Covariance Matrix Adaptation Research Articles

Orthogonal learning covariance matrix for defects of grey wolf optimizer: Insights, balance, diversity, and feature selection

This research’s genesis is in two aspects: first, a guaranteed solution for mitigating the grey wolf optimizer’s (GWO) defect and deficiencies. Second, we provide new open-minding insights and deep views about metaheuristic algorithms. The population-based GWO has been recognized as a popular option for realizing optimal solutions. Despite the popularity, the GWO has structural defects and uncertain performance and has certain limitations when dealing with complex problems such as multimodality and hybrid functions. This paper tries to overhaul the shortcomings of the original process and develops a GWO variant enhanced with a covariance matrix adaptation evolution strategy (CMAES), levy flight mechanism, and orthogonal learning (OL) strategy named GWOCMALOL. The algorithm uses the levy flight mechanism, orthogonal learning strategy, and CMAES to bring more effective exploratory inclinations. We conduct numerical experiments based on various functions in IEEE CEC2014. It is also compared with 10 other algorithms with competitive performances, 7 improved GWO variants, and 11 advanced algorithms. Moreover, for more systematic data analysis, Wilcoxon signed-rank test is used to evaluate the results further. Experimental results show that the GWOCMALOL algorithm is superior to other algorithms in terms of convergence speed and accuracy. The proposed GWO-based version is discretized into a binary tool through the transformation function. We evaluate the performance of the new feature selection method based on 24 UCI data sets.​ Experimental results show that the developed algorithm performs better than the original technique, and the defects are resolved. Besides, we could reach higher classification accuracy and fewer feature selections than other optimization algorithms. A narrative web service at http://aliasgharheidari.com will offer the required data and material about this work.

Hybridizing Niching, Particle Swarm Optimization, and Evolution Strategy for Multimodal Optimization.

Multimodal optimization problems (MMOPs) are common problems with multiple optimal solutions. In this article, a novel method of population division, called nearest-better-neighbor clustering (NBNC), is proposed, which can reduce the risk of more than one species locating the same peak. The key idea of NBNC is to construct the raw species by linking each individual to the better individual within the neighborhood, and the final species of the population is formulated by merging the dominated raw species. Furthermore, a novel algorithm is proposed called NBNC-PSO-ES, which combines the advantages of better exploration in particle swarm optimization (PSO) and stronger exploitation in the covariance matrix adaption evolution strategy (CMA-ES). For the purpose of demonstrating the performance of NBNC-PSO-ES, several state-of-the-art algorithms are adopted for comparisons and tested using typical benchmark problems. The experimental results show that NBNC-PSO-ES performs better than other algorithms.

A tree–seed algorithm based on intelligent search mechanisms for continuous optimization

One of the recently proposed metaheuristic algorithms is tree–seed algorithm, TSA for short. TSA is developed by inspiring the relation between trees and their seeds in order to solve continuous optimization problems, and it has a simple but effective algorithmic structure. The algorithm uses two different solution generating mechanisms in order to improve balance local and global search abilities. However, when the algorithm is analyzed in detail, it is seen that there are some issues in the basic algorithm. These are (i) when trees in the stand approaches to each other, the diversification in the stand is lost, (ii) there is no mechanism to get rid of local minima for a tree, (iii) some of the fitness calculation goes to waste due to seed generation mechanism of basic TSA. In order to address these issues, four different approaches (withering process, sequential seed generation, best-based solution update rule and dimensional selection for the solution update rule) have been proposed for the basic TSA, and all these approaches have been also integrated within algorithmic framework of TSA, named new tree–seed algorithm briefly NTSA, and each of them has been used to solve 28 CEC2013 benchmark functions. In the experimental comparisons, the variants of TSA have been compared with each other, and the better algorithm, NTSA, has been compared with 17 state-of-art algorithms such as artificial bee colony, particle swarm optimization, differential evolution, genetic algorithm, covariance matrix adaptation evolutionary strategy etc. The experimental analysis and comparisons show that the NTSA shows better or similar performance than/with the compared algorithms in terms of solution quality and robustness.

