Nelder-Mead Simplex Search Method Research Articles

A novel opposition-based hybrid cooperation search algorithm with Nelder–Mead for tuning of FOPID-controlled buck converter

This paper introduces a novel metaheuristic algorithm named the opposition-based cooperation search algorithm with Nelder–Mead (OCSANM). This enhanced algorithm builds upon the cooperation search algorithm (CSA) by incorporating opposition-based learning (OBL) and the Nelder–Mead simplex search method. The primary application of this algorithm is the design of a fractional-order proportional–integral–derivative (FOPID) controller for a buck converter system. A comprehensive evaluation is conducted using statistical boxplot analysis, nonparametric statistical tests and convergence response comparisons to assess the algorithm’s performance and confirm its superiority over CSA. Furthermore, the FOPID-controlled buck converter system based on OCSANM is compared with two top-performing algorithms: one using a hybridized approach of Lévy flight distribution with simulated annealing (LFDSA) and the other employing the improved hunger games search (IHGS) algorithm. This comparison encompasses transient and frequency responses, performance indices and robustness analysis. The results reveal the notable advantages of the proposed OCSANM-based system, including 25.8% and 8.7% faster rise times, 26% and 8.8% faster settling times compared with the best-performing approaches, namely LFDSA and IHGS, respectively. In addition, the OCSANM-based system exhibits a 34.7% and 9.6% wider bandwidth than the existing approaches-based systems. Incorporating voltage and current responses of the buck converter’s switched circuit with the OCSANM-based FOPID controller further underscores the algorithm’s effectiveness. To provide a comprehensive assessment, the paper also compares the proposed approach’s time and frequency domain responses with those of 17 other state-of-the-art approaches attempting to control buck converter systems similarly. These findings affirm the effectiveness of the OCSANM in designing FOPID controllers for buck converter systems.

Hybrid beluga whale optimization algorithm with multi-strategy for functions and engineering optimization problems

Beluga Whale Optimization (BWO) is a new metaheuristic algorithm that simulates the social behaviors of beluga whales swimming, foraging, and whale falling. Compared with other optimization algorithms, BWO shows certain advantages in solving unimodal and multimodal optimization problems. However, the convergence speed and optimization performance of BWO still have some performance deficiencies when solving complex multidimensional problems. Therefore, this paper proposes a hybrid BWO method called HBWO combining Quasi-oppositional based learning (QOBL), adaptive and spiral predation strategy, and Nelder-Mead simplex search method (NM). Firstly, in the initialization phase, the QOBL strategy is introduced. This strategy reconstructs the initial spatial position of the population by pairwise comparisons to obtain a more prosperous and higher quality initial population. Subsequently, an adaptive and spiral predation strategy is designed in the exploration and exploitation phases. The strategy first learns the optimal individual positions in some dimensions through adaptive learning to avoid the loss of local optimality. At the same time, a spiral movement method motivated by a cosine factor is introduced to maintain some balance between exploration and exploitation. Finally, the NM simplex search method is added. It corrects individual positions through multiple scaling methods to improve the optimal search speed more accurately and efficiently. The performance of HBWO is verified utilizing the CEC2017 and CEC2019 test functions. Meanwhile, the superiority of HBWO is verified by utilizing six engineering design examples. The experimental results show that HBWO has higher feasibility and effectiveness in solving practical problems than BWO and other optimization methods.

