Comparison of partition evaluation measures in an adaptive partitioning algorithm for global optimization

Özdamar, Linet; Demirhan, Melek

doi:10.1016/s0165-0114(98)00364-9

Cited by 9 publications

(6 citation statements)

References 32 publications

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“…The FT proposed here is related to the fuzzy adaptive partitioning algorithm (FAPA) developed for global optimization [8], [9] and it differs from FAPA in two major aspects. These are 1) FT has to work with a limited number of data collected prior to its implementation, whereas FAPA goes on taking samples under the guidance of the partitioning/assessment process; and 2) FT uses an overlapping partitioning scheme rather than the nonoverlapping approach found in FAPA, and it analyzes the data multiple times with a systematically changing overlap rate to achieve the following three goals: a) To utilize the information extracted from the set of given data more efficiently, because data found in intersection areas of partitions contribute to more than one data sets simultaneously; b) to form and assess different data clusters resulting from applying varying overlap rates between neighboring partitions so that different classification topologies might be obtained for the site and unified; and c) to increase classification reliability by imposing multiple control before including a given block in the set of noncontaminated blocks.…”

Section: Ft Approachmentioning

confidence: 99%

Fuzzy Tessellation Approach for Environmental Site Characterization

Özdamar

Demirhan

2005

IEEE Trans. Syst., Man, Cybern. C

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Environmental site investigations are carried out prior to the reclamation of industrially contaminated sites. It is required to take samples and analyze the laboratory reports to find out the distribution of contaminants over the site. In this study, an algorithm based on fuzzy assessment and overlapped partitioning is proposed to identify the topology of polluted areas in a given industrial site. The primary objective is to locate contaminated zones accurately with sparse data in a preliminary investigation and the second is to reduce the size of the area that is resubjected to expensive sampling methods (such as deep drilling) in the detailed phase of the investigation. If these objectives are achieved, a considerable cost reduction occurs in the process of site characterization.

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Section: Ft Approachmentioning

confidence: 99%

Fuzzy Tessellation Approach for Environmental Site Characterization

Özdamar

Demirhan

2005

IEEE Trans. Syst., Man, Cybern. C

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“…Hansen and Jaumard, 1995; or in a heuristic manner (stochastic approaches, e.g. Ozdamar and Demirhan, 2000;Ozdamar and Demirhan, 2001). Deterministic partitioning algorithms can be classified under two major categories: algorithms based on interval methods (e.g., Moore and Ratschek, 1988) and algorithms based on certain a priori assumptions on functions, such as Lipschitz methods (e.g., Gourdin et al, 1994;Hansen and Jaumard, 1995;Pinter, 1988).…”

Section: Introductionmentioning

confidence: 99%

Global Optimization

2006

Nonconvex Optimization and Its Applications

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Fortran) compilers, spreadsheet-based modeling, algebraic modeling languages (with a focus on optimization), and integrated scientific-technical computing systems. Without going into details on any of these software systems, please consult e.g. the following references and the software products discussed therein.Optimization Technology Center (2005) also offer useful information regarding this point.The individual chapters of the present volume have been written with the objective of addressing both experts and non-experts in the specific application area discussed. Therefore the authors attempted to follow a "tutorial" style, providing sufficient background to the key issues, model formulation and solution approaches presented. Most chapters are strongly application-oriented, in accordance with the overall objectives of this book.We trust that our work will be of interest to researchers and practitioners in academia, research and consulting organizations, and industry. The book presents GO challenges and real-world case studies in sufficient detail, to enable graduate level classroom discussions and independent studies. The book can also be used in the framework of a practically motivated seminar or lecture series on nonlinear modeling and optimization.The contributing authors and myself welcome your comments and suggestions related to this volume. Thanks for your attention, and enjoy the book! References to PrefaceThis illustrative list of references includes books, software systems, and websites that are (mostly or at least partially) related to the practice of nonlinear systems modeling and global optimization, including software and applications. Many of the websites listed below offer extensive further information of relevance.Ali, M.M., Khompatraporn, Ch., and Zabinsky, Z.B. (2005) A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. GAMS/LGO nonlinear solver suite: key features, usage, and numerical performance. (Submitted for publication.) GAMS Solver Documentation Pages http://www.gams.eom/solvers/solvers.htm#LGO. Pinter, J.D. (2005) Nonlinear optimization in modeling environments: software implementations for compilers, spreadsheets, modeling languages, and integrated computing systems. In: Jeyakumar, V. and Rubinov, A.M., Eds.,

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“…Reviews and numerical comparisons of different adaptive partitioning methods can be found in Pintér (1992), and Pintér (1996) among many others and more recently inÖzdamar and Demirhan (2001).…”

Section: Adaptive Partitioning Methodsmentioning

confidence: 99%

“…A large class of global optimization algorithms have adopted Divide and Conquer (Partitioning) approaches. Partitioning approaches divide given domains into smaller sub-spaces whose potential of holding the global optimum is determined either reliably (deterministic approaches), such as Hansen and Jaumard (1995) and Pintér (1996); or in a heuristic manner (stochastic approaches), such asÖzdamar and Demirhan (2000Demirhan ( , 2001).…”

Section: Partitioning Approachesmentioning

confidence: 99%

Parallel global optimization with deterministic approaches

Wu¹

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Global optimization is important both in theory and practical applications. The objectives of the research conducted in this thesis are twofold. The first one is to construct methods which aim to reduce the effort needed to solve global optimization problems. The second objective is to investigate suitable parallel models for those methods to speed up the computation, which is especially important for time-consuming problems. Two partitioning approaches are proposed in this research for unconstrained and constrained problems, respectively. For unconstrained optimization, a new global optimization approach, TRIOPT (TRIangulated OPTimization), is proposed. TRIOPT is based on partitioning the feasible region D geometrically by triangulation so that search can be conducted in smaller subregions of interest. This consequently increases the reliability in locating the global optimum and reduces the number of function evaluations required. The partitions (simplices) are assessed by the aggregated entropies calculated from the transformed values of the vertices, which lead to a dynamic degree of parallel search in the feasible region D. A novelty in the search scheme is that once a partition narrows down to a small size, its vertices are eliminated from the available sample set. This change of global information triggers a re-calculation of transformed values and guides the search to new subregions. TRIOPT employs a Master/Slave architecture for parallel processing according to its algorithmic characteristics. The master processor controls the dynamic degree of parallelization, and the slave processors evaluate the samples. In constrained optimization, interval analysis is applied since it can conveniently check the feasibility of a certain search area rather than a single i

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Comparison of partition evaluation measures in an adaptive partitioning algorithm for global optimization

Cited by 9 publications

References 32 publications

Fuzzy Tessellation Approach for Environmental Site Characterization

Fuzzy Tessellation Approach for Environmental Site Characterization

Global Optimization

Parallel global optimization with deterministic approaches

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