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Some signal processing and multimedia applications can be specified by synchronous dataflow (SDF) models. The problem of SDF mapping to a given set of heterogeneous processors has been known to be NP-hard and widely studied in the design automation field. However, modern embedded applications are becoming increasingly complex with dynamic behaviors changes over time. As a significant extension to the SDF, the multi-mode dataflow (MMDF) model has been proposed to specify such an application with a finite number of behaviors (or modes) and each behavior (mode) is represented by an SDF graph. The multiprocessor mapping of an MMDF is far more challenging as the design space increases with the number of modes. Instead of using traditional genetic algorithm (GA)-based design space exploration (DSE) method that encodes the design space as a whole, this article proposes a novel cooperative co-evolutionary genetic algorithm (CCGA)-based framework to efficiently explore the design space by a new problem-specific decomposition strategy in which the solutions of node mapping for each individual mode are assigned to an individual population. Besides, a problem-specific local search operator is introduced as a supplement to the global search of CCGA for further improving the search efficiency of the whole framework. Furthermore, a fitness approximation method and a hybrid fitness evaluation strategy are applied for reducing the time consumption of fitness evaluation significantly. The experimental studies demonstrate the advantage of the proposed DSE method over the previous GA-based method. The proposed method can obtain an optimization result with 2×−3× better quality using less (1/2−1/3) optimization time.

Memetic computing is a blooming research area, which treats memes as the fundamental building blocks of information transfer. Evolutionary multitasking is an emerging topic in memetic computation, which applies evolutionary algorithm to optimize multiple tasks at a time. A famous class of algorithms for evolutionary multitasking is the multi-factorial evolutionary algorithm (MFEA). Nevertheless, current MFEAs only consider problems with small number of tasks, resulting in a lack of effective information transfer strategy. This study proposes a framework for evolutionary multitasking, called the evolution of biocoenosis through symbiosis with fitness approximation (EBSFA). The EBSFA incorporates evolution of biocoenosis through symbiosis (EBS) with fitness approximation to ameliorate the information transfer. The improvement of EBSFA is three-fold, including (1) the adaptive control of information transfer among tasks, (2) the selection of individuals from the universal offspring pool for evaluation based on fitness approximation, and (3) an ensemble method for improving the accuracy of fitness approximation through k nearest neighbors. Experimental analysis verifies the effectiveness and efficiency of the proposed EBSFA, by comparison with an advanced single-tasking method, the covariance matrix adaptation evolution strategy (CMAES), an illustrious multitasking optimization method, the MFEA-II, and an evolutionary many-tasking method, the EBS on a set of many-tasking benchmark problems. The results show that EBSFA can gain nice solution quality and fast convergence speed. Further analysis validates the effectiveness of the proposed components on improving the information transfer.

Due to the rapid development of Medical IoT recently, how to effectively apply these huge amounts of IoT data to enhance the reliability of the clinical decision making has become an increasing issue in the medical field. These data usually comprise high-complicated features with tremendous volume, and it implies that the simple inference models may less powerful to be practiced. In deep learning, multilayer perceptron (MLP) is a kind of feed-forward artificial neural network, and it is one of the high-performance methods about stochastic scheme, fitness approximation, and regression analysis. To process these high uncertain data, the proposed work based on MLP structure in particular integrates the boosting scheme and dimension-reduction process. In this proposed work, the advanced ReLU-based activation function is used. Also, the weight initialization is applied to improve the stable prediction and convergence. After the improved dimension-reduction process is introduced, the proposed method can effectively learn the hidden information from the reformative data and the precise labels also can be recognized by stacking a small amount of neural network layers with paying few extra cost. The proposed work shows a possible path of embedding dimension reduction in deep learning structure with minor price. In addition to the prediction issue, the proposed method can also be applied to assess risk and forecast trend among different information systems.

