Spherical Search Research Articles

Spherical search algorithm with memory-guided population stage-wise control for bound-constrained global optimization problems

The recently proposed Spherical Search (SS) algorithm replaces the traditional square search pattern with a spherical boundary to provide position-diverse solutions. The algorithm balances its exploration and exploitation performance by utilizing 2 exploration and exploitation sub-populations of equal size. SS has been proven to be highly competitive. However, we observed that when it is used to solve a variety of problems as well as during different searching stages, the fixed sub-population size limits its adaptability and flexibility for achieving continuous exploitation–exploration balance. The balance potential of two operators with distinct characteristics is underdeveloped. As a result, SS and its advanced variants are prone to still easily falling into local optima and lacks certain performance advantages over peer algorithms. In this paper, we further develop SS and propose a memory-guided population stage-wise control strategy based SS, called SSM. By our proposed memory-guided stage-wise evaluation mechanism, SS evaluates the exploitation–exploration balance extent in real time and thus adaptively optimizes and predicts better resource allocation ratio values between its 2 sub-populations and thus achieves significant performance advantages over peer algorithms. The experiments are conducted on 120 benchmark functions and 22 real-world problems, and the results show that SSM significantly outperforms other 13 state-of-the-art evolutionary algorithms. Additionally, we conduct analyses based on method characteristics, convergence process, solution quality robustness testing, population diversity, exploitation and exploration balance, and computational complexity.

SEEI: spherical evolution with feedback mechanism for identifying epistatic interactions

BackgroundDetecting epistatic interactions (EIs) involves the exploration of associations among single nucleotide polymorphisms (SNPs) and complex diseases, which is an important task in genome-wide association studies. The EI detection problem is dependent on epistasis models and corresponding optimization methods. Although various models and methods have been proposed to detect EIs, identifying EIs efficiently and accurately is still a challenge.ResultsHere, we propose a linear mixed statistical epistasis model (LMSE) and a spherical evolution approach with a feedback mechanism (named SEEI). The LMSE model expands the existing single epistasis models such as LR-Score, K2-Score, Mutual information, and Gini index. The SEEI includes an adaptive spherical search strategy and population updating strategy, which ensures that the algorithm is not easily trapped in local optima. We analyzed the performances of 8 random disease models, 12 disease models with marginal effects, 30 disease models without marginal effects, and 10 high-order disease models. The 60 simulated disease models and a real breast cancer dataset were used to evaluate eight algorithms (SEEI, EACO, EpiACO, FDHEIW, MP-HS-DHSI, NHSA-DHSC, SNPHarvester, CSE). Three evaluation criteria (pow1, pow2, pow3), a T-test, and a Friedman test were used to compare the performances of these algorithms. The results show that the SEEI algorithm (order 1, averages ranks = 13.125) outperformed the other algorithms in detecting EIs.ConclusionsHere, we propose an LMSE model and an evolutionary computing method (SEEI) to solve the optimization problem of the LMSE model. The proposed method performed better than the other seven algorithms tested in its ability to identify EIs in genome-wide association datasets. We identified new SNP–SNP combinations in the real breast cancer dataset and verified the results. Our findings provide new insights for the diagnosis and treatment of breast cancer.Availability and implementation: https://github.com/scutdy/SSO/blob/master/SEEI.zip.

A spherical evolution algorithm with two-stage search for global optimization and real-world problems

This paper proposes a spherical evolution algorithm with two-stage search. Spherical search and hypercube search are combined to achieve individuals' evolution. A self-adaptive Gaussian scale factor and a variable scale factor are designed to adaptively control individuals' spherical and hypercube search area according to their search situations. Two search stages frequently switch with four search cases to enhance the balance between exploration and exploitation processes. A directed adjacency matrix is devised to analyze the relationship among individuals from the perspective of graph theory. Experiments compare the proposed algorithm with five algorithms with distinctive search patterns on twenty nine CEC2017 benchmark functions. The diversity analysis and graph theory analysis show the good population diversity and effective information spreading of the proposed algorithm. Twenty two real-world problems evaluate the practicality and optimization ability of the proposed algorithm. Finally, the computational time complexity demonstrates that the proposed algorithm is more efficient than the original spherical evolution algorithm.

Hyper Spherical Search (HSS) Algorithm Based Optimization and Real-Time Stability Study of Tidal Energy Conversion System

Hyper Spherical Search (HSS) Algorithm Based Optimization and Real-Time Stability Study of Tidal Energy Conversion System

The Spherical Evolutionary Multi-Objective (SEMO) Algorithm for Identifying Disease Multi-Locus SNP Interactions.

