Parameter-free Optimization Research Articles

Application of a novel metaheuristic algorithm inspired by stadium spectators in global optimization problems

This paper presents a novel metaheuristic algorithm inspired by the actions of stadium spectators affecting behavior of players during a match which will be called stadium spectators optimizer (SSO) algorithm. The mathematical model of the SSO algorithm is presented and the performance and efficiency of the presented method is tested on some of the well-known mathematical test functions and also CEC-BC-2017 functions. The SSO algorithm is a parameter-free optimization method since it doesn't require any additional parameter setup at any point throughout the optimization process. It seems urgently necessary to design a novel metaheuristic algorithm that is parameter-free and capable of solving any optimization problem without taking into account extra parameters, as the majority of metaheuristic algorithms rely on the configuration of extra parameters to solve different problems efficiently. A positive point for the SSO algorithm can be seen in the results of the suggested technique, which indicate a partial improvement in performance. The results are compared with those of golf optimization algorithm (GOA), Tiki taka optimization algorithm (TTA), Harris Hawks optimization algorithm (HHO), the arithmetic optimization algorithm (AOA), CMA-ES and EBOwithCMAR algorithms. The statistical tests are carried out for the obtained results and the tests reveal the capability of the presented method in solving different optimization problems with different dimensions. SSO algorithm performs comparably and robustly with the state-of-the-art optimization techniques in 14 of the mathematical test functions. For CEC-BC-2017 functions with ten dimensions, EBOwithCMAR performs better than the proposed method. However, for most functions of CEC-BC-2017 with ten dimensions, the SSO algorithm ranks second after EBOwithCMAR, which is an advantage of the SSO since the proposed method performs better than the well-known CMA-ES optimization algorithm. The overall performance of the SSO algorithm in CEC-BC-2017 functions with 10 dimensions was acceptable, in dimension of 30, 50 and 100, the performance of the proposed method in some functions decreased.

Efficient Top-K Feature Selection Using Coordinate Descent Method

Sparse learning based feature selection has been widely investigated in recent years. In this study, we focus on the l2,0-norm based feature selection, which is effective for exact top-k feature selection but challenging to optimize. To solve the general l2,0-norm constrained problems, we novelly develop a parameter-free optimization framework based on the coordinate descend (CD) method, termed CD-LSR. Specifically, we devise a skillful conversion from the original problem to solving one continuous matrix and one discrete selection matrix. Then the nontrivial l2,0-norm constraint can be solved efficiently by solving the selection matrix with CD method. We impose the l2,0-norm on a vanilla least square regression (LSR) model for feature selection and optimize it with CD-LSR. Extensive experiments exhibit the efficiency of CD-LSR, as well as the discrimination ability of l2,0-norm to identify informative features. More importantly, the versatility of CD-LSR facilitates the applications of the l2,0-norm in more sophisticated models. Based on the competitive performance of l2,0-norm on the baseline LSR model, the satisfactory performance of its applications is reasonably expected. The source MATLAB code are available at: https://github.com/solerxl/Code_For_AAAI_2023.

Geomorphological slope units of the Himalayas

ABSTRACT Slope units represent surface slopes by means of polygons delimited by drainage and divide lines obtained on a digital topography. Objective slope unit delineation for a given digital elevation model is still an open issue and, often, a limitation that may dictate the use of a more traditional pixel-based approach for spatial analysis. Availability of slope unit maps facilitates many kinds of studies and allows scholars to focus on specific scientific issues rather than on preparing sound mapping units from scratch for their research. Here, we present a slope unit map of a large portion of the Himalayas. The map is prepared following a widely tested, parameter-free optimization algorithm. The area encompassed by the map is relevant to studies of the well-known 2015 Gorkha earthquake and monsoons, which makes it relevant to a vast portion of the scientific community working in natural hazards including, but not limited to, landslide scientists and practitioners. The map contains 112,674 polygons with average area of 0.38 km and is published in vector form. The map is accompanied by a selection of data including morphometric and thematic quantities. In addition to describing the rationale behind the delineation of the polygonal map and selected data, we describe an application devoted to unsupervised terrain classification. We applied a k-means clustering procedure with two strategies: one at (coarser) basin scale and one at (finer) slope unit scale. We show similarities and differences between the two classification strategies, highlighting the role of the slope unit subdivision in the two cases.