Designing advanced neural architectures to tackle specific tasks involves weeks or even months of intensive investigation by experts with rich domain knowledge. In recent years, neural architecture search (NAS) has attracted the interest of many researchers due to its ability to automatically design efficient neural architectures. Among different search strategies, evolutionary algorithms have achieved significant successes as derivative-free optimization algorithms. However, the tremendous computational resource consumption of the evolutionary neural architecture search dramatically restricts its application. In this paper, we explore how fitness approximation-based evolutionary algorithms can be applied to neural architecture search and propose NAS-EA-FA to accelerate the search process. We further exploit data augmentation and diversity of neural architectures to enhance the algorithm, and present NAS-EA-FA V2. Experiments show that NAS-EA-FA V2 is at least five times faster than other state-of-the-art neural architecture search algorithms like regularized evolution and iterative neural predictor on NASBench-101, and it is also the most effective and stable algorithm on NASBench-201. All the code used in this paper is available at https://github.com/fzjcdt/NAS-EA-FA.

In any video coding solution, motion estimation (ME) and motion compensation (MC) techniques are widely used and they play an inevitable role in reducing the temporal redundancies between successive frames. Block-based motion estimation (BME) is one of the widely utilized techniques in the recently developed video compression standards by JCT-VC including HEVC due to its efficacy and ease of implementation. In BME, the frames in a video sequence are partitioned into a number of non-overlapping blocks. Then, for each of the blocks, a best-matched block is obtained within a definite search region in the reference frame to minimize certain cost function or fitness value such as the sum of absolute difference (SAD), mean of absolute difference (MAD), or mean square error (MSE). However, the key challenge lies in the evaluation of these cost functions, since they are computationally expensive and involves the most time-taking operations in the BME process. Hence, BME-based approaches can be viewed as an optimization problem and meta-heuristic algorithms can be effectively exploited for the problem under consideration. In this paper, a hybrid BME technique using a recently developed optimization algorithm, namely, JAYA algorithm, is proposed. Besides this proposal, several other modules, namely, the fitness approximation technique, search history preservation, and early & adaptive termination criterion are utilized. The main objective behind the use of the aforementioned modules is to avoid the unnecessary evaluation of the fitness function. Exhaustive simulations are carried out to demonstrate the efficacy of the proposed method over that of the benchmark schemes with respect to different performance measures, namely, the peak signal-to-noise ratio ( P S N R ), PSNR degradation ratio ( D P S N R ), search efficiency, structural similarity index measure (SSIM), and computation time. Comparative analysis and quantitative evaluation clearly show that the present technique produces more reliable motion vectors with competitive time complexity as compared to that of the benchmark schemes.

Interactive genetic algorithms (IGAs), proposed in mid 1980s, are effective methods to solve an optimization problem with implicit or fu zzy indices (Dawkins, 1986). These algorithms combine traditional evolution mechanism with a user’s intelligent evaluation, and the user assigns an individual’s fitness rather than a function that is difficult or even impossible to explicitly express. Up to now, they have been successfully applied in many fields, e.g. face identification (Caldwell & Johnston, 1991), fashion design (Kim & Cho, 2000), music composition (Tokui & Iba, 2000), hearing aid fitting (Takagi & Ohsaki, 2007). The obvious character of IGAs, compared with traditional genetic algorithms (TGAs), is that the user assigns an individual’s fitness. The user compares different individuals in the same generation and assigns fitness based on th eir phenotypes through a human-computer interface. The frequent interaction results in user fatigue. Therefore, IGAs often have small population size and a small number of ev olutionary generations (Takagi, 2001), which influences these algorithms’ performance to some degree and restricts their applications in complicated optimization problems. Accordingly, how to evaluate an individual and express its fitness becomes one of the key problems in IGAs. Since user fatigue results from the user’s evaluation on an individual and expression of its fitness, in order to alleviate user fatigue, a possible alternative is to change the approach to express an individual’s fitness. The goal of this chapter is to alleviate user fatigue by adopting some appropriate approaches to express an individual’s fitness. An accurate number is a commonly used approach to express an individual’s fitness. As is well known, the user’s cognitive is uncertain and gradual, therefore the evaluation of an individual by the user and the expression of its fitness should also be uncertain and gradual. It is difficult to reflect the above character if we adopt an accurate number to express an individual’s fitness. We will present two kinds of uncertain numbers to express an individual’s fitness in this chapter, one is an interval described with the lower limit and the upper limit, the other is a fuzzy number described with a Gaussian membership function. These expressions of an individual’s uncertain fitness well accord with the user’s fuzzy cognitive on the evaluated object. In addition, we will propose some effective strategies to compare different individuals in the same generation on condition of an individual’s uncertain fitness. We will obtain the probability of an individual dominance by use of the probability of interval dominance, and

