Stochastic Search Technique Research Articles

An embedded differential evolution approach to adaptive covariance inflation with the ensemble Kalman filter

ABSTRACT The limited ensemble sizes and the neglected model errors in ensemble-based Data Assimilation (DA) usually lead to underestimation of the error variance, and covariance inflation ‘inflates’ the covariance of a forecast or analysis ensemble by some positive factor in each assimilation cycle. In practice, the value of the inflation factor is often set by trial and error. Thus, a variety of adaptive covariance inflation (ACI) algorithms have been proposed to improve assimilation performance by adjusting the optimal parameters. Most of these used traditional optimization algorithms, such as gradient methods and relaxation methods. However, Evolutionary Algorithms(EAs), which encompass a range of population-based stochastic search techniques widely used in various engineering optimization problems, are rarely seen in DA. In this study, we developed a new framework for adaptive inflation factors, introducing differential evolution (DE) algorithm into local ensemble Transform Kalman filter (LETKF) that can explore the most suitable/optimal inflation factors online. A ‘micro-DE’ based data assimilation method can obtain better assimilation results step by step without taking a much longer time. The feasibility and effectiveness of the algorithm is demonstrated in an idealized Lorenz-96 model with simulated observations. Under both perfect and imperfect-model scenarios, it is found that the ‘micro-DE’LETKF method is capable of outperforming the original LETKF with a considerable lower computational cost. The adaptive inflation factor is optimally updated at each assimilation cycle either around the upper bound or around the lower bound, which means that only an adaptive factor helps mitigate the ensemble collapse due to a lack of spread. However, the further study will consider the application of the methodology to more complex atmospheric models.

Solar PV focused LFC studies utilizing an SFS-optimized PID with fractional derivative (PIDDμ), and incorporating BESS and FESS applications

This study investigates the application of a PID controller with a fractional derivative component (PIDDμ), optimized using the stochastic fractional search (SFS) technique, for load frequency control (LFC) in power systems. Additionally, solar PV and battery energy storage systems (BESS) and flywheel energy storage systems (FESS) are integrated as backup sources to enhance the LFC performance. To assess the effectiveness of the proposed approach, three error metrics—Integral Time Absolute Error (ITAE), Integral Time Multiplied Square Error (ITSE), and Integral of Absolute Error (IAE)—are evaluated. The results are compared with recent optimization-based LFC techniques across various scenarios. It is found that the SFS-PIDDμ achieves IAE=0.006786, ITSE=1.07e-05, and ITAE=0.01853, which are significantly lower than the error values produced by other LFC techniques. Furthermore, integrating solar PV, along with BESS and FESS, further reduces these error values. The graphical LFC responses of the SFS-PIDDμ outperform other optimization-based LFC techniques. The robustness of the approach is also validated against random load changes of varying magnitudes and for broader parametric variations.

Energetics and spectroscopic studies of clusters and the temperature dependencies of the isomers: An approach based on a combined recipe of parallel tempering and quantum chemical methods.

A system associated with several number of weak interactions supports numerous number of stable structures within a narrow range of energy. Often, a deterministic search method fails to locate the global minimum geometry as well as important local minimum isomers for such systems. Therefore, in this work, the stochastic search technique, namely parallel tempering, has been executed on the quantum chemical surface of the system for -8 to generate global minimum as well as several number of local minimum isomers. IR spectrum can act as the fingerprint property for such system to be identified. Thus, IR spectroscopic features have also been included in this work. Vertical detachment energy has also been calculated to obtain clear information about number of water molecules in several spheres around the central anion. In addition, in a real experimental scenario, not only the global but also the local minimum isomers play an important role in determining the average value of a particular physically observable property. Therefore, the relative conformational populations have been determined for all the evaluated structures for the temperature range between 20K and 400K. Further to understand the phase change behavior, the configurational heat capacities have also been calculated for different sizes.