Particle Swarm Optimization with a Simplex Strategy to Avoid Getting Stuck on Local Optimum

Heuristic methods, for global optimization, have been receiving much interest in the last years, among which Particle Swarm Optimization (PSO) algorithm can be highlighted. However, the application of heuristic methods can lead to premature convergence. In this work, the addition of a step on the PSO algorithm is proposed. This new step, based in Nelder–Mead simplex search method (NM), consists of repositioning the current particle with global best solution, not for a better position, but away from the current nearest local optimum, to avoid getting stuck on this local optimum. There are other PSO-NM algorithms, but the one we are proposing, has a different strategy. The proposed algorithm was also tested with the repositioning strategy in other particles beyond the current global best particle, depending on the repositioning probability. To evaluate the effectiveness of the proposed methods, and study its better parameters, were used various test functions, and for each test function, various number of particles were used in combination with various probabilities of particles repositioning. A thousand runs were performed for each case, resulting in more than two millions runs. The computational studies showed that the repositioning of of global best particle increases the percentage of success on reaching the global best solution, but better results can be obtained applying the repositioning strategy to other particles with repositioning probabilities between 1–5%.

Multi-strategy modified INFO algorithm: Performance analysis and application to functional electrical stimulation system

A functional electrical stimulation (FES) system holds a significant importance for the paralyzed individuals as it can help them to perform the tasks they are unable to do. It is crucial to develop an efficient control mechanism for the FES system as it acts on the human musculoskeletal system which presents noise and uncertainties. Therefore, this paper proposes a novel control method for efficient operation of the FES system. In this regard, a proportional-integral-derivative controller with filter (PID-F) mechanism is proposed for the first time in literature for efficient operation of the FES system. Besides, a novel multi-strategy based weighted mean of vectors algorithm (m-INFO) is also developed using a modified opposition-based learning and Lévy flight mechanism together with Nelder-Mead simplex search method. Unimodal, multimodal, low-dimensional and CEC2019 benchmark functions are used to demonstrate the excellent performance of the proposed m-INFO algorithm against several other metaheuristic optimizers. The proposed m-INFO algorithm is then used as an efficient tool to design the PID-F controlled FES system. To achieve optimal tuning, a simple yet effective objective function is also proposed. The excellent ability of the developed m-INFO algorithm-based PID-F controller for FES system is demonstrated through comparative statistical, transient response and frequency response analyses using original weighted mean of vectors, marine predators and moth-flame optimization algorithms based PID-F controlled FES systems.

Vehicle-Deployed Off-Axis Integrated Cavity Output Spectroscopic CH4/C2H6 Sensor System for Mobile Inspection of Natural Gas Leakage.

A vehicle-deployed parts-per-billion in volume (ppbv)-level off-axis integrated cavity output spectroscopic (OA-ICOS) CH4/C2H6 sensor system was experimentally presented for mobile inspection of natural gas leakage in urban areas. For the time-division-multiplexing-based dual-gas sensor system, an antivibration 35-cm-long optical cavity with an effective path length of ∼2510 m was fabricated with a high-stability temperature and pressure control design. An Allan deviation analysis yielded a minimum detection limit of 0.2 ppbv for CH4 detection and 10 ppbv for C2H6 detection for a 1 s averaging time. A natural gas leakage source location algorithm was proposed using an improved hybrid Nelder-Mead simplex search method and a particle swarm optimization (NM-PSO) algorithm. For field industrial application, the accuracy of the sensor system and leakage source location algorithm was confirmed through a CH4/C2H6 cylinder leakage experiment on the campus. Furthermore, through natural gas pipeline network inspection measurements in urban areas, three types of leakage sources, including natural gas, biogas, and possible leakage source were respectively located and confirmed using the global positioning system and wind speed and direction measurement system, verifying the reliability and potential application of the vehicle-deployed inspection system for future natural gas pipeline leakage monitoring.

Performance evaluation of a novel improved slime mould algorithm for direct current motor and automatic voltage regulator systems