Single-nucleotide polymorphisms (SNPs), as disease-related biogenetic markers, are crucial in elucidating complex disease susceptibility and pathogenesis. Due to computational inefficiency, it is difficult to identify high-dimensional SNP interactions efficiently using combinatorial search methods, so the spherical evolutionary multi-objective (SEMO) algorithm for detecting multi-locus SNP interactions was proposed. The algorithm uses a spherical search factor and a feedback mechanism of excellent individual history memory to enhance the balance between search and acquisition. Moreover, a multi-objective fitness function based on the decomposition idea was used to evaluate the associations by combining two functions, K2-Score and LR-Score, as an objective function for the algorithm's evolutionary iterations. The performance evaluation of SEMO was compared with six state-of-the-art algorithms on a simulated dataset. The results showed that SEMO outperforms the comparative methods by detecting SNP interactions quickly and accurately with a shorter average run time. The SEMO algorithm was applied to the Wellcome Trust Case Control Consortium (WTCCC) breast cancer dataset and detected two- and three-point SNP interactions that were significantly associated with breast cancer, confirming the effectiveness of the algorithm. New combinations of SNPs associated with breast cancer were also identified, which will provide a new way to detect SNP interactions quickly and accurately.

Development and verification of an unresolved CFD-DEM method applicable to different-sized grids

The traditional unresolved CFD-DEM method is designed for fluid grid sizes larger than particle sizes, and improved methods are imperative when encountering cases with fluid grid sizes comparable to particle sizes. This study attempts to develop an unresolved CFD-DEM method that applies to different-sized grids and can be easily implemented on commercial platforms using unstructured grids, aiming to greatly help engineers solve engineering problems without investing much effort into choosing appropriate simulation methods and designing fluid grids. To this end, the new method considers interphase force correction at the particle level and field smoothing at the cell level by constructing a spherical search area whose size is determined by particle sizes. Mass conservation is strictly guaranteed in the new method, which is essential to simulations involving chemical reactions. The accuracy and universality of the new method are comprehensively evaluated by two test cases. The first test case is conducted in a spouted bed discretized by unstructured grids of three sizes. The results demonstrate that the new method not only applies to comparable-sized grids but can yield the same predictions as the traditional method in large-sized grids. In other words, the new method is universal as long as grid sizes lie at the unresolved level. Thanks to the simplicity of the algorithm, the new method does not compromise calculation efficiency. The second test case is conducted in a draft tube-type feeder discretized by non-uniform unstructured grids. By comparing with experimental measurements, the main features of flow patterns, pressure drop characteristics, and mass flow rates are reasonably predicted, confirming the capability of the new method to simulate complex gas-solid flows with non-uniform unstructured grids. Users do not need to make any adjustments to the new method once it is implemented on commercial platforms. In the future, the new method can potentially become a universal method to simulate gas-solid flows and greatly help engineers solve engineering problems.

Spherical search with epsilon constraint and gradient-based repair framework for constrained optimization

Spherical search with epsilon constraint and gradient-based repair framework for constrained optimization

An Adaptive Dimension Weighting Spherical Evolution to Solve Continuous Optimization Problems

The spherical evolution algorithm (SE) is a unique algorithm proposed in recent years and widely applied to new energy optimization problems with notable achievements. However, the existing improvements based on SE are deemed insufficient due to the challenges arising from the multiple choices of operators and the utilization of a spherical search method. In this paper, we introduce an enhancement method that incorporates weights in individuals’ dimensions that are affected by individual fitness during the iteration process, aiming to improve SE by adaptively balancing the tradeoff between exploitation and exploration during convergence. This is achieved by reducing the randomness of dimension selection and enhancing the retention of historical information in the iterative process of the algorithm. This new SE improvement algorithm is named DWSE. To evaluate the effectiveness of DWSE, in this study, we apply it to the CEC2017 standard test set, the CEC2013 large-scale global optimization test set, and 22 real-world problems from CEC2011. The experimental results substantiate the effectiveness of DWSE in achieving improvement.

Self-Adaptive Spherical Search With a Low-Precision Projection Matrix for Real-World Optimization.

