Use of Direct Search in Automated Optimal Design

1972 ◽  
Vol 94 (2) ◽  
pp. 395-401 ◽  
Author(s):  
M. Pappas
Keyword(s):  
Optimal Design ◽  
Mathematical Programming ◽  
Penalty Function ◽  
Original Method ◽  
Direct Search ◽  
Search Method ◽  
Pattern Search ◽  
Search Procedure ◽  
Optimal Design Problem ◽  
Variable Step

A direct search penalty function procedure is described for treating a rather general mathematical programming form of the optimal design problem. A rotating coordinate modification of the pattern search of Hooke and Jeeves is proposed and compared with the original method, and an earlier variable step modification, as the basic optimal search method. The algorithm is successfully applied to several design examples which indicate that both modifications are comparable and are significantly superior to the original pattern search procedure.

An Improved Direct Search Mathematical Programming Algorithm

1975 ◽  
Vol 97 (4) ◽  
pp. 1305-1310 ◽  
Author(s):  
M. Pappas ◽  
J. Y. Moradi
Keyword(s):  
Mathematical Programming ◽  
Direction Finding ◽  
Direct Search ◽  
Pattern Search ◽  
New Method ◽  
Programming Algorithm ◽  
Test Problems ◽  
Feasible Direction ◽  
Search Termination

An improved, nonlinear, constrained algorithm is presented, coupling a rotating coordinate pattern search with a feasible direction finding procedure used at points of pattern search termination. The procedure is compared with eighteen algorithms, including most of the popular methods, on ten test problems. These problems are such that the majority of codes failed to solve more than half of them. The new method proved superior to all others in the overall generality and efficiency rating, being the only one solving all problems.

scholarly journals Harmony Search Method: Theory and Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
X. Z. Gao ◽  
V. Govindasamy ◽  
H. Xu ◽  
X. Wang ◽  
K. Zenger
Keyword(s):  
Optimal Design ◽  
Optimization Algorithm ◽  
Harmony Search ◽  
Search Method ◽  
Optimal Design Problem ◽  
Pareto Dominance ◽  
The Past ◽  
Challenging Tasks ◽  
Metaheuristic Optimization Algorithm

The Harmony Search (HS) method is an emerging metaheuristic optimization algorithm, which has been employed to cope with numerous challenging tasks during the past decade. In this paper, the essential theory and applications of the HS algorithm are first described and reviewed. Several typical variants of the original HS are next briefly explained. As an example of case study, a modified HS method inspired by the idea of Pareto-dominance-based ranking is also presented. It is further applied to handle a practical wind generator optimal design problem.

Interstellar Search Method With Mesh Adaptive Direct Search for Optimal Design of Brushless DC Motor

2016 ◽  
Vol 52 (3) ◽  
pp. 1-4 ◽  
Author(s):  
ByungKwan Son ◽  
Gyeong-Jae Park ◽  
Jong-Wook Kim ◽  
Yong-Jae Kim ◽  
Sang-Yong Jung
Keyword(s):  
Optimal Design ◽  
Dc Motor ◽  
Direct Search ◽  
Search Method ◽  
Brushless Dc Motor ◽  
Mesh Adaptive Direct Search ◽  
Brushless Dc

Predictive Search for Capacitated Multi-Item Lot Sizing Problems

2021 ◽  
Author(s):  
Tao Wu
Keyword(s):  
Mathematical Programming ◽  
Heuristic Search ◽  
Lot Sizing ◽  
Optimal Solution ◽  
Solution Space ◽  
Search Method ◽  
Benchmark Problems ◽  
Solution Quality ◽  
Programming Technique ◽  
Advanced Analytics

For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.

scholarly journals Regularity results for an optimal design problem with a volume constraint

2014 ◽  
Vol 20 (2) ◽  
pp. 460-487 ◽  
Author(s):  
Menita Carozza ◽  
Irene Fonseca ◽  
Antonia Passarelli di Napoli
Keyword(s):  
Optimal Design ◽  
Design Problem ◽  
Volume Constraint ◽  
Optimal Design Problem ◽  
Regularity Results

scholarly journals A Frame-Based Conjugate Gradients Direct Search Method with Radial Basis Function Interpolation Model

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowei Fang ◽  
Qin Ni
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Direct Search ◽  
Search Method ◽  
Conjugate Gradients ◽  
Test Problems ◽  
Interpolation Model ◽  
Direct Search Method ◽  
Radial Basis Function Interpolation ◽  
Radial Basis

In this paper, we propose a new hybrid direct search method where a frame-based PRP conjugate gradients direct search algorithm is combined with radial basis function interpolation model. In addition, the rotational minimal positive basis is used to reduce the computation work at each iteration. Numerical results for solving the CUTEr test problems show that the proposed method is promising.

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.

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