This study deals with the controlling the speed of a direct current (DC) motor via a fractional order proportional–integral–derivative (FOPID) controller and maintaining the terminal voltage level of an automatic voltage regulator (AVR) via a proportional–integral–derivative plus second order derivative (PIDD2) controller. To adjust the parameters of those controllers, a novel improved slime mould algorithm (ISMA) is proposed. The latter is a novel metaheuristic algorithm developed in this work. The proposed algorithm aims to improve the original SMA in terms of exploration with the aid of a modified opposition-based learning scheme and in terms of exploitation with the aid of the Nelder–Mead simplex search method. A time domain objective function, which includes time response specifications of steady state error and maximum overshoot along with rise and settling times, is used as a performance index to design the FOPID controller-based DC motor system and PIDD2 controller-based AVR system. The performance of the proposed novel approaches for both systems are assessed through time and frequency domain simulations along with statistical tests which show the greater performance of the improved algorithm. Further to this, the efficacy of the proposed approaches for both systems is compared with other available and effective approaches in the literature. The extensive comparative results demonstrate the proposed method to be superior to those state-of-the-art approaches for both DC motor speed and AVR control systems.

Automatic Identification Algorithm of Equivalent Electrochemical Circuit Based on Electroscopic Impedance Data for a Lead Acid Battery

Obtaining tools to analyze and predict the performance of batteries is a non-trivial challenge because it involves non-destructive evaluation procedures. At the research level, the development of sensors to allow cell-level monitoring is an innovative path, and electrochemical impedance spectrometry (EIS) has been identified as one of the most promising tools, as is the generation of advanced multivariable models that integrate environmental and internal-battery information. In this article, we describe an algorithm that automatically identifies a battery-equivalent electrochemical model based on electroscopic impedance data. This algorithm allows in operando monitoring of variations in the equivalent circuit parameters that will be used to further estimate variations in the state of health (SoH) and state of charge (SoC) of the battery based on a correlation with experimental aging data corresponding to states of failure or degradation. In the current work, the authors propose a two-step parameter identification algorithm. The first consists of a rough differential evolution algorithm-based identification. The second is based on the Nelder–Mead Simplex search method, which gives a fine parameter estimation. These algorithm results were compared with those of the commercially available Z-view, an equivalent circuit tool estimation that requires expert human input.

Nelder Mead with Grasshopper Optimization Algorithm for Node Localization in Wireless Sensor Networks

Node localization in wireless sensor network (WSN) becomes essential to calculate the coordinate points of the unknown nodes with the use of known or anchor nodes. The efficiency of the WSN has significant impact on localization accuracy. Node localization can be considered as an optimization problem and bioinspired algorithms finds useful to solve it. This paper introduces a novel Nelder Mead with Grasshopper Optimization Algorithm (NMGOA) for node localization in WSN. The Nelder-Mead simplex search method is employed to improve the effectiveness of GOA because of its capability of faster convergence. At the beginning, the nodes in WSN are arbitrarily placed in the target area and then nodes are initialized. Afterwards, the node executes the NMGOA technique for estimating the location of the unknown nodes and become localized nodes. In the subsequent round, the localized nodes will be included to the collection of anchor nodes to perform the localization process. The effectiveness of the NMGOA model is validated using a series of experiments and results indicated that the NMGOA model has achieved superior results over the compared methods.

An Efficient Hybrid Evolution Strategy Algorithm with Direct Search Method for Global Optimization

The main purpose of this article is to demonstrate how evolution strategy optimizers can be improved by incorporating an efficient hybridization scheme with restart strategy in order to jump out of local solution regions. The authors propose a hybrid (μ, λ)ES-NM algorithm based on the Nelder-Mead (NM) simplex search method and evolution strategy algorithm (ES) for unconstrained optimization. At first, a modified NM, called Adaptive Nelder-Mead (ANM) is used that exhibits better properties than standard NM and self-adaptive evolution strategy algorithm is applied for better performance, in addition to a new contraction criterion is proposed in this work. (μ, λ)ES-NM is balancing between the global exploration of the evolution strategy algorithm and the deep exploitation of the Nelder-Mead method. The experiment results show the efficiency of the new algorithm and its ability to solve optimization problems in the performance of accuracy, robustness, and adaptability.

