Globalized Nelder-Mead Method for Engineering Optimization

Luersen, Marco Antônio; Riche, Rodolphe Le

doi:10.4203/ccp.76.65

Cited by 63 publications

(102 citation statements)

References 9 publications

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“…However, from a numerical point of view, solving the multi-objective problem (1) is much more complex than solving the constrained single objective problem (2). State-of-the-art multiobjective algorithms are evolutionary algorithms (see [14] for a review) which have a slower convergence than other single objective algorithms such as the Globalized and Bounded Nelder-Mead algorithm (see Section 2.4 and [15]). Furthermore, the set of solutions need to be post-processed in order to decide which compromise should be manufactured.…”

Section: Design Formulation 21 Structural and Rtcm Couplings In Compmentioning

confidence: 99%

“…The constrained single objective optimization problems are dealt with by the Globalized and Bounded Nelder-Mead algorithm ( [15]), GBNM. This algorithm is based on repeated direct Nelder-Mead (sometimes also called simplex, [17]) searches, which work on continuous variables, do not need gradient information and, individually, converge faster than probabilistic global search methods such as evolutionary algorithms ( [18]).…”

Section: The Globalized and Bounded Nelder-mead Optimization Algorithmmentioning

confidence: 99%

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Coupled compression RTM and composite layup optimization

Riche

Saouab

Bréard

2003

Composites Science and Technology

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A methodology for studying the implications of taking into account manufacturing at early design stages is presented. It is applied to a rectangular laminate made by RTM and compression (RTCM). The plate is designed for injection time, maximum mold pressure, stiffness and buckling. Semi-analytical, numerically inexpensive models of the processes and structure enable a thorough investigation of the couplings between process and structure by comparing four design formulations: in decoupled problems, either the process or the structure is optimized; then, the process is optimized with targetted low or high structural performance. A globalized Nelder-Mead optimization algorithm is used. The rigour of the method and the relative simplicity of the application case provide a clear description of how maximum mold pressures, injection times and final structures properties are tradedoff.

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Section: Design Formulation 21 Structural and Rtcm Couplings In Compmentioning

confidence: 99%

Section: The Globalized and Bounded Nelder-mead Optimization Algorithmmentioning

confidence: 99%

Coupled compression RTM and composite layup optimization

Riche

Saouab

Bréard

2003

Composites Science and Technology

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“…The local search is performed using Sequential Quadratic Programming (SQP) [15], but the global optimization strategy remains unchanged if another local search algorithm is employed. The search is then turned into an asymptotically global one applying the probabilistic restart procedure proposed by Luersen and Le Riche [13].…”

Section: Local-restart Strategy For Global Optimizationmentioning

confidence: 99%

“…Local search is performed by gradient based techniques and thus local optimality is guaranteed. In order to find the global minimum, the local search is made global by a probabilistic restart procedure presented by Luersen and Le Riche [13]. In this approach, a spatial probability of starting a local search is built based on past searches.…”

Section: Introductionmentioning

confidence: 99%

A local-restart coupled strategy for simultaneous sizing and geometry truss optimization

Torii

López

Luersen

2011

Lat. Am. j. solids struct.

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This paper presents an approach for the global optimization of truss sizing and geometry that is based on a probabilistic restart procedure coupled with a local search algorithm. The resulting algorithm is able to guarantee local optimality and provides a set of local optima which contain, with an increasing probability as the number of restarts increases, the global solution. The optimization problem searches for a truss structure of minimum volume, subject to stress constraints. The design variables are the bars cross-section areas and some nodal coordinates. Several loading conditions are also considered. Finally, four numerical examples are presented and the main aspects of the approach are discussed.

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“…The improvements of the modified NM are summarized as follows: 1 Initialization and boundary. A simplex of size l is initialized at x 0 based on the rule (Luresen and Riche, 2004):…”

Section: End Loopmentioning

confidence: 99%

Forward kinematics analysis of a six‐DOF Stewart platform using PCA and NM algorithm

Wang

Shang

et al. 2009

Industrial Robot: An International Journal

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Purpose -The purpose of this paper is to present an adaptive numerical algorithm for forward kinematics analysis of general Stewart platform. Design/methodology/approach -Unlike the convention of developing a set of kinematic equations and then solving them, an alternative numerical algorithm is proposed in which the principal components of link lengths are used as a bridge to analyze the forward kinematics of a Stewart platform. The values of link lengths are firstly transformed to the values of principal components through principal component analysis. Then, the computation of the values of positional variables is transformed to a two-dimensional nonlinear minimization problem by using the relationships between principal components and positional variables. A hybrid Nelder Mead-particle swarm optimizer (NM-PSO) algorithm and a modified NM algorithm are used to solve the two-dimensional nonlinear minimization problem. Findings -Simulation experiments have been conducted to validate the numerical algorithm and experimental results show that the numerical algorithm is valid and can achieve good accuracy and high efficiency. Originality/value -This paper proposes an adaptive numerical algorithm for forward kinematics analysis of general Stewart platform.

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Globalized Nelder-Mead Method for Engineering Optimization

Cited by 63 publications

References 9 publications

Coupled compression RTM and composite layup optimization

Coupled compression RTM and composite layup optimization

A local-restart coupled strategy for simultaneous sizing and geometry truss optimization

Forward kinematics analysis of a six‐DOF Stewart platform using PCA and NM algorithm

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