Learning from imbalanced datasets is highly demanded in real-world applications and a challenge for standard classifiers that tend to be biased towards the classes with the majority of the examples. Undersampling approaches reduce the size of the majority class to balance the class distributions. Evolutionary-based approaches are prominent, treating undersampling as a binary optimisation problem that determines which examples are removed. However, their utilisation is limited to small datasets due to fitness evaluation costs. This work proposes a two-stage clustering-based surrogate model that enables evolutionary undersampling to compute fitness values faster. The main novelty lies in the development of a surrogate model for binary optimisation which is based on the meaning (phenotype) rather than their binary representation (genotype). We conduct an evaluation on 44 imbalanced datasets, showing that in comparison with the original evolutionary undersampling, we can save up to 83% of the runtime without significantly deteriorating the classification performance.

This paper proposes a surrogate-assisted MOEA/D using SVM-based surrogates adjusted to subproblems (MOEA/D-S$^{3}$), which intends to achieve the following technical advantages. Firstly, in order to construct a proper surrogate while reducing learning cost to construct surrogates, a surrogate is an SVM-classifier that identifies a specific region of good solutions and thus its learning cost should be lower than a popular alternative approach, i.e., fitness approximation. Secondly, relying on the first advantage, multiple surrogates are constructed and each surrogate, like an expert, is adjusted to each subproblem defined in the MOEA/D framework in order to improve diversity and convergence of the Pareto set. Experimental results show that MOEA$/\mathrm{D}- \mathrm{S}^{3}$ outperforms MOEA/D on a number of many-objective benchmark problems.

Block matching algorithm is the most popular motion estimation technique, due to its simplicity of implementation and effectiveness. However, the algorithm suffers from a long computation time which affects its general performance. In order to achieve faster motion estimation, a new block matching algorithm based on stochastic fractal search, SFS, is proposed in this paper. SFS is a metaheuristic technique used to solve hard optimization problems in minimal time. In this work, two main contributions are presented. The first one consists of computing the motion vectors in a parallel structure as opposed to the other hierarchical metaheuristic block matching algorithms. When the video sequence frame is divided into blocks, a multi-population model of SFS is used to estimate the motion vectors of all blocks simultaneously. As a second contribution, the proposed algorithm is modified in order to enhance the results. In this modified version, four ideas are investigated. The random initialization, usually used in metaheuristics, is replaced by a fixed pattern. The initialized solutions are evaluated using a new fitness function that combines two matching criteria. The considered search space is controlled by a new adaptive window size strategy. A modified version of the fitness approximation method, which is known to reduce computation time but causes some degradation in the estimation accuracy, is proposed to balance between computation time and estimation accuracy. These ideas are evaluated in nine video sequences and the percentage improvement of each idea, in terms of estimation accuracy and computational complexity, is reported. The presented algorithms are then compared with other well-known block matching algorithms. The experimental results indicate that the proposed ideas improve the block matching performance, and show that the proposed algorithm outperforms many state-of-the-art methods.