Investigating the impacts of atmospheric diffusion conditions on source parameter identification based on an optimized inverse modelling method

Accurate identification of source parameters (source strength and location) of sudden air pollution accidents (SAPAs) is important for implementation of adequate responses. However, the potential impact of atmospheric diffusion conditions on source parameter identification may be significant. An inversion model that combines the hybrid particle swarm optimization and the Nelder–Mead simplex search method (PSO-NM) with the Gaussian dispersion model was proposed to identify the source parameters and to investigate the influences of different atmospheric conditions on the identifications. A case study based on 68 SO2 leakage tests from the Prairie Grass field experiment was conducted. The source strengths and locations of the 68 tests were estimated by the combined inversion model. The results indicated that the inversion model can effectively get accurate and robust source parameter estimations. The average absolute value of relative deviation of source strength was 13.8% ± 11.4%; the average absolute deviations for parameters x0, y0, z0 and the total distances were 18.9 ± 36.9 m, 2.7 ± 5.2 m, 3.5 ± 9.7 m and 19.6 ± 38.1 m, respectively. A comprehensive evaluation method was also proposed for analyzing the impacts of atmospheric conditions on source parameter estimations. The results showed that the source parameter estimations under atmospheric stability classes E and C have the best accuracy and robustness, followed by stability classes A and D; while the worst occurred under atmospheric stability classes B and F. The analysis results can provide scientific support for the formulation or adjustment of emergency response strategies used in sudden air pollution accidents. The new inversion model proposed is a supplement to the methodology of inversing source parameters.

Optimization of natural frequencies of a slender beam shaped in a linear combination of its mode shapes

This work focuses on the placement of natural frequencies of beams to desired frequency regions. More specifically, we investigate the effects of combining mode shapes to shape a beam to change its natural frequencies, both numerically and experimentally. First, we present a parametric analysis of a shaped beam and we analyze the resultant effects for different boundary conditions and mode shapes. Second, we present an optimization procedure to find the optimum shape of the beam for desired natural frequencies. In this case, we adopt the Nelder-Mead simplex search method, which allows a broad search of the optimum shape in the solution domain. Finally, the obtained results are verified experimentally for a clamped-clamped beam in three different optimization runs. Results show that the method is effective in placing natural frequencies at desired values (experimental results lie within a 10% error to the expected theoretical ones). However, the beam must be axially constrained to have the natural frequencies changed.

On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

The q-Weibull model is based on the Tsallis non-extensive entropy [22] and is able to model various behaviors of the hazard rate function, including bathtub curves, by using a single set of parameters. Despite its flexibility, the q-Weibull has not been widely used in reliability applications partly because of the complicated parameters estimation. In this work, the parameters of the q-Weibull are estimated by the maximum likelihood (ML) method. Due to the intricate system of nonlinear equations, derivative-based optimization methods may fail to converge. Thus, the heuristic optimization method of artificial bee colony (ABC) is used instead. To deal with the slow convergence of ABC, it is proposed an adaptive hybrid ABC (AHABC) algorithm that dynamically combines Nelder-Mead simplex search method with ABC for the ML estimation of the q-Weibull parameters. Interval estimates for the q-Weibull parameters, including confidence intervals based on the ML asymptotic theory and on bootstrap methods, are also developed. The AHABC is validated via numerical experiments involving the q-Weibull ML for reliability applications and results show that it produces faster and more accurate convergence when compared to ABC and similar approaches. The estimation procedure is applied to real reliability failure data characterized by a bathtub-shaped hazard rate.

Solar cell parameters identification using hybrid Nelder-Mead and modified particle swarm optimization

Solar cell modelling primarily involves the formulation of the non-linear current versus voltage (I-V) curve. Determination of parameters plays an important role in solar cell accurate modelling. This paper presents an application of the hybrid Nelder-Mead simplex search method and modified Particle Swarm Optimization technique for identifying the parameters of solar cell and photovoltaic module models. The proposed technique is used to identify the unknown model parameters, namely, the generated photocurrent, saturation current, series resistance, shunt resistance, and ideality factor that govern the current-voltage relationship of a solar cell. A measurement data of 57 mm diameter commercial (R.T.C. France) silicon solar cell and a module consisting of 36 polycrystalline silicon cells (Photowatt-PWP 201) are used to test and verify the consistency of accurately estimating various parameters. Comparative study among different parameter estimation techniques is presented to demonstrate the effectiveness of the proposed approach. Furthermore, to verify the accurateness of the proposed technique, an experimental test bench unit is built using 72 mono-crystalline silicon cells (HIP-210NKHB5-2 module) on different environment conditions.