An improved arithmetic optimization algorithm with multi-strategy for adaptive multi-spectral image fusion

Panchromatic and multi-spectral image fusion, called panchromatic sharpening, is the process of combining the spatial and spectral information of the source image into the fused image to give the image a higher spatial and spectral resolution. In order to improve the spatial resolution and spectral information quality of the image, an adaptive multi-spectral image fusion method based on an improved arithmetic optimization algorithm is proposed. This paper proposed improved arithmetic optimization algorithm, which uses dynamic stochastic search technique and oppositional learning operator, to perform local search and behavioral complementation of population individuals, and to improve the ability of population individuals to jump out of the local optimum. The method combines adaptive methods to calculate the weights of linear combinations of panchromatic and multi-spectral gradients to improve the quality of fused images. This study not only improves the quality and effect of image fusion, but also focuses on optimizing the operation efficiency of the algorithm to have real-time and high efficiency. Experimental results show that the proposed method exhibits strong performance on different datasets, improves the spatial resolution and spectral information quality of the fused images, and has good adaptability and robustness. The source code is available at: https://github.com/starboot/IAOA-For-Image-Fusion.

The Investigation of LSTM-Random Search with Various Standardization and Normalization Technologies

The stock market, being a complex and chaotic system, presents a formidable challenge for prediction. This paper explores the intricacies of stock prediction by focusing on data preprocessing, specifically investigating the impact of different standardization and normalization techniques on LSTM structures. To enhance predictive accuracy, this study employed a stochastic search technique in this study. It is tested using 1520 data points of the closing prices of Bitcoin and Amazon that were obtained from Kaggle between May 1, 2013, and May 14, 2019. It is discovered that the prediction performance under the LSTM framework is significantly impacted by various data preprocessing techniques. The normalization techniques employing MinMaxScaler and MaxAbsScaler performed better for AMZN, a stock with stable prices, and the RobustScaler normalization method yielded the best results for Bitcoin stock prediction, suggesting that it is more useful for datasets with higher volatility. These results provide a useful guide for future research on stock price prediction by highlighting the significance of selecting the right preprocessing technique based on data characteristics and highlighting the benefits of dynamically modifying the lstm structure for stochastic searches.

BAYESIAN NON-HOMOGENEOUS HIDDEN MARKOV MODEL WITH VARIABLE SELECTION FOR INVESTIGATING DRIVERS OF SEIZURE RISK CYCLING.

A major issue in the clinical management of epilepsy is the unpredictability of seizures. Yet, traditional approaches to seizure forecasting and risk assessment in epilepsy rely heavily on raw seizure frequencies, which are a stochastic measurement of seizure risk. We consider a Bayesian non-homogeneous hidden Markov model for unsupervised clustering of zero-inflated seizure count data. The proposed model allows for a probabilistic estimate of the sequence of seizure risk states at the individual level. It also offers significant improvement over prior approaches by incorporating a variable selection prior for the identification of clinical covariates that drive seizure risk changes and accommodating highly granular data. For inference, we implement an efficient sampler that employs stochastic search and data augmentation techniques. We evaluate model performance on simulated seizure count data. We then demonstrate the clinical utility of the proposed model by analyzing daily seizure count data from 133 patients with Dravet syndrome collected through the Seizure Tracker™ system, a patient-reported electronic seizure diary. We report on the dynamics of seizure risk cycling, including validation of several known pharmacologic relationships. We also uncover novel findings characterizing the presence and volatility of risk states in Dravet syndrome, which may directly inform counseling to reduce the unpredictability of seizures for patients with this devastating cause of epilepsy.

Memory, evolutionary operator, and local search based improved Grey Wolf Optimizer with linear population size reduction technique