Since the last three decades, numerous search strategies have been introduced within the framework of different evolutionary algorithms (EAs). Most of the popular search strategies operate on the hypercube (HC) search model, and search models based on other hypershapes, such as hyper-spherical (HS), are not investigated well yet. The recently developed spherical search (SS) algorithm utilizing the HS search model has been shown to perform very well for the bound-constrained and constrained optimization problems compared to several state-of-the-art algorithms. Nevertheless, the computational burdens for generating an HS locus are higher than that for an HC locus. We propose an efficient technique to construct an HS locus by approximating the orthogonal projection matrix to resolve this issue. As per our empirical experiments, this technique significantly improves the performance of the original SS with less computational effort. Moreover, to enhance SS's search capability, we put forth a self-adaptation technique for choosing the effective values of the control parameters dynamically during the optimization process. We validate the proposed algorithm's performance on a plethora of real-world and benchmark optimization problems with and without constraints. Experimental results suggest that the proposed algorithm remains better than or at least comparable to the best-known state-of-the-art algorithms on a wide spectrum of problems.

SSELM-neg: spherical search-based extreme learning machine for drug–target interaction prediction

BackgroundThe experimental verification of a drug discovery process is expensive and time-consuming. Therefore, efficiently and effectively identifying drug–target interactions (DTIs) has been the focus of research. At present, many machine learning algorithms are used for predicting DTIs. The key idea is to train the classifier using an existing DTI to predict a new or unknown DTI. However, there are various challenges, such as class imbalance and the parameter optimization of many classifiers, that need to be solved before an optimal DTI model is developed.MethodsIn this study, we propose a framework called SSELM-neg for DTI prediction, in which we use a screening approach to choose high-quality negative samples and a spherical search approach to optimize the parameters of the extreme learning machine.ResultsThe results demonstrated that the proposed technique outperformed other state-of-the-art methods in 10-fold cross-validation experiments in terms of the area under the receiver operating characteristic curve (0.986, 0.993, 0.988, and 0.969) and AUPR (0.982, 0.991, 0.982, and 0.946) for the enzyme dataset, G-protein coupled receptor dataset, ion channel dataset, and nuclear receptor dataset, respectively.ConclusionThe screening approach produced high-quality negative samples with the same number of positive samples, which solved the class imbalance problem. We optimized an extreme learning machine using a spherical search approach to identify DTIs. Therefore, our models performed better than other state-of-the-art methods.

Spherical Search based constrained optimization algorithm for power flow analysis of islanded microgrids

Conventional power flow (PF) algorithms are ineffective in the droop-regulated islanded microgrids as the slack bus voltage and system operating frequency are presumed constant parameters. Such assumptions are not applicable in the operation of the droop-regulated islanded microgrid. We formulate a novel formulation for islanded microgrids to solve the PF problem as a constrained optimization problem. Non-linear and linear constraints are developed to model the power balance and the various modes of Distributed Generation units (DGs). In islanded microgrids, DGs can be operated in PQ, PV, and droop mode. We propose an optimization algorithm named SS-NR (Spherical Search with Newton–Raphson based repair) for solving the formulated problem. We employ Spherical Search (SS) as a base optimizer to minimize the objective function in this algorithm. Moreover, Newton–Raphson based repair operator is also used within the framework of SS to handle non-linear equality constraints of a PF problem. Then, we compare the performance of the proposed algorithm with the state-of-the-art algorithms of global optimization. The experimental results show that the proposed algorithm performs better than the other contenders in convergence and accuracy. Furthermore, to validate the proposed formulation, we compare SS-NR results with the results of a time-domain simulator and other PF tools. This comparative analysis presents the efficacy of the proposed formulation as well as the proposed algorithm.

Single dendritic neural classification with an effective spherical search-based whale learning algorithm.

McCulloch-Pitts neuron-based neural networks have been the mainstream deep learning methods, achieving breakthrough in various real-world applications. However, McCulloch-Pitts neuron is also under longtime criticism of being overly simplistic. To alleviate this issue, the dendritic neuron model (DNM), which employs non-linear information processing capabilities of dendrites, has been widely used for prediction and classification tasks. In this study, we innovatively propose a hybrid approach to co-evolve DNM in contrast to back propagation (BP) techniques, which are sensitive to initial circumstances and readily fall into local minima. The whale optimization algorithm is improved by spherical search learning to perform co-evolution through dynamic hybridizing. Eleven classification datasets were selected from the well-known UCI Machine Learning Repository. Its efficiency in our model was verified by statistical analysis of convergence speed and Wilcoxon sign-rank tests, with receiver operating characteristic curves and the calculation of area under the curve. In terms of classification accuracy, the proposed co-evolution method beats 10 existing cutting-edge non-BP methods and BP, suggesting that well-learned DNMs are computationally significantly more potent than conventional McCulloch-Pitts types and can be employed as the building blocks for the next-generation deep learning methods.