Inverse methodology for identification the thermal diffusivity and subsurface defect of CFRP composite by lock-in thermographic phase (LITP) profile reconstruction

An inverse analysis methodology is developed to simultaneously identify the thermal diffusivities and subsurface defect of carbon fiber reinforced polymer (CFRP) laminate through lock-in thermographic phase (LITP) profile reconstruction. A hybrid algorithm that combines simulation annealing algorithm (SA) and Nelder–Mead simplex search method (NM) is proposed to minimize the objective function constructed by LITP profile for determination of the thermal diffusivities (αx and αz) and subsurface defect characteristics (size D and depth HD). For the hybrid method, SA is used to find a better feasible initial-guessed solution for NM. Numerical examples show that LITP has the merit of identifying the thermal diffusivities of CFRP laminate by inverse analysis. In comparison with SA and NM, respectively, the hybrid method can be converged to yield good estimates faster and more efficiently. Experimental and simulation LITP of defective regions are used to determine the thermal diffusivities and the size and depth of subsurface defect. The results show that the estimated thermal diffusivities and the size and depth of defect are in good agreement with the reference values, and the relative deviations are less than 5%. Nevertheless, this approach can only be applied for the determination of thermal diffusivities of CFRP laminate with subsurface defect.

Inverse heat transfer approach for nondestructive estimation the size and depth of subsurface defects of CFRP composite using lock-in thermography

An inverse heat transfer approach is developed to characterize the size and depth of subsurface defects in CFRP composite materials through the reconstruction phase profile of lock-in thermography (LIT) obtained by finite element simulation. This work mainly focuses on the application of hybrid method that integrates simulation annealing algorithm (SA) and Nelder–Mead simplex search method (NM) for determination of the sizes and depths of subsurface defects within the CFRP laminate materials. For this purpose, an 808nm laser is used for imposing a modulated heat excitation on the CFRP laminate specimen, and the thermal images are collected using an infrared camera. The hybrid method is employed to find the optimal solutions of the objective or cost function constructed by phase profile of LIT between an experimental configuration and numerical solution for a CFRP specimen. The experimental results show that the size and depth of subsurface defects are effectively obtained through inverse solving the constructed objective or cost function by the hybrid method. The estimated maximum errors for the size and depth are less than 5% and 4% for given subsurface defects by the proposed method, respectively.

Quantum-behaved Particle Swarm Optimization with Nelder-Mead Simplex Search Method

This paper proposes a novel hybrid algorithm based on quantum-behaved particle swarm optimization (QPSO) algorithm and Nelder-Mead (NM) simplex search method for continuous optimization problems, abbreviated as QPSO-NM. This hybrid algorithm is very easy to be implemented since it does not require continuity and differentiability of objective functions, and it also combines powerful global search ability of QPSO with precise local search of NM simplex method. In a suite of the first 10 test functions taken from CEC2005, QPSO-NM algorithm is compared with other four popular competitors and six special algorithms that are dedicated to solve CEC2005 test function suite. It is showed by the computational results that QPSO-NM outperforms other algorithms in terms of both convergence rate and solution accuracy. The proposed algorithm is extremely effective and efficient at locating optimal solutions for continues optimization.

