Nelder-Mead Simplex Search Algorithm Research Articles

Meta-Optimization of Dimension Adaptive Parameter Schema for Nelder–Mead Algorithm in High-Dimensional Problems

Although proposed more than half a century ago, the Nelder–Mead simplex search algorithm is still widely used. Four numeric constants define the operations and behavior of the algorithm. The algorithm with the original constant values performs fine on most low-dimensional, but poorly on high-dimensional, problems. Therefore, to improve its behavior in high dimensions, several adaptive schemas setting the constants according to the problem dimension were proposed in the past. In this work, we present a novel adaptive schema obtained by a meta-optimization procedure. We describe a schema candidate with eight parameters subject to meta-optimization and define an objective function evaluating the candidate’s performance. The schema is optimized on up to 100-dimensional problems using the Parallel Simulated Annealing with Differential Evolution global method. The obtained global minimum represents the proposed schema. We compare the performance of the optimized schema with the existing adaptive schemas. The data profiles on the Gao–Han modified quadratic, Moré–Garbow–Hilstrom, and CUTEr (Constrained and Unconstrained Testing Environment, revisited) benchmark problem sets show that the obtained schema outperforms the existing adaptive schemas in terms of accuracy and convergence speed.

Extended Horizon ECMS Control of PHEVs With 2D Electricity Price Adaptation Policy

This article proposes new improvements to the ECMS-based control of plug-in hybrid electric vehicles (PHEVs) using macro-level trip forecast information. First, the dynamic programming (DP) optimization is applied to a power-split PHEV model to obtain the optimal powertrain trajectories for benchmarking the energy economy of the proposed controllers. An instantaneous energy cost minimization process is then formulated to compute the optimal mix of fuel and electricity, subject to the state and input constraints. To improve the speed and accuracy of the energy management system, the Nelder-Mead simplex search algorithm is used for the instantaneous optimizations. To account for the battery capacity limitation, an adaptive electricity pricing policy is introduced to control battery discharge rate based on the remaining trip distance, average speed, and elevation forecasts. The parameters of the proposed policy are optimized for a group of 5 urban and highway drive cycles to obtain a robust controller which can serve a wide spectrum of driving patterns. To further improve the energy economy, an extended-horizon optimization algorithm is proposed to account for control input transitions between consecutive time steps. Finally, a revised speed forecast formula is implemented during the low-SOC intervals to lift battery SOC ahead of high-demand periods. The combination of the proposed schemes enables reaching over 99% average optimality compared to a finely discretized DP optimization for the adopted drive cycles, and above 98% optimality for a test PHEV drive cycle.

Improved Nelder–Mead algorithm in high dimensions with adaptive parameters based on Chebyshev spacing points

In spite of being one of the most popular optimization methods, Nelder–Mead's simplex search algorithm with the default choice of parameters performs poorly on high-dimensional problems. The work presented here concerns such values of the Nelder–Mead algorithm's parameters that help improve the convergence and success rate of the algorithm in high dimensions. In this work, a novel way of assigning parameters to the Nelder–Mead simplex search algorithm is proposed. The proposed scheme is based on Chebyshev spacing points and adapts itself to the dimension of the problem. The numerical experiments conducted for this study show that the proposed scheme is better not just in comparison with the original Nelder–Mead algorithm but it outperforms the other existing adaptive schemes as well.

Optimal Design of an Intelligent Mobile Microcontroller: Assembling and Maintaining Objects in 3D

Abstract Mobile microcontrollers are one of the areas of application artificial intelligent. The aim of this research is to develop an ideal design for mobile microcontrollers can move in a vacuum in order to conduct the installation with little cost. This design of mobile microcontrollers gives them the ability to move an arm with high starting torque enable it to perform their tasks efficiently. The main objective of this paper is to present an optimal design of mobile microcontrollers have an arm with high starting torque and with low cost. To verify this objective, Nelder Mead simplex search algorithm is used to obtain the optimal values of manufacturing parameters. The results depict a reduction of the total cost that represents cost of unit weight of copper, cost of unit weight of iron, the laminations cost, the copper cost and the rotor-end-ring cost by 4.64% and a reduction in the angular velocity by 25%.

