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IMPROVED LIPSCHITZ boundS WITH THE FIRST NORM FOR FUNCTION VALUES OVER MULTIDIMENSIONAL SIMPLEX

MATHEMATICAL MODELLING AND ANALYSIS 2008年第4期13卷 553-563页

作者： Paulavicius, R. Zilinskas, J. Inst Math & Informat LT-08663 Vilnius Lithuania

A branch and bound algorithm for global optimization is proposed, where the maximum of an tipper bounding function based on Lipschitz condition and the first norm over a simplex is used as the upper bound of function. fit this case the graph of bounding function is intersection of n-dimensional pyramids and its maximum point. is found solving a system of linear equations. The efficiency of the proposed global optimization algorithm is evaluated experimentally.

关键词： global optimization branch and bound algorithms Lipschitz optimization the first norm

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Selection of optimal feed trays in a closed-loop system of distillation columns

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THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING 2008年第4期42卷 386-397页

作者： Ostrovskii, G. M. Ziyatdinov, N. N. Lapteva, T. V. Ryjov, D. A. Karpov Res Inst Phys Chem Moscow 103064 Russia Kazan State Technol Univ Kazan 420015 Tatarstan Russia

A new approach is suggested to solve the problem of discrete-continuous optimization of a distillation column system involving both continuous regime search variables and discrete variables (feed tray numbers). The approach is based on the simultaneous use of the branch-and-bound algorithm and the structural parameter method. The efficiency of this approach is demonstrated by solving the problem of discrete-continuous optimization of a system for separating the ethylene-propane fraction in ethylene production.

关键词： Concurrency Structural parameter Closed loop systems ethylene production feed table discrete transforms branch and bound algorithms Distillation columns Induction loop systems

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New dominance rules and exploration strategies for the 1|r _i |aU _i scheduling problem

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2012年第3期51卷 1253-1274页

作者： Kao, Gio K. Sewell, Edward C. Jacobson, Sheldon H. Hall, Shane N. Univ Illinois Dept Comp Sci Urbana IL 61801 USA So Illinois Univ Dept Math & Stat Edwardsville IL 62026 USA USAF Scott AFB IL 62225 USA

The paper proposes a new exact approach, based on a branch, bound, and Remember (BB&R) algorithm that uses the Cyclic Best First Search (CBFS) strategy, for the 1|r (i) |aU (i) scheduling problem, a single machine scheduling problem, where the objective is to find a schedule with the minimum number of tardy jobs. The search space is reduced using new and improved dominance properties and tighter upper bounds, based on a new dynamic programming algorithm. Computational results establish the effectiveness of the BB&R algorithm with CBFS for a broad spectrum of problem instances. In particular, this algorithm was able to solve all problems instances, up to 300 jobs, while existing best known algorithms only solve problems instances up to 200 jobs. Furthermore, the BB&R algorithm with CBFS runs one to two orders of magnitude faster than the current best known algorithm on comparable instances.

关键词： branch and bound algorithms Scheduling theory and algorithms Dynamic programming

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Global optimization techniques for solving the general quadratic integer programming problem

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 1998年第2期10卷 149-163页

作者： Thoai, NV Univ Trier Dept Math D-54286 Trier Germany

We consider the problem of minimizing a general quadratic function over a polytope in the n-dimensional space with integrality restrictions on all of the variables. (This class of problems contains, e.g., the quadratic 0-1 program as a special case.) A finite branch and bound algorithm is established, in which the branching procedure is the so-called "integral rectangular partition", and the bound estimation is performed by solving a concave programming problem with a special structure. Three methods for solving this special concave program are proposed.