Self-Adapting Spherical Search Algorithm with Differential Evolution for Global Optimization

The spherical search algorithm is an effective optimizer to solve bound-constrained non-linear global optimization problems. Nevertheless, it may fall into the local optima when handling combination optimization problems. This paper proposes an enhanced self-adapting spherical search algorithm with differential evolution (SSDE), which is characterized by an opposition-based learning strategy, a staged search mechanism, a non-linear self-adapting parameter, and a mutation-crossover approach. To demonstrate the outstanding performance of the SSDE, eight optimizers on the CEC2017 benchmark problems are compared. In addition, two practical constrained engineering problems (the welded beam design problem and the pressure vessel design problem) are solved by the SSDE. Experimental results show that the proposed algorithm is highly competitive compared with state-of-the-art algorithms.

Spherical search algorithm with adaptive population control for global continuous optimization problems

Spherical search algorithm (SSA) calculates the spherical boundary and generates new solutions on it by two sub-populations jointly. Many researches have shown that SSA is a promising algorithm, but in some cases, the fixed sub-population size causes it to be prone to search inadequately and easily falling into local optimum. In this paper, a new improved algorithm, named SSAP, is proposed to alleviate these problems. In SSAP, we propose a novel population control strategy to efficiently balance exploration and exploitation. This strategy adaptively adjusts the number of individuals in both sub-populations to improve the search performance of the algorithm. It is realized by adjusting the frequency of search patterns through a cumulative index. Comparative experiments conducted on a large number of benchmark functions show that SSAP significantly outperforms other state-of-the-art algorithms. Additionally, SSAP is used to solve real-world problems to further verify its validity. Finally, the search characteristics and population diversity of SSAP are analyzed.

Improved spherical search with local distribution induced self-adaptation for hard non-convex optimization with and without constraints

Most metaheuristic optimizers rely heavily on precisely setting their control parameters and search operators to perform well. Considering the complexity of real-world problems, it is always preferable to adjust control parameter values automatically rather than clamping them to a fixed value. In recent years, Spherical Search (SS) has emerged as a population-based stochastic optimization method that exploits the concepts of random projection matrices in linear algebra. As a result of the success of SS in solving non-convex, real-parameter optimization problems of various complexity, we have significantly extended SS in this paper by introducing a set of new algorithms, collectively known as Self Adaptive Spherical Search (SASS). Our proposal aims to enhance the performance of SS by using different projection matrix schemes in conjunction with improved search-direction calculations and an adaptive modification of parameter values. In our proposed adaptation scheme, parameters are modified to relevant values by applying a self-adaptive process that does not rely upon prior knowledge of the correlation between the parameter values and characteristics of the problem space. Consequently, we may apply the algorithms to bound and nonlinearly constrained optimization problems. For the benchmark suites derived from the most recent IEEE Congress on Evolutionary Computation (CEC) competitions, simulation results indicate that the SASS family of algorithms performs better than or is comparable to state-of-the-art algorithms from the other paradigms concerning robustness and convergence.

An evolutionary algorithm based on approximation method and related techniques for solving bilevel programming problems.

In the engineering and economic management fields, optimisation models frequently involve different decision-making levels. These are known as multi-level optimisation problems. Because the decision-making process of such problems are hierarchical, they are also called a hierarchical optimisation problems. When the problem involves only two-level decision-making, the corresponding optimisation model is referred to as a bilevel programming problem(BLPP). To address the complex nonlinear bilevel programming problem, in this study, we design an evolutionary algorithm embedded with a surrogate model-that it is a approximation method and correlation coefficients. First, the isodata method is used to group the initial population, and the correlation coefficients of the individuals in each group are determined based on the rank of the leader and follower objective functions. Second, for the offspring individuals produced by the evolutionary operator, the surrogate model is used to approximate the solution of the follower's programming problem, during which the points in the population are screened by combining the correlation coefficients. Finally, a new crossover operator is designed by the spherical search method, which diversifies the generated offspring. The simulation experimental results demonstrate that the proposed algorithm can effectively obtain an optimal solution.