This research investigates the hypothesis that the use of different fitness measures at the different generations of genetic programming (GP) is more effective than the convention of applying the same fitness measure individually throughout GP. A genetic algorithm (GA) is used to induce the sequence in which fitness measures should be applied over the GP generations. Subsequently, the performance of a GP system applying the evolved fitness measure sequence is compared with the conventional GP approach. The former approach is shown to significantly outperform standard GP on varied benchmark problems. Furthermore, the evolved fitness measure sequences are shown to generalize within a problem class: therefore, the sequences can be evolved off-line for different problem classes. Critically, sequences trained on the problem classes are also shown to generalize to complex, real-world problems. Overall, the findings of the study are in favor of the hypothesis. This study has revealed the effectiveness of dynamic fitness measures when applied to benchmark and real-world problems.

A significant part of the world's energy consumption is related to the building sector. Consequently, the execution of improving buildings' energy performance actions is a primary approach to reduce energy dissipation . Building simulation-based optimization is a popular tool for this task; however, it requires the direct coupling of a simulation model with an optimization algorithm that involves intensive and laborious computation. This study aims to reduce computational costs by proposing an optimization procedure based on combining surrogate models with a multi-objective evolutionary algorithm to optimize the building's energy consumption and its occupants' thermal comfort simultaneously. The case study of an existing office building in Kermanshah, Iran was selected to implement and evaluate this suggested optimization strategy . In this study, the input variables are chosen so that, for the studied building, they could be changed without difficulty and high costs. EnergyPlus simulates the situations set by design-of-experiments. The best subsets regression method identifies the regression models which could fit the simulation results with as few factors as possible. These regression models are implemented inside the NSGA-II algorithm for optimization. The optimal solution results show that using the applied multi-objective optimization method, it is possible to decrease the building's annual gas and electricity consumption, compared to the baseline case, by up to 21.3% and 9.7%, respectively, while keeping up the indoor environment in the limit of the thermal comfort zone.

Neural network architectures can be regularised by adding a penalty term to the objective function, thus minimising network complexity in addition to the error. However, adding a term to the objective function inevitably changes the surface of the objective function. This study investigates the landscape changes induced by the weight elimination penalty function under various parameter settings. Fitness landscape metrics are used to quantify and visualise the induced landscape changes, as well as to propose sensible ranges for the regularisation parameters. Fitness landscape metrics are shown to be a viable tool for neural network objective function landscape analysis and visualisation.

Differential evolution (DE) is one of the most powerful and versatile evolutionary algorithms for efficiently solving complex real-world optimization problems in recent years. Since its introduction in 1995, the research focus in DE has mostly been on the variant side with so many new algorithms proposed based on the original DE algorithm. However, each new algorithm is only suitable for certain fitness landscapes, and, therefore, some types of optimization problems cannot be solved efficiently. To tackle this issue, this paper presents a new self-feedback DE algorithm, named the SFDE; its optimal variation strategy is selected by extracting the local fitness landscape characteristics in each generation population and combing the probability distributions of unimodality and multimodality in each local fitness landscape. The proposed algorithm is tested on a suite of 17 benchmark functions, and the experimental results demonstrated its advantages in a high search dimension in that it can ensure that the population moves to a better fitness landscape, then speeds up convergence to the global optimum, and avoids falling into local optima.

Escaping local optima is one of the major obstacles to function optimisation. Using the metaphor of a fitness landscape, local optima correspond to hills separated by fitness valleys that have to be overcome. We define a class of fitness valleys of tunable difficulty by considering their length, representing the Hamming path between the two optima and their depth, the drop in fitness. For this function class we present a runtime comparison between stochastic search algorithms using different search strategies. The (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document}1+1) EA is a simple and well-studied evolutionary algorithm that has to jump across the valley to a point of higher fitness because it does not accept worsening moves (elitism). In contrast, the Metropolis algorithm and the Strong Selection Weak Mutation (SSWM) algorithm, a famous process in population genetics, are both able to cross the fitness valley by accepting worsening moves. We show that the runtime of the (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document}1+1) EA depends critically on the length of the valley while the runtimes of the non-elitist algorithms depend crucially on the depth of the valley. Moreover, we show that both SSWM and Metropolis can also efficiently optimise a rugged function consisting of consecutive valleys.