Developing a novel parameter-free optimization framework for flood routing

The Muskingum model is a popular hydrologic flood routing technique; however, the accurate estimation of model parameters challenges the effective, precise, and rapid-response operation of flood routing. Evolutionary and metaheuristic optimization algorithms (EMOAs) are well suited for parameter estimation task associated with a wide range of complex models including the nonlinear Muskingum model. However, more proficient frameworks requiring less computational effort are substantially advantageous. Among the EMOAs teaching–learning-based optimization (TLBO) is a relatively new, parameter-free, and efficient metaheuristic optimization algorithm, inspired by the teacher-student interactions in a classroom to upgrade the overall knowledge of a topic through a teaching–learning procedure. The novelty of this study originates from (1) coupling TLBO and the nonlinear Muskingum routing model to estimate the Muskingum parameters by outflow predictability enhancement, and (2) evaluating a parameter-free algorithm’s functionality and accuracy involving complex Muskingum model’s parameter determination. TLBO, unlike previous EMOAs linked to the Muskingum model, is free of algorithmic parameters which makes it ideal for prediction without optimizing EMOAs parameters. The hypothesis herein entertained is that TLBO is effective in estimating the nonlinear Muskingum parameters efficiently and accurately. This hypothesis is evaluated with two popular benchmark examples, the Wilson and Wye River case studies. The results show the excellent performance of the “TLBO-Muskingum” for estimating accurately the Muskingum parameters based on the Nash–Sutcliffe Efficiency (NSE) to evaluate the TLBO’s predictive skill using benchmark problems. The NSE index is calculated 0.99 and 0.94 for the Wilson and Wye River benchmarks, respectively.

Parameter-free optimization algorithm for iterative wavefront shaping.

Optical focusing through scattering media has a significant impact on optical applications in biological tissues. Recently, iterative wavefront shaping (WFS) has been successfully used to focus light through or inside scattering media, and various heuristic algorithms have been introduced to improve the performance. While these results are encouraging, more efforts are needed to tune parameters towards robust and optimum optimization. Moreover, optimal parameters might differ for different scattering samples and experimental conditions. In this Letter, we propose a "smart" parameter-free algorithm by combining a traditional genetic algorithm with a bat algorithm, and the mutation rate can be automatically calculated through real-time feedback. Using this method in iterative WFS, one can achieve robust and optimum performance without a parameter tuning process.

A new efficient two-stage method for damage localization and quantification in shell structures

The article proposes a new efficient two-stage approach for damage localization and quantification in shell structures using a modal flexibility sensitivity-based damage indicator abbreviated as MFBDI and a recently developed parameter-free optimization algorithm named golden ratio optimization method (GROM). In the first stage, the damage indicator MFBDI is employed to localize possible damage elements in the monitored shell structure. These possible damage elements also help define the search space of optimization problem in the next step. In the second stage, the GROM as a robust optimization solver is implemented to update the finite element (FE) model of the shell structure for refined localization of damage and quantification of its severity. The accuracy and efficiency of the proposed two-stage approach are demonstrated by two numerical simulation examples including a hypar shell and a spherical shell. The simultaneous influences of spatially-incomplete and inaccurate vibration data on damage prediction results are also taken into consideration. The obtained results reveal that the proposed approach can provide an efficient and accurate damage localization and quantification procedure for the studied shell structures.

Free-form optimization method for frame structures aiming at controlling time-dependent responses

In this paper, a parameter-free optimization method for controlling the time-dependent response of frame structures is proposed. The proposing method deals with three optimization problems, including a vibration displacement minimization problem, a vibration displacement control problem, and a dynamic compliance minimization problem, which is the special case of the vibration minimization problems. These time-dependent optimum design problems are formulated as distributed-parameter optimization problems and the sensitivity functions for the shape variation to obtain the optimal shape are derived based on the material derivative method, Lagrange multiplier method, and the adjoint method. The derived sensitivity function is applied to the H1 gradient method for frames, which is a gradient method in the function space to determine the optimal shape variation. With the proposed method, the optimal shape for time-dependent response problems such as a forced vibration, a free vibration, or a transient response is obtained while minimizing the objective functional and maintaining the smoothness of a frame structure. Several numerical design examples including a continuous dynamic force or an impulse force as an input force are shown to verify and validate the effectiveness of the proposed method and the results are discussed.