Optimization of multi-modal functions is challenging even for evolutionary and swarm-based algorithms as it requires an efficient exploration for finding the promising region of the search space, and effective exploitation to precisely find the global optimum. Grey Wolf Optimizer (GWO) is a recently developed metaheuristic algorithm that is inspired by nature with a relatively small number of parameters for tuning. However, GWO and most of its variants may suffer from the lack of population diversity, premature convergence, and the inability to preserve a good balance between exploratory and exploitative behaviors. To address these limitations, this work proposes a new variant of GWO incorporating memory, evolutionary operators, and a stochastic local search technique. It further integrates Linear Population Size Reduction (LPSR) technique. The proposed algorithm is comprehensively tested on 23 numerical benchmark functions, high dimensional benchmark functions, 13 engineering case studies, four data classifications, and three function approximation problems. The benchmark functions are mostly taken from the CEC 2005 and CEC 2010 special sessions, and they include rotated, shifted functions. The engineering case studies are from the CEC 2020 real-world non-convex constrained optimization problems. The performance of the proposed GWO is compared with popular metaheuristics, namely, particle swarm optimization (PSO), gravitational search algorithm (GSA), slap swarm algorithm (SSA), differential evolution (DE), self-adaptive differential evolution (SADE), basic GWO and its three recently improved variants. Statistical analysis and Friedman tests have been conducted to thoroughly compare their performance. The obtained results demonstrate that the proposed GWO outperforms the algorithms compared for the benchmark functions and engineering case studies tested.

Crime in Philadelphia: Bayesian Clustering with Particle Optimization

Accurate estimation of the change in crime over time is a critical first step toward better understanding of public safety in large urban environments. Bayesian hierarchical modeling is a natural way to study spatial variation in urban crime dynamics at the neighborhood level, since it facilitates principled “sharing of information” between spatially adjacent neighborhoods. Typically, however, cities contain many physical and social boundaries that may manifest as spatial discontinuities in crime patterns. In this situation, standard prior choices often yield overly smooth parameter estimates, which can ultimately produce mis-calibrated forecasts. To prevent potential over-smoothing, we introduce a prior that partitions the set of neighborhoods into several clusters and encourages spatial smoothness within each cluster. In terms of model implementation, conventional stochastic search techniques are computationally prohibitive, as they must traverse a combinatorially vast space of partitions. We introduce an ensemble optimization procedure that simultaneously identifies several high probability partitions by solving one optimization problem using a new local search strategy. We then use the identified partitions to estimate crime trends in Philadelphia between 2006 and 2017. On simulated and real data, our proposed method demonstrates good estimation and partition selection performance. Supplementary materials for this article are available online.

K-RBBSO Algorithm: A Result-Based Stochastic Search Algorithm in Big Data

Clustering is widely used in client-facing businesses to categorize their customer base and deliver personalized services. This study proposes an algorithm to stochastically search for an optimum solution based on the outcomes of a data clustering process. Fundamentally, the aforementioned goal is achieved using a result-based stochastic search algorithm. Hence, shortcomings of existing stochastic search algorithms are identified, and the k-means-initiated rapid biogeography-based silhouette optimization (K-RBBSO) algorithm is proposed to overcome them. The proposed algorithm is validated by creating a data clustering engine and comparing the performance of the K-RBBSO algorithm with those of currently used stochastic search techniques, such as simulated annealing and artificial bee colony, on a validation dataset. The results indicate that K-RBBSO is more effective with larger volumes of data compared to the other algorithms. Finally, we describe some prospective beneficial uses of a data clustering algorithm in unsupervised learning based on the findings of this study.

Learning MAX-SAT from contextual examples for combinatorial optimisation

Combinatorial optimisation problems are ubiquitous in artificial intelligence. Designing the underlying models, however, requires substantial expertise, which is a limiting factor in practice. The models typically consist of hard and soft constraints, or combine hard constraints with an objective function. We introduce a novel setting for learning combinatorial optimisation problems from contextual examples. These positive and negative examples show – in a particular context – whether the solutions are good enough or not. We develop our framework using the MAX-SAT formalism as it is a simple yet powerful setting having these features. We study the learnability of MAX-SAT models. Our theoretical results show that high-quality MAX-SAT models can be learned from contextual examples in the realisable and agnostic settings, as long as the data satisfies an intuitive “representativeness” condition. We also contribute two implementations based on our theoretical results: one leverages ideas from syntax-guided synthesis while the other makes use of stochastic local search techniques. The two implementations are evaluated by recovering synthetic and benchmark models from contextual examples. The experimental results support our theoretical analysis, showing that MAX-SAT models can be learned from contextual examples. Among the two implementations, the stochastic local search learner scales much better than the syntax-guided implementation while providing comparable or better models.