Parameter estimation of proton exchange membrane fuel cells using eagle strategy based on JAYA algorithm and Nelder-Mead simplex method

Building an accurate mathematical model is vital for the simulation, control, evaluation, management, and optimization of proton exchange membrane fuel cells (PEMFCs). Usually this work is processed through building a mathematical model based on empirical or semi-empirical equations firstly and then estimating the unknown model parameters using optimization technologies. In this study, a simple two stage eagle strategy based on JAYA algorithm and Nelder-Mead simplex algorithm is proposed for effectively estimating the unknown model parameters of PEMFCs. In the proposed strategy, JAYA algorithm is employed for the coarse global exploration, and Nelder–Mead simplex search algorithm is employed for the intensive local search. The effectiveness of the proposed strategy is verified through estimation experiments with 7 and 9 unknown parameters. Compared with the basic JAYA algorithm and four other newly reported excellent meta-heuristic algorithms including Grey Wolf Optimizer, Grasshopper Optimization Algorithm, Salp Swarm Optimizer, and Multi-Verse Optimizer, the proposed strategy possesses better performance in terms of accuracy, convergence speed, and stability, thus it is a promising approach for parameter estimation of PEMFC.

Effect of vertical ground temperature distribution on parameter estimation of in-situ thermal response test with unstable heat rate

This paper proposed a parameter estimation method for identifying ground thermal conductivity and volumetric heat capacity using the Nelder-Mead Simplex search algorithm (NMSA) in in-situ thermal response test (TRT) with unstable heat rate, the duct storage system (DST) model for borehole heat exchanger (BHE) was applied to do with variable heat rate and the vertical ground temperature distribution in initial soil temperature. The parameter estimation was carried out using the in-situ TRT data in Qingdao, and the effect of vertical ground temperature distribution on estimated results was compared and analyzed. The relative error of estimated ground thermal conductivity using the regression temperature fitted by the test temperatures from the 5th m depth to the 120th m depth decreased by about 9.1% than that corresponding to the integral mean temperature calculated by test temperatures from the 5th m depth to the 120th m depth. However, the estimated volumetric heat capacity is hardly sensitive to initial soil temperature, and the relative errors are not higher than 2% no matter how to do with initial soil temperature.

Strategy for kinetic parameter estimation—Thermal degradation of polyurethane elastomers

AbstractThe kinetics of the thermal degradation of polyurethane (PU) elastomers based on poly(ether polyol) soft segments and an aromatic type of diisocyanate were investigated by thermogravimetric analysis (TGA) under a nitrogen atmosphere employing four heating rates. The corresponding kinetic parameters of the two degradation stages were estimated by minimizing the output error functional and by the Kissinger method. In evaluating the kinetic parameters of the two‐step PU thermal decomposition, a differential thermogravimetry curve was applied as an objective functional in a regression procedure. Parameter estimation was obtained by minimizing the weighted quadratic output error functional with the modified Nelder–Mead simplex search algorithm. The confidence regions in the preexponential factor‐activation energy space were established for both the first and second stages of degradation. The effect of the molecular weight of the soft segment and the content of the hard segment on the activation energy of the degradation process was constructed by response surface methodology. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 764–772, 2007

Kinetic Parameters Estimation for Thermal Degradation of Polyurethane Elastomers

In this work, thermogravimetric analysis is used to determine the kinetic parameters of thermal degradation of polyurethane (PU) elastomers, based on poly(ether polyol) soft segment and aromatic-type diisocyanates. To determine the kinetic parameters of PU thermal decomposition, a nonlinear regression procedure is applied. Parameter estimation is obtained by minimizing the weighted quadratic output error functional with the modified Nelder-Mead simplex search algorithm. The confidence region of pre-exponential factor-activation energy are established both for the first and second steps of degradation. The effect of the soft segment molecular weight and hard segment content on the activation energy of the degradation process has been studied.