A new hybrid imperialist swarm-based optimization algorithm for university timetabling problems

Generating timetables for an institution is a challenging and time consuming task due to different demands on the overall structure of the timetable. In this paper, a new hybrid method which is a combination of a great deluge and artificial bee colony algorithm (INMGD-ABC) is proposed to address the university timetabling problem. Artificial bee colony algorithm (ABC) is a population based method that has been introduced in recent years and has proven successful in solving various optimization problems effectively. However, as with many search based approaches, there exist weaknesses in the exploration and exploitation abilities which tend to induce slow convergence of the overall search process. Therefore, hybridization is proposed to compensate for the identified weaknesses of the ABC. Also, inspired from imperialist competitive algorithms, an assimilation policy is implemented in order to improve the global exploration ability of the ABC algorithm. In addition, Nelder–Mead simplex search method is incorporated within the great deluge algorithm (NMGD) with the aim of enhancing the exploitation ability of the hybrid method in fine-tuning the problem search region. The proposed method is tested on two differing benchmark datasets i.e. examination and course timetabling datasets. A statistical analysis t-test has been conducted and shows the performance of the proposed approach as significantly better than basic ABC algorithm. Finally, the experimental results are compared against state-of-the art methods in the literature, with results obtained that are competitive and in certain cases achieving some of the current best results to those in the literature.

Inverse analysis of conductive-convective wet triangular fin for predicting thermal properties and fin dimensions

The present work deals with the application of Homotopy Analysis Method (HAM) in conjunction with Nelder–Mead simplex search method (SSM) to study a triangular wet fin. At first, analytical expression has been derived using HAM to calculate the local temperature field. Then using SSM, the important parameters, namely, thermal conductivity of the material, surface heat transfer coefficient and dimensions of the fin, have been estimated separately for attaining the prescribed temperature field. The transport phenomena involve simultaneous heat and mass transfers. It is found from the present study that many feasible solutions can satisfy a given thermal condition, which will offer the flexibility in selecting the fin material, adjusting the thermal conditions and regulating the fin dimensions. Further, it is determined that the allowable error in the temperature measurement should be limited within ± 15% and a good reconstruction of the temperature field is possible using the HAM–SSM combination.

Application of Simplex Search Method for Predicting Unknown Parameters in an Annular Fin Subjected to Thermal Stresses

This article presents an inverse approach aimed at estimating the unknown parameters such as the coefficient of thermal expansion and the Biot number for satisfying a prescribed thermal stresses field in radial fin geometry. The variation of temperature with the radius of fin is obtained by solving the heat conduction-convection equation using regular perturbation method and applying proper boundary conditions. A closed form solution for the temperature dependent stress field has been derived by employing the classical elasticity theory coupled with semi-analytical solution for the temperature field. Using the data obtained from a forward method based on the analytical solution, two unknown parameters such as the coefficient of thermal expansion and the Biot number of the fin are simultaneously estimated by an inverse technique using the Nelder-Mead simplex search method. Effects of measurement errors and number of measurement points have been analyzed in detail. It is found that even with 10 measurement points a fairly good reconstruction of the stress field can be achieved.

Regression modelling and optimisation of cutting parameters through Nelder-Mead simplex search and CCFD during drilling of sisal-glass/vinyl ester composites

Drilling of holes in the assembly of structural frames of automobile and aircrafts are inevitable in order to make joining of parts. The drilling induced damage imparts reduced life and efficiency of parts. The present study attempts an effort to correlate drilling induced damage with drilling parameters during drilling on the Sisal-glass/vinyl ester hybrid composites. Diameter of drill, speed and feed rate were considered as significant factors and they control or minimise the drilling induced damages. Experiments were conducted under various cutting conditions as per design of experiments. Mathematical models for thrust force, torque and delamination factor were developed using non-linear regression equations. Optimisations of controlling parameters were done using Nelder-Mead simplex search method and central composite face centred design (CCFD). Analysis of variance (ANOVA) was used to study the effect of process parameters on drilling responses. The results revealed that the delamination can be effectively reduced in drilling of sisal-glass fibre composite materials by applying the lower feed rate values.