Reinforcement Learning for Central Pattern Generation in Dynamical Recurrent Neural Networks.

Lifetime learning, or the change (or acquisition) of behaviors during a lifetime, based on experience, is a hallmark of living organisms. Multiple mechanisms may be involved, but biological neural circuits have repeatedly demonstrated a vital role in the learning process. These neural circuits are recurrent, dynamic, and non-linear and models of neural circuits employed in neuroscience and neuroethology tend to involve, accordingly, continuous-time, non-linear, and recurrently interconnected components. Currently, the main approach for finding configurations of dynamical recurrent neural networks that demonstrate behaviors of interest is using stochastic search techniques, such as evolutionary algorithms. In an evolutionary algorithm, these dynamic recurrent neural networks are evolved to perform the behavior over multiple generations, through selection, inheritance, and mutation, across a population of solutions. Although, these systems can be evolved to exhibit lifetime learning behavior, there are no explicit rules built into these dynamic recurrent neural networks that facilitate learning during their lifetime (e.g., reward signals). In this work, we examine a biologically plausible lifetime learning mechanism for dynamical recurrent neural networks. We focus on a recently proposed reinforcement learning mechanism inspired by neuromodulatory reward signals and ongoing fluctuations in synaptic strengths. Specifically, we extend one of the best-studied and most-commonly used dynamic recurrent neural networks to incorporate the reinforcement learning mechanism. First, we demonstrate that this extended dynamical system (model and learning mechanism) can autonomously learn to perform a central pattern generation task. Second, we compare the robustness and efficiency of the reinforcement learning rules in relation to two baseline models, a random walk and a hill-climbing walk through parameter space. Third, we systematically study the effect of the different meta-parameters of the learning mechanism on the behavioral learning performance. Finally, we report on preliminary results exploring the generality and scalability of this learning mechanism for dynamical neural networks as well as directions for future work.

Metaheuristic Optimization Algorithm for Signals Classification of Electroencephalography Channels

Digital signal processing of electroencephalography (EEG) data is now widely utilized in various applications, including motor imagery classification, seizure detection and prediction, emotion classification, mental task classification, drug impact identification and sleep state classification. With the increasing number of recorded EEG channels, it has become clear that effective channel selection algorithms are required for various applications. Guided Whale Optimization Method (Guided WOA), a suggested feature selection algorithm based on Stochastic Fractal Search (SFS) technique, evaluates the chosen subset of channels. This may be used to select the optimum EEG channels for use in Brain-Computer Interfaces (BCIs), the method for identifying essential and irrelevant characteristics in a dataset, and the complexity to be eliminated. This enables (SFS-Guided WOA) algorithm to choose the most appropriate EEG channels while assisting machine learning classification in its tasks and training the classifier with the dataset. The (SFS-Guided WOA) algorithm is superior in performance metrics, and statistical tests such as ANOVA and Wilcoxon rank-sum are used to demonstrate this.

A Systematic Literature Review on Particle Swarm Optimization Techniques for Medical Diseases Detection.

Artificial Intelligence (AI) is the domain of computer science that focuses on the development of machines that operate like humans. In the field of AI, medical disease detection is an instantly growing domain of research. In the past years, numerous endeavours have been made for the improvements of medical disease detection, because the errors and problems in medical disease detection cause serious wrong medical treatment. Meta-heuristic techniques have been frequently utilized for the detection of medical diseases and promise better accuracy of perception and prediction of diseases in the domain of biomedical. Particle Swarm Optimization (PSO) is a swarm-based intelligent stochastic search technique encouraged from the intrinsic manner of bee swarm during the searching of their food source. Consequently, for the versatility of numerical experimentation, PSO has been mostly applied to address the diverse kinds of optimization problems. However, the PSO techniques are frequently adopted for the detection of diseases but there is still a gap in the comparative survey. This paper presents an insight into the diagnosis of medical diseases in health care using various PSO approaches. This study presents to deliver a systematic literature review of current PSO approaches for knowledge discovery in the field of disease detection. The systematic analysis discloses the potential research areas of PSO strategies as well as the research gaps, although, the main goal is to provide the directions for future enhancement and development in this area. This paper gives a systematic survey of this conceptual model for the advanced research, which has been explored in the specified literature to date. This review comprehends the fundamental concepts, theoretical foundations, and conventional application fields. It is predicted that our study will be beneficial for the researchers to review the PSO algorithms in-depth for disease detection. Several challenges that can be undertaken to move the field forward are discussed according to the current state of the PSO strategies in health care.