A steady state analysis of the optimization quality of a classical self-adaptive evolution strategy (ES) on a class of robust optimization problems is presented. A novel technique for calculating progress rates for nonquadratic noisy fitness landscapes is presented. This technique yields asymptotically exact results in the infinite population size limit. This technique is applied to a class of functions with noise-induced multimodality. The resulting progress rate formulas are compared with high-precision experiments. The influence of fitness resampling is considered and the steady state behavior of the ES is derived and compared with simulations. The questions whether one should sample and average fitness values and how to choose the truncation ratio are discussed giving rise to further research perspectives.

Error threshold is the upper bound of the mutation rate such that the genetic information can pass on during reproduction. In Eigen’s original proposal, the fitness landscape consists of a single peak along with other background sequences. However, realistic fitness landscapes are far more complicated and thus obstruct deeper understanding from either analytic or numerical approaches. Here we propose a variational approach to derive the error thresholds in generic fitness landscapes. When applying to the Eigen model, it delivers the correct error threshold and reveals the scaling relations between relevant parameters. For the fitness landscape with a peak–mesa profile, the two-dimensional phase diagram in the mesa fitness and the mutation rate can be computed with minimal cost. When the mesa fitness is larger than some critical value, upon increasing the mutation rate, the quasispecies changes from the peak to the mesa and then dissolves into the random background. The phase boundaries can be computed analytically within the effective-fitness approximation. At the end, the universal phase diagram in terms of the rescaled variables is explained in detail.

Our methods for analyzing stochastic fitness are mostly approximations, and the assumptions behind these approximations are not always well understood. Furthermore, many of these approximations break down when fitness variance is high. This review covers geometric mean growth, diffusion approximations, and Markov processes. It discusses where each is appropriate, the conditions under which they break down, and their advantages and disadvantages, with special attention to the case of high fitness variance. A model of sessile and site-attached coastal species is used as a running example, and fully worked calculations and code are provided. Summary: The logarithm of geometric mean growth is usually only appropriate when (a) an invader growth rate is needed and (b) fitness variability is driven by environmental fluctuations. The usual approximation breaks down when fitness variance is high. Diffusion approximations can provide a reasonable guide to the expected change in frequency over a time step if expected fitnesses and fitness variances are appropriately scaled by the average expected fitness. Diffusion approximations can perform less well for fixation probabilities, especially since further approximations may be required. Fixation probabilities can be calculated exactly using a Markov process, regardless of how large fitness variance is, although an analytic expression is frequently not possible. If an analytic expression is desired, it may be worth using a diffusion approximation and checking it with a Markov process calculation.

A theorem characterizing the property of the optimal solution is presented.A hybrid evolutionary algorithm (HEA) is proposed.Extreme machine learning is used to approximate the fitness of most individuals.Two heuristics are incorporated to generate a good initial population.The proposed algorithm is computationally effective. This paper considers the two-stage capacitated facility location problem (TSCFLP) in which products manufactured in plants are delivered to customers via storage depots. Customer demands are satisfied subject to limited plant production and limited depot storage capacity. The objective is to determine the locations of plants and depots in order to minimize the total cost including the fixed cost and transportation cost. However, the problem is known to be NP-hard. A practicable exact algorithm is impossible to be developed. In order to solve large-sized problems encountered in the practical decision process, an efficient alternative approximate method becomes more valuable. This paper aims to propose a hybrid evolutionary algorithm framework with machine learning fitness approximation for delivering better solutions in a reasonable amount of computational time. In our study, genetic operators are adopted to perform the search process and a local search strategy is used to refine the best solution found in the population. To avoid the expensive consumption of computational time during the fitness evaluating process, the framework uses extreme machine learning to approximate the fitness of most individuals. Moreover, two heuristics based on the characteristics of the problem is incorporated to generate a good initial population. Computational experiments are performed on two sets of test instances from the recent literature. The performance of the proposed algorithm is evaluated and analyzed. Compared with other algorithms in the literature, the proposed algorithm can find the optimal or near-optimal solutions in a reasonable amount of computational time. By employing the proposed algorithm, facilities can be positioned more efficiently, which means the fixed cost and the transportation cost can be decreased significantly, and organizations can enhance competitiveness by using the optimized facility location scheme.