Identification of miRNA Biomarkers for Diverse Cancer Types Using Statistical Learning Methods at the Whole-Genome Scale.

Genome-wide analysis of miRNA molecules can reveal important information for understanding the biology of cancer. Typically, miRNAs are used as features in statistical learning methods in order to train learning models to predict cancer. This motivates us to propose a method that integrates clustering and classification techniques for diverse cancer types with survival analysis via regression to identify miRNAs that can potentially play a crucial role in the prediction of different types of tumors. Our method has two parts. The first part is a feature selection procedure, called the stochastic covariance evolutionary strategy with forward selection (SCES-FS), which is developed by integrating stochastic neighbor embedding (SNE), the covariance matrix adaptation evolutionary strategy (CMA-ES), and classifiers, with the primary objective of selecting biomarkers. SNE is used to reorder the features by performing an implicit clustering with highly correlated neighboring features. A subset of features is selected heuristically to perform multi-class classification for diverse cancer types. In the second part of our method, the most important features identified in the first part are used to perform survival analysis via Cox regression, primarily to examine the effectiveness of the selected features. For this purpose, we have analyzed next generation sequencing data from The Cancer Genome Atlas in form of miRNA expression of 1,707 samples of 10 different cancer types and 333 normal samples. The SCES-FS method is compared with well-known feature selection methods and it is found to perform better in multi-class classification for the 17 selected miRNAs, achieving an accuracy of 96%. Moreover, the biological significance of the selected miRNAs is demonstrated with the help of network analysis, expression analysis using hierarchical clustering, KEGG pathway analysis, GO enrichment analysis, and protein-protein interaction analysis. Overall, the results indicate that the 17 selected miRNAs are associated with many key cancer regulators, such as MYC, VEGFA, AKT1, CDKN1A, RHOA, and PTEN, through their targets. Therefore the selected miRNAs can be regarded as putative biomarkers for 10 types of cancer.

Engagement Enhancement Based on Human-in-the-Loop Optimization for Neural Rehabilitation

Enhancing patients' engagement is of great benefit for neural rehabilitation. However, physiological and neurological differences among individuals can cause divergent responses to the same task, and the responses can further change considerably during training; both of these factors make engagement enhancement a challenge. This challenge can be overcome by training task optimization based on subjects' responses. To this end, an engagement enhancement method based on human-in-the-loop optimization is proposed in this paper. Firstly, an interactive speed-tracking riding game is designed as the training task in which four reference speed curves (RSCs) are designed to construct the reference trajectory in each generation. Each RSC is modeled using a piecewise function, which is determined by the starting velocity, transient time, and end velocity. Based on the parameterized model, the difficulty of the training task, which is a key factor affecting the engagement, can be optimized. Then, the objective function is designed with consideration to the tracking accuracy and the surface electromyogram (sEMG)-based muscle activation, and the physical and physiological responses of the subjects can consequently be evaluated simultaneously. Moreover, a covariance matrix adaption evolution strategy, which is relatively tolerant of both measurement noises and human adaptation, is used to generate the optimal parameters of the RSCs periodically. By optimization of the RSCs persistently, the objective function can be maximized, and the subjects' engagement can be enhanced. Finally, the performance of the proposed method is demonstrated by the validation and comparison experiments. The results show that both subjects' sEMG-based motor engagement and electroencephalography based neural engagement can be improved significantly and maintained at a high level.