Workspace and Accuracy Analysis on a Novel 6-UCU Bone-attached Parallel Manipulator

With the increasingly more extensive application of the medical surgical robot in the clinic, higher requirements have been put forward for medical robots. The bone-attached robot, a popular orthopedic robot in recent years, has a tendency of miniaturization and refinement. Thus, a bone-attached parallel manipulator (PM) based on 6-UCU (universal-cylindrical-universal) configuration is proposed, which is characterized by small volume, compact structure, high precision and six-dimensional force feedback. To optimize the structure and make it more compact, the workspace of the 6-UCU PM is analyzed based on the analysis of three kinds of constraint, and workspace model is established through spherical coordinate search method. This study also analyzes the influence of structural parameters on workspace, which may contribute to improving the efficiency of design and ensuring small-sized robots possess relatively large workspace. Moreover, to improve the motion accuracy, an error modeling method is developed based on the structure of 6-UCU PMs. According to this established error model, the output pose error curves are drawn using MATLAB software when the structure parameters change, and the influence of the structure and pose parameters change on the output pose error of PMs is analyzed. The proposed research provides the instruction to design and analysis of small PMs such as bone-attached robots.

Sound classification using evolving ensemble models and Particle Swarm Optimization

Automatic sound classification attracts increasing research attention owing to its vast applications, such as robot navigation, environmental sensing, musical instrument classification, medical diagnosis, and surveillance. In this research, we propose an ensemble convolutional bidirectional Long Short-Term Memory (CBiLSTM) network with optimal hyper-parameter selection for undertaking sound classification. We first transform each audio signal into a spectrogram representation using the Short-time Fourier transform (STFT). A Particle Swarm Optimization (PSO) variant is subsequently proposed to optimize the learning rate, weight decay, numbers of filters and hidden units in the convolutional and BiLSTM layers, respectively, in order to extract effective spatial–temporal characteristics from the spectrogram inputs. To tackle the issue of stagnation in optimization, the proposed algorithm incorporates local exploitation using secant and Newton–Raphson methods, promising leader generation using regular and irregular super-ellipse formulae, and three-dimensional spherical search coefficients. Moreover, it takes into account multiple fused elite signals in conjunction with numerical analysis based exploitation to balance between diversification and intensification. A variety of CBiLSTM networks with distinctive optimized settings are devised. An ensemble model is then constructed by incorporating a set of three yielded networks based on a majority voting scheme. Evaluated using several audio data sets, our ensemble CBiLSTM networks outperform those with default and optimal settings identified by other search methods, existing deep architectures and state-of-the-art related studies. In addition to sound classification tasks, the proposed PSO algorithm also outperforms a number of classical and advanced search methods for solving diverse unimodal and multimodal benchmark functions with statistical significance.

Hybridised differential evolution and equilibrium optimiser with learning parameters for mechanical and aircraft wing design

Metaheuristics (MHs) have been widely used for aeroelastic optimisation of aircraft wings and other types of aircraft structures. Using such methods offers some advantages e.g. flexibility for coding, robustness, global optimisation capability, and a derivative-free feature. Moreover, unconventional design problems can be posed when using metaheuristics. This paper proposes a new hybrid algorithm, named HDEEO-LP, with a learning control parameter for aeroelastic optimisation. The new optimiser is obtained from hybridising differential evolution and the recently invented equilibrium optimisation, while a learning scheme for control parameter tuning is integrated. The new method is tested against a number of established and recently invented MHs, such as a grey wolf optimiser (GWO), a salp swarm algorithm (SSA), an equilibrium optimiser (EO), an artificial bee colony (ABC), teaching–learning based optimisation (TLBO), water cycle algorithm (WCA), self-adaptive spherical search algorithm (SASS) using the CEC-RW-2020 test suite and the Goland wing aeroelastic optimisation. The results reveal that the proposed hybrid algorithm is among the top performers.

A Cooperative Coevolution Wingsuit Flying Search Algorithm with Spherical Evolution

The algorithm wingsuit flying search (WFS) mimics the procedure of landing the vehicle. The outstanding feature of WFS is parameterless and of rapid convergence. However, WFS also has its shortcomings, sometimes it will inevitably be trapped into local optima, thereby yield inferior solutions owing to its relatively weak exploration ability. Spherical evolution (SE) adopts a novel spherical search pattern that takes aim at splendid search ability. Cooperative coevolution is a useful parallel structure for reconciling algorithmic performance. Considering the complementary strengths of both algorithms, we herein propose a new hybrid algorithm that is comprised of SE and WFS using cooperative coevolution. During the search for optimal solutions in WFS, we replaced the original search matrix and introduced the spherical mechanism of SE, in parallel with coevolution to enhance the competitiveness of the population. The two distinct search dynamics were combined in a parallel and coevolutionary way, thereby getting a good search performance. The resultant hybrid algorithm, CCWFSSE, was tested on the CEC2017 benchmark set and 22 CEC 2011 real-world problems. The experimental data obtained can verify that CCWFSSE outperforms other algorithms in aspects of effectiveness and robustness.