Achieving robustness with a limited distortion level is a challenging design problem for watermarking systems in multimedia applications with a guaranteed quality requirement. In this paper, we provide an intelligent system for watermarking through incorporating a meta-heuristic technique along with an embedding method to achieve an optimized performance. The optimization objective is to provide the maximum possible robustness without exceeding a predetermined distortion limit. Hence, the quality level of the watermarking method could be guaranteed through that constraint optimization. A new fitness function is defined to provide the required convergence toward the optimum solution for the defined optimization problem. The fitness function is based on dividing its applied solution population into two groups, where each group is ranked according to a different objective. Thus, the multi-objectives in the problem are decoupled and solved through two single-objective sub-problems. Unlike existing watermarking optimization techniques, the proposed work does not require weighting factors. To illustrate the effectiveness of the proposed approach, we employ a recent watermarking technique, and then use it as the embedding method to be optimized. The Artificial Bee Colony is selected as the meta-heuristic optimization method in which the proposed fitness function is used. Experimental results show that the imposed quality constraint is satisfied, and that the proposed method provides enhanced robustness under different attacks for various quality thresholds. The presented approach offers a robust solution that can be applied to numerous multimedia applications such as film industry, intelligent surveillance and security systems.

Noisy optimization is currently receiving increasing popularity for its widespread applications in engineering optimization problems, where the objective functions are often found to be contaminated with noisy sensory measurements. In absence of knowledge of the noise-statistics, discriminating better trial solutions from the rest becomes difficult in the “selection” step of an evolutionary optimization algorithm with noisy objective/s. This paper provides a thorough survey of the present state-of-the-art research on noisy evolutionary algorithms for both single and multi-objective optimization problems. This is undertaken by incorporating one or more of the five strategies in traditional evolutionary algorithms. The strategies include (i) fitness sampling of individual trial solution, (ii) fitness estimation of noisy samples, (iii) dynamic population sizing over the generations, (iv) adaptation of the evolutionary search strategy, and (v) modification in the selection strategy.

Display Omitted A new composite fitness evaluation function is proposed for many-objective cases.The convergence, diversity and user preferences are considered in this function.The proposed fitness function guides the search to the preferred region of the Pareto front.Using the proposed function in an EMO algorithm led to better results.The algorithm has comparable performance with a reasonable amount of computing. It has been shown that the multi-objective evolutionary algorithms (MOEAs) act poorly in solving many-objective optimization problems which include more than three objectives. The research emphasis, in recent years, has been put into improving the MOEAs to enable them to solve many-objective optimization problems efficiently. In this paper, we propose a new composite fitness evaluation function, in a novel way, to select quality solutions from the objective space of a many-objective optimization problem. Using this composite function, we develop a new algorithm on a well-known NSGA-II and call it FR-NSGA-II, a fast reference point based NSGA-II. The algorithm is evaluated for producing quality solutions measured in terms of proximity, diversity and computational time. The working logic of the algorithm is explained using a bi-objective linear programming problem. Then we test the algorithm using experiments with benchmark problems from DTLZ family. We also compare FR-NSGA-II with four competitive algorithms from the extant literature to show that FR-NSGA-II will produce quality solutions even if the number of objectives is as high as 20.