Metaheuristic Optimization of Insulin Infusion Protocols Using Historical Data with Validation Using a Patient Simulator

Metaheuristic search algorithms are used to develop new protocols for optimal intravenous insulin infusion rate recommendations in scenarios involving hospital in-patients with Type 1 Diabetes. Two metaheuristic search algorithms are used, namely, Particle Swarm Optimization and Covariance Matrix Adaption Evolution Strategy. The Glucose Regulation for Intensive Care Patients (GRIP) serves as the starting point of the optimization process. We base our experiments on a methodology in the literature to evaluate the favorability of insulin protocols, with a dataset of blood glucose level/insulin infusion rate time series records from 16 patients obtained from the Waikato District Health Board. New and significantly better insulin infusion strategies than GRIP are discovered from the data through metaheuristic search. The newly discovered strategies are further validated and show good performance against various competitive benchmarks using a virtual patient simulator.

MMES: Mixture Model-Based Evolution Strategy for Large-Scale Optimization

This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a mixture model, which facilitates exploiting the rich variable correlations of the problem landscape within a limited time budget. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model based evolution strategy (MMES) -- a CMA-ES variant for large-scale optimization. The numerical simulations show that, while significantly reducing the time complexity of CMA-ES, MMES preserves the rotational invariance, is scalable to high dimensional problems, and is competitive against the state-of-the-arts in performing global optimization.

Evolution of biocoenosis through symbiosis with fitness approximation for many-tasking optimization

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.

Source mask optimization using the covariance matrix adaptation evolution strategy.

Source mask optimization (SMO) is one of the indispensable resolution enhancement techniques to guarantee the image fidelity and process robustness for the 2Xnm technology node and beyond. The optimization capacity and convergence efficiency of SMO are important, especially for full-chip SMO. An SMO method using the covariance matrix adaptation evolution strategy (CMA-ES), together with a new source representation method, is proposed in this paper. Based on the forward vector imaging formulation, the encoding and decoding methods of the source and the mask, and the constructed merit function, the source and the mask are optimized using the CMA-ES algorithm. The solution search space and the search step size are adaptively updated during the optimization procedure. Considering the sparsity of the optimal source, the source is represented by a set of ideal point sources with unit intensity and adjustable positions. The advantageous spatial frequency components of the source for imaging performance improvement are identified through the aggregation of the point sources. Simulations and comparisons verify the superior optimization capacity and convergence efficiency of the proposed method.

Optimizing Production Schedule of Coalbed Methane Wells Using a Stochastic Evolution Algorithm

Production optimization of coalbed methane (CBM) is a complex constrained nonlinear programming problem. Finding an optimal decision is challenging since the coal seams are generally heterogeneous with widespread cleats, fractures, and matrix pores, and the stress sensitivities are extremely strong; the production of CBM wells needs to be adjusted dynamically within a reasonable range to fit the complex physical dynamics of CBM reservoirs to maximize profits on a long-term horizon. To address these challenges, this paper focuses on the step-down production strategy, which reduces the bottom hole pressure (BHP) step by step to expand the pressure drop radius, mitigate the formation damage, and improve CBM recovery. The mathematical model of CBM well production schedule optimization problem is formulated. The objective of the optimization model is to maximize the cumulative gas production and the variables are chosen as BHP declines of every step. BHP and its decline rate constraints are also considered in the model. Since the optimization problem is high dimensional, nonlinear with many local minima and maxima, covariance matrix adaptation evolution strategy (CMA-ES), a stochastic, derivative-free intelligent algorithm, is selected. By integrating a reservoir simulator with CMA-ES, the optimization problem can be solved successfully. Experiments including both normal wells and real featured wells are studied. Results show that CMA-ES can converge to the optimal solution efficiently. With the increase of the number of variables, the converge rate decreases rapidly. CMA-ES needs 3 or even more times number of function evaluations to converge to 100% of the optimum value comparing to 99%. The optimized schedule can better fit the heterogeneity and complex dynamic changes of CBM reservoir, resulting a higher production rate peak and a higher stable period production rate. The cumulative production under the optimized schedule can increase by 20% or even more. Moreover, the effect of the control frequency on the production schedule optimization problem is investigated. With the increases of control frequency, the converge rate decreases rapidly and the production performance increases slightly, and the optimization algorithm has a higher risk of falling into local optima. The findings of this study can help to better understanding the relationship between control strategy and CBM well production performance and provide an effective tool to determine the optimal production schedule for CBM wells.