关键词： quadratic integer programming branch and bound algorithms concave minimization global optimization

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NP-StructurePredictor: Prediction of Unknown Natural Products in Plant Mixtures

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JOURNAL OF CHEMICAL INFORMATION AND MODELING 2017年第12期57卷 3138-3148页

作者： Harn, Yeu-Chern Su, Bo-Han Ku, Yuan-Ling Lin, Olivia A. Chou, Cheng-Fu Tseng, Y. Jane Natl Taiwan Univ Grad Inst Networking & Multimedia 1 Roosevelt Rd Sect 4 Taipei 10617 Taiwan NTU Ctr Genom Med Metabolom Core Lab 7F2 Syujhou Rd Taipei 10055 Taiwan Natl Taiwan Univ Dept Comp Sci & Informat Engn 1 Roosevelt Rd Sect 4 Taipei 10617 Taiwan Med & Pharmaceut Ind Technol & Dev Ctr 7F9 Wuquan Rd Taipei 24886 Taiwan Natl Taiwan Univ Grad Inst Biomed Elect & Bioinformat 1 Roosevelt Rd Sect 4 Taipei 10617 Taiwan Natl Taiwan Univ Drug Res Ctr Coll Med 1 Jen Ai Rd Sect 1 Taipei 10051 Taiwan

Identification of the individual chemical constituents of a mixture, especially solutions extracted from medicinal plants, is a time-consuming task. The identification results are often limited by challenges such as the development of separation methods and the availability of known reference standards. A novel structure elucidation system, NP-StructurePredictor, is presented and used to accelerate the process of identifying chemical structures in a mixture based on a branch and bound algorithm combined with a large collection of natural product databases. NP-StracturePredictor requires only targeted molecular weights calculated from a list of m/z values from liquid chromatography-mass spectrometry (LC-MS) experiments as input information to predict the chemical structures of individual components matching the weights in a mixture. NP-StructurePredictor also provides the predicted structures with statistically calculated probabilities so that the most likely chemical structures of the natural products and their analogs can be proposed accordingly. Four data sets consisting of different Chinese herbs with mixtures containing known compounds were selected for validation studies, and all their components were correctly identified and highly predicted using NP-StructurePredictor. NP-StructurePredictor demonstrated its applicability for predicting the chemical structures of novel compounds by returning highly accurate results from four different validation case studies.

关键词： highly accurate branch and bound algorithms Natural products chemical structure mixtures Reference Standards Chemical composition chemical compounds validation study Plants, Medicinal Molecular weights Analog Dataset

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Assessment of a non-adaptive deterministic global optimization algorithm for problems with low-dimensional non-convex subspaces

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OPTIMIZATION METHODS & SOFTWARE 2014年第2期29卷 430-441页

作者： Kearfott, Ralph Baker Castille, Jessie M. Tyagi, Gaurav Univ Louisiana Lafayette Dept Math Lafayette LA 70504 USA

The optimum and at least one optimizing point for convex nonlinear programs can be approximated well by the solution to a linear program (a fact long used in branch and bound algorithms). In more general problems, we can identify subspaces of non-convex variables' such that, if these variables have sufficiently small ranges, the optimum and at least one optimizing point can be approximated well by the solution of a single linear program. If these subspaces are low-dimensional, this suggests subdividing the variables in the subspace a priori, then producing and solving a fixed, known number of linear programs to obtain an approximation to the solution. The total amount of computation is much more predictable than that required to complete a branch and bound algorithm, and the scheme is embarrassingly parallel', with little need for either communication or load balancing. We compare such a non-adaptive scheme experimentally to our GlobSol branch and bound implementation, on those problems from the COCONUT project Lib1 test set with non-convex subspaces of dimension four or less, and we discuss potential alterations to both the non-adaptive scheme and our branch and bound process that might change the scope of applicability.

关键词： non-convex optimization branch and bound algorithms linear relaxations

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Solving sum-of-ratios fractional programs using efficient points

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OPTIMIZATION 2001年第5-6期49卷 447-466页

作者： Dür, M Horst, R Van Thoai, N Univ Trier Dept Math D-54286 Trier Germany Vienna Univ Econ Dept Stat A-1090 Vienna Austria

Constrained maximization of a sum of p > 1 ratios is a difficult nonconvex optimization problem (even if all functions involved are linear) with many applications in management sciences. In this paper, we first give a brief introductory survey of this problem. Then we propose a general branch-and-bound algorithm which uses rectangular partitions in the Euclidean space of dimension p. Theoretically, this algorithm is applicable under very general assumptions. Practically, we give an efficient implementation for affine fractions. Here the bounding procedures use dual constructions and the calculation of efficient points of a corresponding multiple-objective optimization problem. Finally, we present some promising numerical results.

