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Conventional Optimization Techniques for Manufacturing Applications
Published in R. Saravanan, Manufacturing Optimization through Intelligent Techniques, 2017
The pattern search method works by iteratively creating a set of search directions. The created search directions should be such that they completely span the search space. In other words, they should be such that starting from any point in the search space, any other point in the search space can be reached by traversing along these search directions only. In an N-dimensional problem, this requires at least N linearly independent search directions. For example, in a two-variable function, at least two search directions are required to go from any one point to any other point. Among many possible combinations of N search directions, some combinations may be able to reach the destination faster (with fewer iterations) and some may require more iterations.
Advances in Inverse Planning Algorithm and Strategy
Published in Siyong Kim, John Wong, Advanced and Emerging Technologies in Radiation Oncology Physics, 2018
Masoud Zarepisheh, Baris Ungun, Ruijiang Li, Yinyu Ye, Stephen Boyd, Lei Xing
Pattern search seeks an improving direction in the positive basis to improve the current solution, and it concludes that the solution is optimal if there is no improving direction (Conn et al. 2009; Rocha et al., 2013). The positive basis here is defined as set of vectors V={v1,v2,…,vm}, which represents possible gantry and MLC motions: It contains two directions for each leaf (moving to the right and left) as well as two directions corresponding to each delivery angle (moving clockwise and counterclockwise). Pattern search has two search strategies known as search step and poll step. In the poll step, one aims to improve the current solution by moving toward one of the directions in V (poll directions); in the search step, one examines a finite set of directions where each is a non-negative and integer combination of the poll directions. A random combination of the poll directions can be used to construct directions for the search step. Given the construction of the positive basis, the poll step aims to improve the current solution by moving an individual leaf (toward the right or left) or changing a beam angle (clockwise or counterclockwise), and the search step aims to make an improvement by changing multiple leaves and/or beam angles.
Nonlinear Programming
Published in Albert G. Holzman, Mathematical Programming, 2020
Although the pattern search method may require a great number of function evaluations in order to reach a point that approximates the minimum of a function, it is regarded as an easily programmed and reliable method. Its main feature consists of following "ridges" and "valleys." The pattern moves can take long steps in the assumed direction of valleys, whereas the exploratory moves find the way back to these valleys if a pattern move has climbed out of them.
A Novel Hybrid Optimization Approach for Optimal Allocation of Distributed Generation and Distribution Static Compensator with Network Reconfiguration in Consideration of Electric Vehicle Charging Station
Published in Electric Power Components and Systems, 2023
Arvind Pratap, Prabhakar Tiwari, Rakesh Maurya, Bindeshwar Singh
The previously cited references did not examine the impact of EVCSs with DGs and DSTATCOMs employing NR on RDN. The impact of EVCS planning with various scenarios of optimal DG and DSTATCOM sizing and sitting with NR has never been addressed. Additionally, the optimization problem has been tackled for the first time using a hybrid of AVOA and pattern search (PS) in this article. The key contributions of this study are as follows: Impact assessment of EVCS loading on RDN with simultaneous NR and DGs/DSTATCOMs installation.A MOF is developed by taking into consideration both technical and economic aspects. Economic factors include optimizing DG and DSTATCOM investment costs, while technical considerations include ILP reduction, IVD reduction, and VSI improvement.A novel HAVOPS technique is presented to optimize the MOF. The advantage of the proposed algorithm is that it employs PS to fine-tune the best results of the AVOA algorithm.The effectiveness of HAVOPS algorithms to solve problems on large-scale systems has been compared with well-known meta-heuristic algorithms such as AVOA [31], AGTO [32], MPA [33], GWO [34], and GA [35].
Optimal Power Flow Using a Hybrid Improved Harris Hawks Optimization Algorithm-Pattern Search Method
Published in IETE Journal of Research, 2023
Ramanaiah Upputuri, Niranjan Kumar, Chintalapudi V. Suresh
The PS is a relatively new optimization method capable of solving a wide range of optimization problems. This approach has various advantages, including a simple construction to implement and a minimal computing burden. The operator used in the pattern search technique has efficient and improves the method’s search abilities. The IHHO determines the initial point, designated A0, for this algorithm. The pattern or direction vectors would be produced as [0 1], [19], [1 0], and [0 1], and additional to A0 to compute the mesh points as A0 + [0 1], A0 + [19], A0 + [1 0], and A0 + [0–1]. The pattern search would calculate the objective function value for each mesh point and choose the one that is lesser than A0. The PS would then assign A1 to this position on the model. The primary mesh would be multiplied by 2 in the next iteration, which is the expansion factor. As a result, the mesh points for this step would be A1 + 2 * [0 1], A1 + 2 *[19], A1 + 2 * [1 0], and A1 + 2 * [0–1], with the method stopping when the termination requirement is met. If the objective functions of the mesh points do not improve, the initial point is reused. The contraction factor is 0.4, and the procedure continues to meet the termination indexes.
A splitting algorithm for simulation-based optimization problems with categorical variables
Published in Engineering Optimization, 2019
Zuzana Nedělková, Christoffer Cromvik, Peter Lindroth, Michael Patriksson, Ann-Brith Strömberg
A splitting algorithm to explore the multidimensional discrete search space of design points for the tyres selection problem as well as other simulation-based optimization problems with categorical variables is developed and presented. The splitting strategy used in the algorithm developed is inspired by that presented by Fuchs and Neumaier (2010a); it uses only the objective function evaluations and is therefore applicable to simulation-based optimization problems. The strategy exploits the structure of a convex relaxation of the discrete search space, represented by a minimum spanning tree among the edges of a complete graph defined on the design points (see Graham and Hell 1985). The use of this knowledge may have significant advantages, since the objective function typically depends more on the selection of the design point rather than on the values of the integer choices stemming from numbering of the design points and not representing any physical entity. The splitting strategy is complemented by a global underestimation of the objective function in order to determine approximate lower bounds along the search tree. The bounds are then used within a multilevel coordinate search (see Huyer and Neumaier 1999) to decide on which node of the search tree to split. A pattern search algorithm (see Audet and Dennis Jr 2004) is used to obtain a feasible solution from a relaxed solution and also to improve the current smallest objective value.