Pixel-Level Weed Classification Using Evolutionary Selection of Local Binary Pattern in a Stochastic Optimised Ensemble

In the early growth stages of young crops, weeds compete for living resources while often grow close together and with overlaps. Conventional weeding techniques such as mechanical weeding and herbicide application are not precision methods. To allow for high precision target and spraying of weeds, autonomous field robots equipped with computer vision systems could be deployed to manage and control the weeds in the crop line. The robots are therefore required to classify weeds at pixel-level accuracy with high recall rates. This paper presents a pixel-level weed classification model using rotation-invariant uniform local binary pattern (LBP) features. The model design is based on an ensemble with a two-level optimisation structure. The first-level leverages on Genetic Algorithm (GA) optimisation to select the best rotation-invariant uniform LBP configurations. The second level utilises covariance matrix adaptation evolution strategy (CMA-ES) in the Neural Network (NN) ensemble to select the best combinations of voting weights of the predicted outcome for each classifier. This model design allows for different feature inputs selected by GA for each of the NN classifiers in the ensemble, unlike classical ensembles which share the same input data. For ensemble weight optimisation, we compared differential evolution, particle swarm optimisation, and CMA-ES. A crop/weed field image dataset public dataset consisting of 60 images of weeds and carrots at early true leaf stage was used for validation with existing works. The results demonstrated that our LBP-based pixel-level classifier exhibits excellent predictive capability with high recall and F1 scores when compared to the literature. It was found that CMA-ES optimised ensemble gave the best configuration and demonstrated a classification accuracy of 87.9%, which exceeded the existing statistical feature classification of 85.9%. This highlights some potentialities for chip-based application-specific integrated circuit LBP pixel-level weed classification in smart agriculture applications.

Deep neural annealing model for the semantic representation of documents

As a result of the growing production of unstructured textual data, techniques for representing words and documents in the vector space have emerged recently. The Brazilian Public Ministry has received several textual requests that are send by citizens with different needs, such as those involved in cases of domestic violence against women, others requesting intensive care unit admissions, and more. The time spent in classifying, detecting similar requests and distributing them is essential to optimize and save public resources. Therefore, we adopted the neural model with the Simulated Annealing (SA), a classic global optimization algorithm with low computational complexity, because of the need to reduce the daily training time, providing a more friendly graphic visualization of documents in high dimensions, supporting the judicial decision process. The physical analogy of the SA meta-heuristic associated with the continuous representation of documents in the vector space contribute greatly to the friendly visualization of a high-dimensional dataset, maintaining a comparable score with other deep models and optimization algorithms, such as Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and Bayesian Optimization (BO).

An evolutionary approach to black-box optimization on matrix manifolds

Optimization on matrix manifolds is a class of methods for solving matrix optimization problems, subject to constraints which admit the structure of a Riemannian manifold. These problems are intractable for traditional evolutionary algorithms due to the non-Euclidean nature. This paper generalizes the classical technique of covariance matrix adaptation to matrix manifolds, and proposes a manifold evolution strategy named ManES. By exploiting the manifold structure, we turn an originally constrained problem into a sequence of unconstrained ones in the Euclidean subspace. The proposed algorithm is coordinate-free, in the sense that it is independent of the choice of basis and requires no global coordinate system. All genetic operators take the form of matrix transformations and thus are computationally efficient. The algorithm exhibits state-of-the-art performance on four benchmark problems and one real-world application posed on three different kinds of matrix manifolds.