关键词： sum-of-ratios fractional programs global optimization efficient points branch and bound algorithms

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GROUPED VARIABLE SELECTION WITH DISCRETE OPTIMIZATION: COMPUTATIONAL AND STATISTICAL PERSPECTIVES

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ANNALS OF STATISTICS 2023年第1期51卷 1-32页

作者： Hazimeh, Hussein Mazumder, Rahul Radchenko, Peter Google Res Mountain View CA 94043 USA MIT Sloan Sch Management 77 Massachusetts Ave Cambridge MA 02139 USA Univ Sydney Univ Sydney Business Sch Sydney NSW Australia

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on optimal solutions for the l(0)-regularized formulation, a problem that is relatively unexplored due to computational challenges. Our methodol-ogy covers both high-dimensional linear regression and nonparametric sparse additive modeling with smooth components. Our algorithmic framework con-sists of approximate and exact algorithms. The approximate algorithms are based on coordinate descent and local search, with runtimes comparable to popular sparse learning algorithms. Our exact algorithm is based on a stan-dalone branch-and-bound (BnB) framework, which can solve the associated mixed integer programming (MIP) problem to certified optimality. By ex-ploiting the problem structure, our custom BnB algorithm can solve to opti-mality problem instances with 5 x 10(6) features and 103 observations in min-utes to hours-over 1000 times larger than what is currently possible using state-of-the-art commercial MIP solvers. We also explore statistical proper-ties of the l(0)-based estimators. We demonstrate, theoretically and empiri-cally, that our proposed estimators have an edge over popular group-sparse estimators in terms of statistical performance in various regimes. We provide an open source implementation of our proposed framework.

关键词： Group variable selection sparsity nonparametric additive models l(0) regularization mixed integer programming branch and bound algorithms

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ON THE APPLICATION OF FUZZY-SETS THEORY TO THE OPTIMAL FLOOD-CONTROL PROBLEM ARISING IN WATER-RESOURCES SYSTEMS

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FUZZY SETS AND SYSTEMS 1992年第2期48卷 155-172页

作者： ESOGBUE, AO THEOLOGIDU, M GUO, KJ School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta GA 30332 USA

We first survey the application of fuzzy sets theory to various problems occurring in water resources systems. The problem of optimal flood control planning by an appropriate integration of structural and non-structural measures with the objective of optimizing the flood damage reduction due to recurrent floods is modeled via fuzzy sets methodologies. A two level optimization model appropriate for planning decisions first on a regional or local level and then on a national level is proposed. A third phase involving coordination is appended. In particular, a fuzzy optimization model involving an adroit combination of fuzzy dynamic programming-type reasoning and a branch and bound-type search procedure is offered as a more utilitarian approach than its crisp equivalent. The performance of the algorithm is illustrated with an example.

关键词： FUZZY SETS MODELING FUZZY DYNAMIC PROGRAMMING branch and bound algorithms FLOOD CONTROL WATER RESOURCES SYSTEMS PLANNING

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EXPERIMENTAL COMPARISON OF algorithms FOR THE PROBLEM OF THE MAXIMUM SET OF PAIRWISE INCOMPARABLE VERTICES IN A DIGRAPH

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CYBERNETICS AND SYSTEMS ANALYSIS 1992年第5期28卷 788-791页

作者： VOITISHIN, YV

Two branch-and-bound algorithms are analyzed for the problem of the maximum set of pairwise incomparable vertices in a digraph with additional constraints.

关键词： directed graphs Set (Psychology) Pairwise algorithms vertex head solidification redundant constraint set branch and bound algorithms Set

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