Diverse Depth-First Search in Satisificing Planning

Diverse best-first search (DBFS) is a successful algorithm for satisficing planning that is built on top of greedy best-first search and uses stochastic search techniques to select the next ``best'' state that is not always in agreement with the heuristic function. DBFS thus considers a diversity of search directions and avoids search plateaus caused by inaccurate heuristic estimation. However, the scalability of DBFS is still limited by the available memory resource, as in any planning system that uses best-first search at its core. This paper presents the diverse depth-first search (DDFS) algorithm that overcomes the memory bottleneck of DBFS. DDFS requires much less memory than DBFS yet it successfully incorporates DBFS' randomized node selection scheme for effective search diversification. Additionally, DDFS is enhanced with a transposition table to avoid duplicate search effort commonly found in depth-first search. Experimental results in solving problems used in previous International Planning Competitions show that DDFS can solve instances that remain unsolvable by DBFS due to its excessive memory requirements.

Cognitive population initialization for swarm intelligence and evolutionary computing

Cognitive computing has been commonly used to address different forms of optimization issues. Swarm intelligence (SI) and evolutionary computing (EC) are population-based intelligent stochastic search techniques promoted to search for their food from the intrinsic way of bee swarming and human evolution. Initialization of populations is a critical factor in the Particle swarm optimization (PSO) algorithm that significantly affects diversity and convergence. Quasi-random sequences based on cognitive computing are more helpful in initializing the population than applying the random distribution for initialization to maximize diversity and convergence. The capacity of PSO is expanded to make it suitable for the optimization problem by adding new initialization techniques based on cognitive computing using the sequence of low discrepancies. The employed low discrepancies sequences included WELL named WE-PSO to solve the optimization problems in large-scale search spaces. The proposed approach has been tested on fifteen well-known uni-modal and multi-modal benchmark test problems extensively used in the literature. Also, WE-PSO efficiency has been compared to standard PSO, and two other Sobol-based PSO (SOB-PSO) and Halton-based PSO (HAL-PSO) initialization approach. The results were obtained to validate the efficiency and effectiveness of the proposed approach. Mean fitness values obtained using WE-PSO designate that WE-PSO is better than standard techniques in multi-modal problems. The computational results also show that the proposed technique outperformed and has a higher accuracy rate than the classical approaches. Besides, the proposed work’s result offers a foresight of how the proposed initialization approach has a significant effect on the importance of cost function, convergence, and diversity.

Stochastic local search: a state-of-the-art review

The main objective of this paper is to provide a state-of-the-art review, analyze and discuss stochastic local search techniques used for solving hard combinatorial problems. It begins with a short introduction, motivation and some basic notation on combinatorial problems, search paradigms and other relevant features of searching techniques as needed for background. In the following a brief overview of the stochastic local search methods along with an analysis of the state-of-the-art stochastic local search algorithms is given. Finally, the last part of the paper present and discuss some of the most latest trends in application of stochastic local search algorithms in machine learning, data mining and some other areas of science and engineering. We conclude with a discussion on capabilities and limitations of stochastic local search algorithms.