Development of a Metaheuristic Programming Method for Synthesis of Nonlinear Models

The solution of the problem of building nonlinear models (mathematical expressions, functions, algorithms, and programs) based on an experimental data set, a set of variables, or a set of basic functions and operations is considered. A metaheuristic programming method for the evolutionary synthesis of nonlinear models has been developed; in this method, a chromosome is represented in the form of a vector of real numbers and allows the use of various bio-inspired (nature-inspired) optimization algorithms in the search for models. The efficiency of the proposed algorithm is estimated using ten bio-inspired algorithms (two modifications of the genetic programming algorithm, differential evolution algorithm, particle swarm optimization algorithm, artificial bee colony algorithm, teaching-learning-based optimization algorithm and two of its modifications, covariance matrix adaptation evolution strategy, and simultaneous heat transfer search algorithm) and compared with the results of standard algorithms of genetic programming, grammatical evolution, and Cartesian genetic programming. The experiments have shown a significant advantage of this approach as compared to the above-mentioned algorithms in terms of both the time needed for finding the solution (greater than by an order of magnitude in most cases) and the probability of finding a given function (model) (greater than twice in many cases).

A Reference Vector-Based Simplified Covariance Matrix Adaptation Evolution Strategy for Constrained Global Optimization.

During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other successful MOO frameworks, such as the reference vector (RV) and the decomposition-based ones, have not drawn sufficient attention from the COP researchers. In this article, we utilize the concepts of the RV-based MOO to design a ranking strategy for the solutions of a COP. We first transform the COP into a biobjective optimization problem (BOP) and then solve it by using the covariance matrix adaptation evolution strategy (CMA-ES), which is arguably one of the most competitive evolutionary algorithms of current interest. We propose an RV-based ranking strategy to calculate the mean and update the covariance matrix in CMA-ES. Besides, the RV is explicitly tuned during the optimization process based on the characteristics of COPs in a RV-based MOO framework. We also propose a repair mechanism for the infeasible solutions and a restart strategy to facilitate the population to escape from the infeasible region. We test the proposal extensively on two well-known benchmark suites comprised of 36 and 112 test problems (at different scales) from the IEEE CEC (Congress on Evolutionary Computation) 2010 and 2017 competitions along with a real-world problem related to power flow. Our experimental results suggest that the proposed algorithm can meet or beat several other state-of-the-art constrained optimizers in terms of the performance on a wide variety of problems.

Finite Distribution Estimation-Based Dynamic Window Approach to Reliable Obstacle Avoidance of Mobile Robot

This article proposes, a novel obstacle avoidance algorithm for a mobile robot based on finite memory filtering (FMF) in unknown dynamic environments. To overcome the limitations of the existing dynamic window approach (DWA), we propose a new version of the DWA, called the finite distribution estimation-based dynamic window approach (FDEDWA), which is an algorithm that avoids dynamic obstacles through estimating the overall distribution of obstacles. FDEDWA estimates the distribution of obstacles through the FMF, and predicts the future distribution of obstacles. The FMF is derived to minimize the effect of the measurement noise through the Frobenius norm, and covariance matrix adaptation evolution strategy. The estimated information is used to derive the control input for the robust mobile robot navigation effectively. FDEDWA allows for the fast perception of the dynamic environment, and superior estimation performance, and the mobile robot can be controlled by a more optimal path while maintaining real-time performance. To demonstrate the performance of the proposed algorithm, simulations, and experiments were carried out under dynamic environments by comparing the latest dynamic window for dynamic obstacle, and the existing DWA.