We aim to find robust solutions in optimization settings where there is uncertainty associated with the operating/environmental conditions, and the fitness of a solution is hence best described by a distribution of outcomes. In such settings, the nature of the fitness distribution (reflecting the performance of a particular solution across a set of operating scenarios) is of potential interest in deciding solution quality, and previous work has suggested the inclusion of robustness as an additional optimization objective. However, there has been limited investigation of different robustness criteria, and the impact this choice may have on the sample size needed to obtain reliable fitness estimates. Here, we investigate different single and multi-objective formulations for robust optimization, in the context of a real-world problem addressed via simulation-based optimization. For the (limited evaluation) setting considered, our results highlight the value of an explicit robustness criterion in steering an optimizer towards solutions that are not only robust (as may be expected), but also associated with a profit that is, on average, higher than that identified by standard single-objective approaches. We also observe significant interactions between the choice of robustness measure and the sample size employed during fitness evaluation, an effect that is more pronounced for our multi-objective models. HighlightsSuperior solutions are obtained by optimizing robustness as an additional objective.The standard deviation of outcomes is considered as robustness measure.It provides improved guidance compared to a measure based on worst-case performance.Reliable fitness estimates appear to be more crucial in multi-objective formulations.

Display Omitted MUGPSO provides efficiency for optimization problems associated with computationally expensive analysis and simulation tasks.Meta-models are constructed using GRNN and updated as the PSO run proceeds for better approximation of the solution space.MUGPSO is compared with PSO without meta-modeling and other meta-modeling methods using ten benchmark problems.Solution quality obtained by MUGPSO is promising while providing best results on a few of the ten benchmark problems. Swarm intelligence (SI) and evolutionary computation (EC) algorithms are often used to solve various optimization problems. SI and EC algorithms generally require a large number of fitness function evaluations (i.e., higher computational requirements) to obtain quality solutions. This requirement becomes more challenging when optimization problems are associated with computationally expensive analyses and/or simulation tasks. To tackle this issue, meta-modeling has shown successful results in improving computational efficiency by approximating the fitness or constraint functions of these complex optimization problems. Meta-modeling approaches typically use polynomial regression, kriging, radial basis function network, and support vector machines. Less attention has been given to the generalized regression neural network approach, and yet, it offers several advantages. Specifically, the model construction process does not require iterations. Its only one parameter is known to be less sensitive and usually requires less effort in selecting an optimal parameter. We use generalized regression neural network in this paper to construct meta-models and to approximate the fitness function in particle swarm optimization. To assess the performance and quality of these solutions, the proposed meta-modeling approach is tested on ten benchmark functions. The results are promising in terms of the solution quality and computational efficiency, especially when compared against the results of particle swarm optimization without meta-modeling and several other meta-modeling methods in previously published literature.

Display Omitted Using Discrete-time Fourier transform (DTFT) and dynamic time warping (DTW) distance to analyze dynamic fitness landscape.The measures are extracted from the frequency spectrum and the time domain of fitness landscape.The criteria evaluate the variation of fitness landscape from outline, keenness, period, fitness values and similarity.The proposed measures are adaptable for dynamic fitness landscape and have generality.The proposed measures supplement the existing metrics for evaluating the characteristics of dynamic optimization problem. Dynamic optimization problems (DOPs) have attracted increasing attention in recent years. Analyzing the fitness landscape is essential to understand the characteristics of DOPs and may provide guidance for the algorithm design. Existing measures for analyzing the dynamic fitness landscape, such as the dynamic fitness distance correlation and the severity of change, cannot give a comprehensive evaluation of the landscape and have many disadvantages. In this paper, we used Discrete-time Fourier transform (DTFT) and dynamic time warping (DTW) distance to acquire information of fitness landscape from frequency and time domains. Five measures are proposed, including the stationarity of amplitude change, the keenness, the periodicity, the change degree of average fitness and the similarity. They can reflect the features of fitness landscape from the aspects of outline, keenness, period, fitness value and similarity degree, respectively. These criteria can obtain essential information that cannot be acquired by existing criteria, and do not depend on the distribution of variables, the prior information of solutions and algorithms. To illustrate the performance of the five measures, experiments are conducted based on three types of standard DOPs with a two-peak function. In addition, we also apply these criteria on the test task scheduling problem for illustrating the fairness and adaptability. The experiment results show that these criteria can reflect the change characteristics of dynamic fitness landscape, and are consistent with the theoretical analysis.