The Nelder–Mead simplex algorithm with perturbed centroid for high-dimensional function optimization

Fajfar, Iztok; Bűrmen, Árpád; Puhan, Janez

doi:10.1007/s11590-018-1306-2

Cited by 22 publications

(7 citation statements)

References 10 publications

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“…However, the objective function from the previous sections is suitable for a narrow class of applications. Thus, to perform a comparison of different parallel versions of Nelder-Mead method we minimise the Rosenbrock objective function that is widely used by researchers in the field of optimisation theory (Fajfar et al, 2018), (Stripinis et al, 2018).…”

Section: The Comparison Of Different Nelder-mead Parallelisation Methodsmentioning

confidence: 99%

A Three-Level Parallelisation Scheme and Application to the Nelder-Mead Algorithm

Kriauzienė

Bugajev

Čiegis

2020

Mathematical Modelling and Analysis

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We consider a three-level parallelisation scheme. The second and third levels define a classical two-level parallelisation scheme and some load balancing algorithm is used to distribute tasks among processes. It is well-known that for many applications the efficiency of parallel algorithms of these two levels starts to drop down after some critical parallelisation degree is reached. This weakness of the twolevel template is addressed by introduction of one additional parallelisation level. s an alternative to the basic solver some new or modified algorithms are considered on this level. The idea of the proposed methodology is to increase the parallelisation degree by using possibly less efficient algorithms in comparison with the basic solver. As an example we investigate two modified Nelder-Mead methods. For the selected application, a Schro¨dinger equation is solved numerically on the second level, and on the third level the parallel Wang’s algorithm is used to solve systems of linear equations with tridiagonal matrices. A greedy workload balancing heuristic is proposed, which is oriented to the case of a large number of available processors. The complexity estimates of the computational tasks are model-based, i.e. they use empirical computational data.

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Section: The Comparison Of Different Nelder-mead Parallelisation Methodsmentioning

confidence: 99%

A Three-Level Parallelisation Scheme and Application to the Nelder-Mead Algorithm

Kriauzienė

Bugajev

Čiegis

2020

Mathematical Modelling and Analysis

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“…e six scenarios were simulated to yield six sets of parameters that best describe the behavior under each scenario. e Nelder-Mead algorithm [28] is used in the optimization routine to minimize the objective function, which measures the least square error from the video benchmark. e objective function (5) has units in meters and can be interpreted as the average distance between the predicted trajectories and the real ones.…”

Section: Model Calibrationmentioning

confidence: 99%

Social Force Model Calibration for Preschool Children Evacuations Based on Multiscenario Experiments

She

Liu

et al. 2022

Journal of Advanced Transportation

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The social force model has been widely used in simulating and analyzing pedestrian behavior. Like any agent-based models, the fidelity of the social force model largely relies on its numerical parameters that characterizes pedestrians’ behaviors. While parameters describing normal walking behaviors have been observed and calibrated in field experiments, those describing behaviors under abnormal and urgent circumstances have rarely been studied but are of practical significance in evaluating safety functionality of facilities, particularly those serving children or elders. Specifically aiming at providing a set of social force model parameters characterizing children’s behavior during evacuation, this study conducted evacuation experiments with preschool children under multiple emergency scenarios involving impaired-vision and flame scenarios and benchmarked against a normal scenario. A simulation-calibration framework is developed based on the social force model to calibrate evacuation behavior parameters by minimizing trajectory distance. The numerical approximation results indicate evident parameter disparities of preschool children from adults. This study can improve evacuation strategies and the designing/evaluation process of dedicated facilities layouts such as kindergarten corridors, activity rooms, and playgrounds.

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“…Fortunately, there are many studies in the literature on variants of the Nelder-Mead Simplex search method: Lagarias et al [ 31 ] and McKinnon [ 56 ] did convergence analysis; Gao and Han [ 54 ] and Mehta [ 57 ] proposed adaptive parameters; and Fajfar et al [ 58 ] using the perturbed centroid to improve performance for problems with higher dimensions in Nelder-Mead Simplex method. Those studies contributed to make Nelder-Mead Simplex a more robust, reliable and competitive technique for solving nonlinear optimization problems.…”

Section: Theorymentioning

confidence: 99%

A new hybrid optimization approach using PSO, Nelder-Mead Simplex and Kmeans clustering algorithms for 1D Full Waveform Inversion

et al. 2022

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The FWI is formulated as a nonlinear optimization problem that traditionally uses local (derivative-based) minimization to find the scalar field of properties that best represents the field seismic data. This problem has a high computational cost and accuracy limited to local minima, in addition to suffering from a slow convergence rate (Cycle Skipping). Therefore, we developed a two-phase hybrid optimization algorithm based on DFO algorithms. The first use global minimization and clustering technique. The second use local minimization. In phase 1 we adopted the modified PSO and K-means algorithms and in phase 2, we adopted the ANMS. We call the hybrid algorithm of the PSO-Kmeans-ANMS. Where K-means is responsible for dividing swarms of particles into 2 clusters at every instant. This strategy aims to automatically balance the mechanisms of exploration and exploitation of the parameter search space by the hybrid algorithm, allowing one to find more precise solutions and consequently improving its convergence. The PSO-Kmeans-ANMS algorithm was validated on the set of 12 benchmark functions and applied to the FWI 1D problem. We compared PSO-Kmeans-ANMS with classic PSO, modified PSO, and ANMS algorithms. The metrics used were are the average execution time and the success rate (an error of ± 4% of the optimal solution). In all validation experiments and the FWI application, the PSO-Kmeans-ANMS performed well in terms of robustness and computational efficiency. In the case of FWI, there was a significant reduction in computational cost, thus presenting a relevant result.

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The Nelder–Mead simplex algorithm with perturbed centroid for high-dimensional function optimization

Cited by 22 publications

References 10 publications

A Three-Level Parallelisation Scheme and Application to the Nelder-Mead Algorithm

A Three-Level Parallelisation Scheme and Application to the Nelder-Mead Algorithm

Social Force Model Calibration for Preschool Children Evacuations Based on Multiscenario Experiments

A new hybrid optimization approach using PSO, Nelder-Mead Simplex and Kmeans clustering algorithms for 1D Full Waveform Inversion

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