more samples are involved and the sample distribution presents a trend or a manifold, the SVR model is utilized as a second-level surrogate model to achieve a better local search. The model transition is determined by the multifractal analysis on the solution set. Experimental results on ZDT and DTLZ standard test cases demonstrate that the time for EGO modeling can be reduced, and the accuracy can be better balanced by comparing to existing SVR and EGO methods.

GAMBIT: A Parameterless Model-Based Evolutionary Algorithm for Mixed-Integer Problems.

Learning and exploiting problem structure is one of the key challenges in optimization. This is especially important for black-box optimization (BBO) where prior structural knowledge of a problem is not available. Existing model-based Evolutionary Algorithms (EAs) are very efficient at learning structure in both the discrete, and in the continuous domain. In this article, discrete and continuous model-building mechanisms are integrated for the Mixed-Integer (MI) domain, comprising discrete and continuous variables. We revisit a recently introduced model-based evolutionary algorithm for the MI domain, the Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT). We extend GAMBIT with a parameterless scheme that allows for practical use of the algorithm without the need to explicitly specify any parameters. We furthermore contrast GAMBIT with other model-based alternatives. The ultimate goal of processing mixed dependences explicitly in GAMBIT is also addressed by introducing a new mechanism for the explicit exploitation of mixed dependences. We find that processing mixed dependences with this novel mechanism allows for more efficient optimization. We further contrast the parameterless GAMBIT with Mixed-Integer Evolution Strategies (MIES) and other state-of-the-art MI optimization algorithms from the General Algebraic Modeling System (GAMS) commercial algorithm suite on problems with and without constraints, and show that GAMBIT is capable of solving problems where variable dependences prevent many algorithms from successfully optimizing them.

A novel model-based multi-objective evolutionary algorithm

In multi-objective evolutionary algorithm MOEA, modelling method is a crucial part. Moreover, variable linkages enable the modelling process more complex for multi-objective optimisation problems. The Karush-Kulm-Tucker condition shows that the Pareto set of a continuous MOP with m objectives is a piecewise continuous m-1-dimensional manifold. How to use this regularity property to model continuous MOP with variable linkages has been the research focus. In this paper, a model-based multi-objective evolutionary algorithm based on regression analysis MMEA-RA for continuous multi-objective optimisation problems with variable linkages is put forward. In the algorithm, the optimisation problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is m-1-dimensional piecewise continuous manifold. The least squares algorithm is used to build such a model. Systematic experiments have shown that, compared with two state-of-the-art algorithms, MMEA-RA performs excellent on a set of test instances with variable linkages.

A Novel Multiobjective Evolutionary Algorithm Based on Regression Analysis

As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m − 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m − 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

A model-adaptive evolutionary algorithm for optimization

Many applications in engineering and science rely on the optimization of computationally expensive functions. A successful approach in such scenarios is to couple an evolutionary algorithm with a mathematical model which replaces the expensive function. However, models introduce several difficulties, such as their inherent inaccuracy, and the difficulty of matching a model to a particular problem. To address these issues, this paper proposes a model-based evolutionary algorithm with two main implementations: (a) it combats model inaccuracy with a tailored trust-region approach to manage the model during the search, and to ensure convergence to an optimum of the true expensive function, and (b) during the search it continuously selects an optimal model type out of a set of candidate models, resulting in a model-adaptive optimization search. Extensive performance analysis shows the efficacy of the proposed algorithm.