Mendelian evolutionary theory optimization algorithm

This study presented a new multi-species binary coded algorithm, Mendelian evolutionary theory optimization (METO), inspired by the plant genetics. This framework mainly consists of three concepts: first, the “denaturation” of DNA’s of two different species to produce the hybrid “offspring DNA”. Second, the Mendelian evolutionary theory of genetic inheritance, which explains how the dominant and recessive traits appear in two successive generations. Third, the Epimutation, through which organism resist for natural mutation. The above concepts are reconfigured in order to design the binary meta-heuristic evolutionary search technique. Based on this framework, four evolutionary operators—(1) Flipper, (2) Pollination, (3) Breeding, and (4) Epimutation—are created in the binary domain. In this paper, METO is compared with well-known evolutionary and swarm optimizers: (1) binary hybrid GA, (2) bio-geography-based optimization, (3) invasive weed optimization, (4) shuffled frog leap algorithm, (5) teaching–learning-based optimization, (6) cuckoo search, (7) bat algorithm, (8) gravitational search algorithm, (9) covariance matrix adaptation evolution strategy, (10) differential evolution, (11) firefly algorithm and (12) social learning PSO. This comparison is evaluated on 30 and 100 variables benchmark test functions, including noisy, rotated, and hybrid composite functions. Kruskal–Wallis statistical rank-based nonparametric H-test is utilized to determine the statistically significant differences between the output distributions of the optimizer, which are the result of the 100 independent runs. The statistical analysis shows that METO is a significantly better algorithm for complex and multi-modal problems with many local extremes.

Comparative Study of Heuristic Algorithms for Electrical Impedance Tomography

Based on electrical measurements from electrodes placed around the boundary of a body, electrical impedance tomography (EIT) is an imaging procedure that recovers the spatial distribution of the conductivities in the interior of a body. Recent studies have shown promising results in reconstructing EIT images using heuristic algorithms. This work presents a study of the applicability of six heuristic algorithms – firefly algorithm (FA), novel bat algorithm (NBA), genetic algorithm with new multi-parent crossover (GA-MPC), success history-based adaptive differential evolution with linear population size reduction with semiparameter adaptation hybrid with covariance matrix adaptation evolutionary strategy (LSHADE-SPACMA), ensemble sinusoidal differential covariance matrix adaptation (LSHADE-cnEpSin), and effective butterfly optimizer with covariance matrix adapted retreat phase (EBOwithCMAR) – for the EIT image reconstruction problem. These algorithms have never been employed to solve the EIT inverse problem. Series of numerical tests were carried out to compare the performance of the selected algorithms.

Single-Parameter-Tuned Attitude Control for Quadrotor with Unknown Disturbance

In this paper, methods are presented for designing a quadrotor attitude control system with disturbance rejection ability, wherein only one parameter needs to be tuned for each axis. The core difference between quadrotor platforms are extracted as critical gain parameters (CGPs). Reinforcement learning (RL) technology is introduced in order to automatically optimize the controlling law for quadrotors with different CGPs, and the CGPs are used to extend the RL state list. A deterministic policy gradient (DPG) algorithm that is based on an actor-critic structure in a model-free style is used as the learning algorithm. Mirror sampling and reward shaping methods are designed in order to eliminate the steady-state errors of the RL controller and accelerate the training process. Active disturbance rejection control (ADRC) is applied to reject unknown external disturbances. A set of extended state observers (ESOs) is designed to estimate the total disturbance to the roll and pitch axes. The covariance matrix adaptation evolution strategy (CMA-ES) algorithm is used to automatically tune the ESO parameters and improve the final performance. The complete controller is tested on an F550 quadrotor in both simulation and real flight environments. The quadrotor can hover and move around stably and accurately in the air, even with a severe disturbance.

Evolving collective cognition for object identification in foraging robotic swarms

This paper focuses on the collective cognition by robotic swarms. The robotic swarms expected to perform tasks that are beyond the capability of a single robot by collective behavior that emerge from local interactions, similar to biological swarms. However, the robotic swarms have to rely on the collective cognition more than biological swarms when considering the limitation in sensory capabilities and the cost of each robot. In this paper, we develop controllers for a robotic swarm to accomplish a foraging task that requires collective cognition. In this task, robots have to both collectively distinguish two objects, namely food and poison, and cooperatively transport food objects to the nest. We applied an evolutionary robotics approach with the covariance matrix adaptation evolution strategy to develop controllers for robotic swarms. The results of computer simulations show that collective cognition was successfully developed, which allows the robots to transport only food objects. In addition, we also perform experiments to examine the scalability and the flexibility of the developed controllers.