On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems

A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at every iteration. The step-length is computed by an Armijo-like rule which is responsible to escape the point from local minimum to global minimum at every iteration due to q-derivative. Further, the rate of convergence is proved as a superlinear in a local neighborhood of a minimum point based on q-derivative. Finally, the numerical experiments show better performance.

Balancing composite motion optimization

Meta-heuristic algorithms play an important role in the optimization field thanks to their robustness and programming simplicity. Many meta-heuristic methods have been devised in recent years. Inspired by nature, they usually simulate natural or human-specific phenomena in a better way. A large amount of them are based on complicated behaviors requiring several implementation steps and algorithm-specific control parameters, which impedes users and limits solutions to different types of optimization problems. Hence, designing effective simple and parameter-free optimization methods attracts much attention. In this paper, we propose a novel population-based optimization algorithm based on balancing composite motions (BCMO). The core idea is balancing composite motion properties of individuals in solution space. Equalizing global and local searches via a probabilistic selection model creates a movement mechanism of each individual. Four test suites selected in the literature, which vary from numerical benchmarks to practical problems, to demonstrate the performance of BCMO include: (1) 23 classical benchmark functions, (2) CEC 2005 benchmark functions, (3) CEC 2014 benchmark functions, and (4) 3 real engineering design problems. The statistical results reveal the promising performance and application of BCMO in a variety of optimization and practical problems with constrained and unknown search spaces.

Optimum shape design of thin-walled cross sections using a parameter-free optimization method

In this paper, a parameter-free method is presented for optimizing the cross-sectional shape of thin-walled structures, which are often demanded at the early stage in structural designs. The thin-walled cross section is minimized subject to constraints of sectional properties including torsion constant, moment of inertia of area, centroid and shear center of the cross section. The problem is formulated as a distributed shape optimization problem, and the shape gradient function is derived using the Lagrange multipliers and the material derivative method. The H1 gradient method, which was proposed as a gradient method in a Hilbert space, is applied to determine the smooth optimal shape. The constraint conditions are satisfied using a linearised constraint equation. The validity of this parameter-free method is verified through several design examples for obtaining the optimal shape of a thin-walled cross section under the constraints of sectional properties.

Order reduction of linear time-invariant systems using Eigen permutation and Jaya algorithm

ABSTRACTThis article presents a new mixed method for order reduction of higher order linear time-invariant systems using Eigen permutation and the Jaya optimization algorithm. The Jaya algorithm is an algorithm-specific parameter-free optimization which requires tuning of standard control parameters only. On the other hand, the Eigen permutation retains the dominant poles of the original system with simultaneous cluster formation of the remaining real and complex poles. The numerator and the denominator polynomials of the reduced order model are determined using the Jaya optimization and Eigen permutation approaches, respectively. The proposed method results in a stable reduced order model for a stable higher order system. The effectiveness of the proposed method is validated using numerical examples of single-input–single-output and multiple-input–multiple-output systems. Furthermore, the results are compared with well-known existing techniques available in the literature.

