A global search method for optimizing nonlinear systems

1988 ◽  
Vol 18 (6) ◽  
pp. 965-977 ◽  
Author(s):  
B.E. Stuckman
Keyword(s):  
Nonlinear Systems ◽  
Global Search ◽  
Search Method

Generalized Field-Development Optimization With Derivative-Free Procedures

SPE Journal ◽  
2014 ◽  
Vol 19 (05) ◽  
pp. 891-908 ◽  
Author(s):  
Obiajulu J. Isebor ◽  
David Echeverría Ciaurri ◽  
Louis J. Durlofsky
Keyword(s):  
Computational Cost ◽  
Optimization Method ◽  
Optimal Number ◽  
Global Search ◽  
Search Method ◽  
Pattern Search ◽  
Mixed Integer ◽  
Categorical Variables ◽  
Field Development ◽  
Derivative Free

Summary The optimization of general oilfield development problems is considered. Techniques are presented to simultaneously determine the optimal number and type of new wells, the sequence in which they should be drilled, and their corresponding locations and (time-varying) controls. The optimization is posed as a mixed-integer nonlinear programming (MINLP) problem and involves categorical, integer-valued, and real-valued variables. The formulation handles bound, linear, and nonlinear constraints, with the latter treated with filter-based techniques. Noninvasive derivative-free approaches are applied for the optimizations. Methods considered include branch and bound (B&B), a rigorous global-search procedure that requires the relaxation of the categorical variables; mesh adaptive direct search (MADS), a local pattern-search method; particle swarm optimization (PSO), a heuristic global-search method; and a PSO-MADS hybrid. Four example cases involving channelized-reservoir models are presented. The recently developed PSO-MADS hybrid is shown to consistently outperform the standalone MADS and PSO procedures. In the two cases in which B&B is applied, the heuristic PSO-MADS approach is shown to give comparable solutions but at a much lower computational cost. This is significant because B&B provides a systematic search in the categorical variables. We conclude that, although it is demanding in terms of computation, the methodology presented here, with PSO-MADS as the core optimization method, appears to be applicable for realistic reservoir development and management.

Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods

1997 ◽  
Vol 119 (4) ◽  
pp. 504-510 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Design Space ◽  
Initial Guess ◽  
Global Search ◽  
Search Method ◽  
Fourier Descriptors ◽  
Path Generation ◽  
Local Optima ◽  
Structural Error ◽  
Synthesis Of Mechanisms

Generally, success in synthesis of mechanisms for path generation is limited to finding a reasonable local optima at best in spite of a very good initial guess. The most widely used Structural Error objective function is not effective in leading to practical solutions as it misrepresents the nature of the design problem by requiring the shape, size, orientation and position of the coupler curve to be optimized all at once. In this paper, we present an effective objective function based on Fourier descriptors that evaluates only the shape differences between two curves. This function is first minimized using a stochastic global search method derived from simulated annealing followed by Powell’s method. The size, orientation and position of the desired curve are addressed in a later stage by determining analogous points on the desired and candidate curves. In spite of highly non-linear mechanisms design space, our method discovers near-global and practical solutions consistently without requiring any initial guess.

scholarly journals A New Line Search Method to Solve the Nonlinear Systems of Monotone Equations

2019 ◽  
Vol 14 (7) ◽  
pp. 10080-10086 ◽  
Author(s):  
Karrar Habeeb Hashim ◽  
Nabiha Kahtan Dreeb ◽  
Hasan Hadi Dwail ◽  
Mohammed Maad Mahdi ◽  
H.A. Wasi ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Line Search ◽  
Search Method ◽  
Monotone Equations ◽  
Line Search Method

scholarly journals A Global Search Method for Inputs and Outputs in Data Envelopment Analysis: Procedures and Managerial Perspectives

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1155
Author(s):  
Wai-Peng Wong
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Global Search ◽  
Search Method ◽  
Performance Estimation ◽  
Data Envelopment ◽  
Dea Models ◽  
Key Variables ◽  
Effective Decision ◽  
Effective Decision Making

Effective decision-making techniques are essentially dependent on the capacity to balance (symmetry) requirements and their fulfilment, that is, the capacity to accurately identify a collection of factors that have the greatest influence on performance. Data envelopment analysis (DEA) is a useful nonparametric method in operations research for performance estimation by measuring the efficiency scores of the decision-making units. In this paper, we develop a global search method (GSM) for selecting the key input and output variables in DEA models. The GSM measures the effects of variables with respect to the efficiency scores directly, i.e., by considering the average change when a variable is added or removed from the analysis. It aims to produce DEA models that include only the key variables with the largest impact on the results. The effectiveness of the GSM is demonstrated using a case study from 15 US banks, with the results analyzed and discussed. The outcomes indicate that the GSM yields useful insight for decision-makers to make informed decisions in undertaking their problems.

Sign in / Sign up

Export Citation Format

Share Document