An Estimation of Distribution Algorithm With Filtering and Learning

Estimation of distribution algorithm (EDA) is an efficient population-based stochastic search technique. Since it was proposed, many attempts have been made to improve its performance in the context of nonlinear continuous optimization. However, the success of EDA depends on the accuracy of modeling, the effectiveness of sampling, and the ability of exploration. An effective EDA often needs to take some measures to adjust the model and to guide sampling. In this article, we propose a novel EDA which applies the idea of Kalman filtering to revise the modeling data and a learning strategy to improve sampling. The filtering scheme modifies the modeling data set using an estimation error matrix based on historic solution data. During the sampling process, the learning strategy determines the region to sample next based on the sampling outcomes so far, instead of completely random sampling. The proposed EDA also employs a multivariate probabilistic model based on copula function and can quickly reach the promising area in which the optimal solution is likely to be located. A collection of general benchmark functions are used to test the performance of the proposed algorithm. Computational experiments show that the EDA is effective. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In many process industries, there exist black-box operation optimization problems and large-scale nonlinear optimization problems with variable coupling. For these problems, it is difficult to establish mechanism models between input and output. However, real-time data can be measured from the system through sensors. We can utilize this process information to optimize the system so as to attain the desired objective. In this article, we propose a novel estimation of distribution algorithm (EDA) which applies a filtering scheme to revise the modeling data and a learning strategy to improve sampling, which can solve the problems with the characteristics of nonlinearity, variable coupling, and large scale. Computational experiments show that the EDA is effective. In the future, the proposed algorithm can be applied to some practical optimization problems such as operation optimization in blast furnace, which is considered as a continuous production process with variable coupling. The algorithm has the potential to help optimizing the process control parameters.

A new penalty/stochastic approach to an application of the covering problem: The gamma knife treatment

The covering problem of a three dimensional body using different radii spheres is considered. The motivating application – the treatment planning of Gamma Knife radiosurgery – is briefly discussed. We approach the problem only by the geometric covering point of view, that is, given a set of spheres and a body, the objective is to cover the body using the smallest possible number of spheres, regardless of the dosage issue. In order to solve this mathematical programming problem, we consider an approach based on the application of penalty and stochastic local search techniques. Finally, some illustrative results and comparisons are presented.

A New Initialization Approach in Particle Swarm Optimization for Global Optimization Problems.

Particle swarm optimization (PSO) algorithm is a population-based intelligent stochastic search technique used to search for food with the intrinsic manner of bee swarming. PSO is widely used to solve the diverse problems of optimization. Initialization of population is a critical factor in the PSO algorithm, which considerably influences the diversity and convergence during the process of PSO. Quasirandom sequences are useful for initializing the population to improve the diversity and convergence, rather than applying the random distribution for initialization. The performance of PSO is expanded in this paper to make it appropriate for the optimization problem by introducing a new initialization technique named WELL with the help of low-discrepancy sequence. To solve the optimization problems in large-dimensional search spaces, the proposed solution is termed as WE-PSO. The suggested solution has been verified on fifteen well-known unimodal and multimodal benchmark test problems extensively used in the literature, Moreover, the performance of WE-PSO is compared with the standard PSO and two other initialization approaches Sobol-based PSO (SO-PSO) and Halton-based PSO (H-PSO). The findings indicate that WE-PSO is better than the standard multimodal problem-solving techniques. The results validate the efficacy and effectiveness of our approach. In comparison, the proposed approach is used for artificial neural network (ANN) learning and contrasted to the standard backpropagation algorithm, standard PSO, H-PSO, and SO-PSO, respectively. The results of our technique has a higher accuracy score and outperforms traditional methods. Also, the outcome of our work presents an insight on how the proposed initialization technique has a high effect on the quality of cost function, integration, and diversity aspects.

On the use of a multilayer perceptron based surrogate model in evolutionary optimization

Nature-inspired stochastic search techniques such as Evolutionary Algorithms (EAs) are known for their ability to solve complex optimization problems. However, they typically require numerous function evaluations in their search process to find global optimums. This is a drawback if EAs are used in optimization problems that have computationally expensive functions. Surrogate models have been used as cheap approximations to replace these functions. In this study, we propose a dynamically retrained multilayer perceptron-based surrogate model that is coupled with a genetic algorithm (GA) to reduce the number of function evaluations in the optimization process. The proposed method has been successfully applied to some test functions and real-world aerodynamic shape optimization problems. It is also shown that it converges more quickly towards the Pareto-optimal front with fewer function evaluations compared to a stand-alone GA in all optimization problems.