A generative design technique for exploring shape variations

Because innovative and creative design is essential to a successful product, this work brings the benefits of generative design in the conceptual phase of the product development process so that designers/engineers can effectively explore and create ingenious designs and make better design decisions. We proposed a state-of-the-art generative design technique (GDT), called Space-filling-GDT (Sf-GDT), for the creation of innovative designs. The proposed Sf-GDT has the ability to create variant optimal design alternatives for a given computer-aided design (CAD) model. An effective GDT should generate design alternatives that cover the entire design space. Toward that end, the criterion of space-filling is utilized, which uniformly distribute designs in the design space thereby giving a designer a better understanding of possible design options. To avoid creating similar designs, a weighted-grid-search approach is developed and integrated into the Sf-GDT. One of the core contributions of this work lies in the ability of Sf-GDT to explore hybrid design spaces consisting of both continuous and discrete parameters either with or without geometric constraints. A parameter-free optimization technique, called Jaya algorithm, is integrated into the Sf-GDT to generate optimal designs. Three different design parameterization and space formulation strategies; explicit, interactive, and autonomous, are proposed to set up a promising search region(s) for optimization. Two user interfaces; a web-based and a Windows-based, are also developed to utilize Sf-GDT with the existing CAD software having parametric design abilities. Based on the experiments in this study, Sf-GDT can generate creative design alternatives for a given model and outperforms existing state-of-the-art techniques.

Improved DV-Hop localization algorithm using teaching learning based optimization for wireless sensor networks

Node localization is one of the most critical issues for wireless sensor networks, as many applications depend on the precise location of the sensor nodes. To attain precise location of nodes, an improved distance vector hop (IDV-Hop) algorithm using teaching learning based optimization (TLBO) has been proposed in this paper. In the proposed algorithm, hop sizes of the anchor nodes are modified by adding correction factor. The concept of collinearity is introduced to reduce location errors caused by anchor nodes which are collinear. For better positioning coverage, up-gradation of target nodes to assistant anchor nodes has been used in such a way that those target nodes are upgraded to assistant anchor nodes which have been localized in the first round of localization. For further improvement in localization accuracy, location of target nodes has been formulated as optimization problem and an efficient parameter free optimization technique viz. TLBO has been used. Simulation results show that the proposed algorithm is overall 47, 30 and 22% more accurate than DV-Hop, DV-Hop based on genetic algorithm (GADV-Hop) and IDV-Hop using particle swarm optimization algorithms respectively and achieves high positioning coverage with fast convergence.

直交異方性材料からなるシェル構造体の材料自由配向のための最適化手法

In this study, we propose a parameter-free optimization method of material orientation for a shell structure consisting of orthotropic materials. We consider the compliance as an objective function and minimize it under the state equation constraint. The material orientation distribution is the design variables to be determined. This optimum design problem is formulated as a distributed-parameter optimization problem, and the sensitivity function with respect to the orientation variation is theoretically derived based on the variational method. The optimum orientation variations are determined by the H1 gradient method with the Poisson's equation, where the sensitivity function is applied as the internal heat generation on the shell surface, a driving force to vary the orientation in order to reduce the objective function while maintaining the smooth material orientation distribution. The optimum and continuously distributed orientation variations are determined as the temperature distribution of this fictitious heat transfer analysis without design parameterization. The optimum design examples show that the optimum the material orientation for the minimum compliance can be effectively obtained with the proposed optimization method.

A Multi-Objective TRIBES/OC-SVM Approach for the Extraction of Areas of Interest from Satellite Images

In this work, we are interested in the extraction of areas of interest from satellite images by introducing a MOTRIBES/ OC-SVM approach. The One-Class Support Vector Machine (OC-SVM) is based on the estimation of a support that includes training data. It identifies areas of interest without including other classes from the scene. We propose generating optimal training data using the Multi-Objective TRIBES (MO-TRIBES) to improve the performances of the OC-SVM. The MO-TRIBES is a parameter-free optimization technique that manages the search space in tribes composed of agents. It makes different behavioral and structural adaptations to minimize the false positive and false negative rates of the OC-SVM. We have applied our proposed approach for the extraction of earthquakes and urban areas. The experimental results and comparisons with different state-of-the-art classifiers confirm the efficiency and the robustness of the proposed approach.

Parameter free structural optimization applied to the shape optimization of smart structures

This contribution applies structural shape optimization techniques to actuated smart structures. In order to combine these two disciplines, the idea of Optimal Actuation and an enlarged filtering scheme are presented. A parameter free optimization scheme is used, which allows the treatment of different branches of structural optimization using an identical framework.

