A constrained optimization algorithm based on the simplex search method

Mehta, Vivek Kumar; DasGupta, Bhaskar

doi:10.1080/0305215x.2011.598520

Cited by 53 publications

(8 citation statements)

References 19 publications

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“…In high-dimensional problems, our numerical studies show that the new implementation outperforms the standard Nelder–Mead technique. After that, a modified simplex search algorithm for handling constraints is proposed in the study of Mehta and Dasgupta (2012). Numerous evolutionary algorithms documented in the literature are outperformed by the proposed technique, as the findings show.…”

Section: Literature Reviewmentioning

confidence: 93%

A remanufacturing inventory model to control the carbon emission using cap-and-trade regulation with the hexagonal fuzzy number

Arora

Singh

Sharma

et al. 2021

BIJ

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PurposeThe awareness for protecting the environment has resulted in remanufacturing and recycling policies in manufacturing industries. Carbon emission is one of the most important elements affecting the environment. Carbon emission due to production and transportation creates complicated situations for the manufacturing firms by affecting the manufacturer's carbon quota. The ecological consequences posed in a reverse logistic model are the subject of this study.Design/methodology/approachThe present study explores the fuzzy model of economic production for both remanufacturing and recycling with uncertain cost parameters under the cap-and-trade rule to control the carbon emission due to different modes of transportation. Due to imprecise cost parameters, the hexagonal fuzzy numbers are set to fuzzify the overall cost, which leads to correct decisions in a more confident way. The result is defuzzified by using graded mean integration.FindingsThis study offers an explicit condition to control the carbon emission of the manufacturer and reduce the optimum cost. The findings indicate that the collection of used goods that can be remanufactured must be increased. The model is validated numerically. Sensitivity analysis explores the various aspects of different parameters on net cost to accomplish the fuzzy production model.Originality/valueUnder fuzzy inference, the research offers a relevant contribution in the field of recycling with controlling carbon emission by using the cap-and-trade policy. This study provides a trading strategy for a manufacturer's decision to avoid losses.

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Section: Literature Reviewmentioning

confidence: 93%

A remanufacturing inventory model to control the carbon emission using cap-and-trade regulation with the hexagonal fuzzy number

Arora

Singh

Sharma

et al. 2021

BIJ

View full text Add to dashboard Cite

show abstract

“…Therefore, the simplex dose should be carefully selected initially. The standard level indicates that only the reflection function can be used as proposed [16] we standardize the Nelder-Mead Downhill Simplex system on a quiet test bed. The multistory strategy is used in two stages.…”

Section: Downhill Simplex Methodsmentioning

confidence: 99%

Nelder–Mead Simplex Search Method - A Study

Selvam¹,

Ramachandran²,

Vimala³

2022

Data Analytics and Artificial Intelligence

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Nelder-Mead in n dimensions facilitates the set of n + 1 test points. It finds a new test point, Makes one of the old test points new, and so the technique progresses into objective behavior process is measured at each test point. The Nelder-Mead Simplex system uses Simplex to find the minimum space. The algorithm operates using a design framework with n + 1 points (called simplex), Where n is for simplex based operation Number of input dimensions. The Nelder-Mead method is one of the most popular non-derivative methods, using only the values of f to search. Only in the simplex formation of n + 1 will the points / moving / contraction of this simplex be in a positive direction. Strictly speaking, Nelder-Mead is not a truly universal optimization algorithm; however, in it works reasonably well for many non-local problems. Direct search is the gradient of the objective process Optimization is a method for solving problems that require no information. All of the points approaching an optimal point Pattern search algorithms that calculate the sequence. The existence of local trust is a key factor in defining the difficulty of the global optimization problem because it is relatively easy to improve locally and relatively difficult to improve locally. Slope Descent is an optimal method Machine learning models and to train neurological networks commonly used. Training data these models allow learning over time, and pricing function is particularly active in gradient descent. The barometer is an optimization algorithm that measures its accuracy at each parameter update and can be repeated by comparing optimal or different solutions. A satisfactory the solution will be found. With the advent of computers, optimization has become of computer aided design activities has become a part of Gradient Decent (GT) is a functional first-order upgrade algorithm Local minimum of the given function and Used to determine the maximum. This method is commonly used to reduce cost / loss performance in machine learning (ML) and deep learning (DL). The problem with finding optimal points in such situations is referred to as derivative-free optimization, and algorithms that do not use derivatives or defined variants are called derivative-free algorithms.

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“…However, the constrained problem can be transformed into an unconstrained problem by applying coordinate transformations and penalty functions. Then, the unconstrained minimization problem is solved using the Nelder-Mead algorithm or MATLAB's built-in function fminsearch [34][35][36]. Since our optimization problem ( 4) is constrained with scalar bounds, it is sufficient to use the coordinate transformation techniques [37] detailed in Section 3.1.…”

Section: Nelder-mead Algorithm For the Optimal Completion Of Incomple...mentioning

confidence: 99%

“…A modified Nelder-Mead algorithm [35] has also been proposed for solving a general nonlinear constrained optimization problem that handles linear and nonlinear (in)equality constraints. Several benchmark problems have been examined and compared with various methods (the α constrained method with mutation [53]; the genetic algorithm [54]; and the bees algorithm [55]-to mention a few) to evaluate the performance of their algorithm.…”

Section: Nelder-mead Algorithmmentioning

confidence: 99%

Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

2021

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Pairwise comparison matrices play a prominent role in multiple-criteria decision-making, particularly in the analytic hierarchy process (AHP). Another form of preference modeling, called an incomplete pairwise comparison matrix, is considered when one or more elements are missing. In this paper, an algorithm is proposed for the optimal completion of an incomplete matrix. Our intention is to numerically minimize a maximum eigenvalue function, which is difficult to write explicitly in terms of variables, subject to interval constraints. Numerical simulations are carried out in order to examine the performance of the algorithm. The results of our simulations show that the proposed algorithm has the ability to solve the minimization of the constrained eigenvalue problem. We provided illustrative examples to show the simplex procedures obtained by the proposed algorithm, and how well it fills in the given incomplete matrices.

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A constrained optimization algorithm based on the simplex search method

Cited by 53 publications

References 19 publications

A remanufacturing inventory model to control the carbon emission using cap-and-trade regulation with the hexagonal fuzzy number

A remanufacturing inventory model to control the carbon emission using cap-and-trade regulation with the hexagonal fuzzy number

Nelder–Mead Simplex Search Method - A Study

Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

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