Comparative performance analysis of teaching learning based optimization for automatic load frequency control of multi-source power systems

• Application of teaching learning based optimization to AGC problems. • PID controller gains have been optimized by teaching learning based optimization. • Dynamic performance is analyzed for single area system and multi area with HVDC link. • Dynamic performances of TLBO based PID controller are better than DE-PID controller. • Sensitivity analysis is done to load changes and different cost functions. This paper presents a new population based parameter free optimization algorithm as teaching learning based optimization (TLBO) and its application to automatic load frequency control (ALFC) of multi-source power system having thermal, hydro and gas power plants. The proposed method is based on the effect of the influence of teacher on the output of learners and the learners can enhance their knowledge by interactions among themselves in a class. In this extensive study, the algorithm is applied in multi area and multi-source realistic power system without and with DC link between two areas in order to tune the PID controller which is used for automatic generation control (AGC). The potential and effectiveness of the proposed algorithm is compared with that of differential evolution algorithm (DE) and optimal output feedback controller tuning performance for the same power systems. The dynamic performance of proposed controller is investigated by different cost functions like integral of absolute error (IAE), integral of squared error (ISE), integral of time weighted squared error (ITSE) and integral of time multiplied absolute error (ITAE) and the robustness of the optimized controller is verified by its response toward changing in load and system parameters. It is found that the dynamic performance of the proposed controller is better than that of recently published DE optimized controller and optimal output feedback controller and also the proposed system is more robust and stable to wide changes in system loading, parameters, size and locations of step load perturbation and different cost functions.

Support vector machine with parameter optimization by a novel hybrid method and its application to fault diagnosis

The performance of support vector machine (SVM) heavily depends on its parameters. The parameter optimization for SVM is still an ongoing research issue. The current parameter optimization methods either are easy to fall into local optimal solution, or are time consuming. Moreover, some optimization methods depend also on the choice of parameters for them, provoking thus a vicious circle. In view of this, a new hybrid method is proposed to optimize the parameters of SVM in this paper. It uses the inter-cluster distance in the feature space (ICDF) to determine a small and effective search interval from a larger kernel parameter search space, while a hybrid of the barebones particle swarm optimization and differential evolution (BBDE) is used to search the optimal parameter combination in the new search space. The ICDF shows the degree the classes are separated. The BBDE is a new, almost parameter-free optimization algorithm. Some benchmark datasets are used to evaluate the proposed algorithm. Furthermore, the proposed method is used to diagnose the faults of rolling element bearings. Experiments and engineering application show that the proposed method outperforms other methods both mentioned in this paper and published in other literature. A new hybrid method is used to optimize the parameters of SVM.ICDF measure is used to determine a small yet effective search interval for kernel parameter.An almost parameter-free evolutionary algorithm, BBDE, is used to search the optimal parameters of SVM.The proposed method is tested on several benchmark datasets as well as fault diagnosis for rolling element bearings.Experimental results show the outstanding performance of the proposed method.

Feature selection algorithm based on bare bones particle swarm optimization

Abstract Feature selection is a useful pre-processing technique for solving classification problems. As an almost parameter-free optimization algorithm, the bare bones particle swarm optimization (BPSO) has been applied to the topic of optimization on continuous or integer spaces, but it has not been applied to feature selection problems with binary variables. In this paper, we propose a new method to find optimal feature subset by the BPSO, called the binary BPSO. In this algorithm, a reinforced memory strategy is designed to update the local leaders of particles for avoiding the degradation of outstanding genes in the particles, and a uniform combination is proposed to balance the local exploitation and the global exploration of algorithm. Moreover, the 1-nearest neighbor method is used as a classifier to evaluate the classification accuracy of a particle. Some international standard data sets are selected to evaluate the proposed algorithm. The experiments show that the proposed algorithm is competitive in terms of both classification accuracy and computational performance.

Data Clustering using almost parameter free Differential Evolution technique

The paper presents a comparative analysis of data clustering by Particle swarm optimization (PSO) and differential evolution (DE) techniques. It is clearly reveled from the simulation results that almost parameter free optimization technique such as Differential evolution could provide better performance compared to PSO where in many parameters are to be tuned. To exhibit the numerical optimizing capability of DE we have demonstrated the capability of this by optimizing few benchmark functions.