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第一届最优化与系统生物学国际研讨会

作者： Wei-Xiang Wang You-Lin Shang Lian-Sheng Zhang Department of Mathematics Shanghai University Department of Mathematics Henan University of Science and Technology Department of Applied Mathematics Tongji University

We introduce a new T-F function for solving discrete general minimization problems with a general function over box-constrained domain. A T-F function is constructed at a local minimizer of the objective function such that it achieves local maximum at the current solution. Moreover, a local minimizer of the T-F function leads to a new solution to the original problem with lower objective function value. Iteration follows in this manner to reach a global minimizer. Promising computational results are included and show the efficiency of the T-F function method.

关键词： nonlinear integer programming global optimization T-F function method local minimizer global minimizer.

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nonlinear integer BILEVEL programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1994年第3期72卷 574-587页

作者： JAN, RH CHERN, MS NATL CHIAO TUNG UNIV DEPT COMP & INFORMAT SCIHSINCHU 30050TAIWAN NATL TSING HUA UNIV DEPT IND ENGNHSINCHU 30043TAIWAN

In many decentralized organizations, resource planning with sequential decision making can be formulated as a multi-level programming problem. In such cases, the decision variables are partitioned among the decision makers. Each of the decision makers optimizes his/her own objective function. This paper presents an algorithm using parametric analysis to solve a typical kind of nonlinear integer multilevel programming problems, called separable integer monotone bilevel programming (SIMBP), and then extends the algorithm for solving a parametric SIMBP problem. A numerical example with application of reliability optimization is given to illustrate the solution method.

关键词： MULTILEVEL programming nonlinear integer programming PARAMETRIC programming

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Generalized nonlinear Lagrangian formulation for bounded integer programming

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JOURNAL OF GLOBAL OPTIMIZATION 2005年第2期33卷 257-272页

作者： Xu, YF Liu, CL Li, D Fudan Univ Sch Management Shanghai 200433 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

Several nonlinear Lagrangian formulations have been recently proposed for bounded integer programming problems. While possessing an asymptotic strong duality property, these formulations offer a success guarantee for the identification of an optimal primal solution via a dual search. Investigating common features of nonlinear Lagrangian formulations in constructing a nonlinear support for nonconvex piecewise constant perturbation function, this paper proposes a generalized nonlinear Lagrangian formulation of which many existing nonlinear Lagrangian formulations become special cases.

关键词： duality gap integer programming Lagrangian relaxation nonlinear integer programming nonlinear Lagrangian formulation

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Solving a class of two-stage stochastic nonlinear integer programs using value functions

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JOURNAL OF GLOBAL OPTIMIZATION 2025年第1期91卷 129-153页

作者： Zhang, Junlong Oezaltin, Osman Y. Trapp, Andrew C. Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China North Carolina State Univ Edward P Fitts Dept Ind & Syst Engn Raleigh NC 27695 USA Worcester Polytech Inst WPI Business Sch Worcester MA 01609 USA

We propose a level-set characterization of the value function of a class of nonlinear integer programs with finite domain. We study the theoretical properties of this characterization and show the equivalence between the set of level-set minimal vectors and a set of non-dominated right-hand side vectors. We use these properties to develop a solution approach for two-stage nonconvex integer programs with stochastic right-hand sides. The proposed approach can solve problems with pure integer variables in both stages. We demonstrate the effectiveness of the proposed approach using a nonlinear generalized assignment problem with uncertain capacity. We also conduct computational experiments using two-stage quadratically-constrained quadratic integer programs with stochastic right-hand sides. The proposed value function-based approach can solve instances whose extensive forms are among the largest stochastic quadratic integer programs solved in the literature with respect to the number of rows and variables in extensive form, and with considerably more rows.

关键词： nonlinear integer programming Value function Stochastic programming Generalized assignment problem

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An efficient algorithm for real-time network reconfiguration in large scale unbalanced distribution systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 1996年第1期11卷 511-517页

作者： Wang, JC Chiang, HD Darling, GR NEW YORK STATE ELECT & GAS CORP ELECT DISTRIBUT ENGN & PLANNING DEPTBINGHAMTONNY 13902

Real-time applications demand fast computation, this paper proposes an efficient algorithm for real-time network reconfiguration on large unbalanced distribution networks. A novel formulation of the network reconfiguration to achieve loss minimization and load balancing is given. To reduce computational requirements for the solution algorithm, well justified power how and loss reduction formulas in terms of the on/off status of network switches are proposed for efficient system updating. The algorithm relies only on a few full power flow studies based on system states attained by explicit expressions using backward-forward sweeps for efficient computation of system's states at the critical system operating points. The solution algorithm runs in an amount of time linearly proportional to the number of tie switches and the number of sectionalizing switches in the system. The solution algorithm has been implemented into a software package and tested on unbalanced distribution systems including a system with 292-buses, 76-laterals, 7 transformers, 45 switches and 255 line sections under diverse system conditions.

关键词： network reconfiguration real-time applications loss formula nonlinear integer programming unbalanced distribution systems large scale systems

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A computational study of a nonlinear minsum facility location problem

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COMPUTERS & OPERATIONS RESEARCH 2012年第11期39卷 2625-2633页

作者： Carrizosa, Emilio Ushakov, Anton Vasilyev, Igor Russian Acad Sci Siberian Branch Inst Syst Dynam & Control Theory Irkutsk 664033 Russia Univ Seville Inst Matemat E-41012 Seville Spain

A discrete location problem with nonlinear objective is addressed. A set of p plants is to be open to serve a given set of clients. Together with the locations, the number p of facilities is also a decision variable. The objective is to minimize the total cost, represented as the transportation cost between clients and plants, plus an increasing nonlinear function of p. Two Lagrangean relaxations are considered to derive lower bounds. Dual information is also used to design a core heuristic. Computational results are given, showing that nearly optimal solutions are obtained in short running times. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： p-median problem Lagrangean relaxation Core heuristic nonlinear integer programming

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A cut-based algorithm for the nonlinear dual of the minimum cost network flow problem

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ALGORITHMICA 2004年第3期39卷 189-208页

作者： Ahuja, RK Hochbaum, DS Orlin, JB Univ Florida Gainesville FL 32611 USA Univ Calif Berkeley Ind Engn & Operat Res Berkeley CA 94720 USA Univ Calif Berkeley Walter A Haas Sch Business Berkeley CA 94720 USA MIT Sloan Sch Management Cambridge MA 02139 USA

We consider a convex, or nonlinear. separable minimization problem with constraints that are 44 dual to the minimum cost network flow problem. We show how to reduce this problem to a polynomial number of minimum s.t-cut problems. The solution of the reduced problem utilizes the technique for solving integer programs on monotone inequalities in three variables, and a so-called proximity-scaling technique that reduces a convex problem to its linear objective counterpart. The problem is solved in this case in a logarithmic number 14 of calls. O(log U). to a minimum cut procedure, where U is the range of the variables. For a convex problem on n variables the minimum cut is solved on a graph with O(n(2)) nodes. Among the consequences of this result is a new cut-based scaling algorithm for the minimum cost network flow problem. When the objective function is an arbitrary nonlinear function we demonstrate that this constrained problem is solved in pseudopolynomial time by applying a minimum cut procedure to a graph on O(nU) nodes.

关键词： nonlinear integer programming convex integer programming total unimodularity minimum cut network flow

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Discrete mass and stiffness modifications for the inverse eigenstructure assignment in vibrating systems: Theory and experimental validation

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2012年第1期64卷 211-220页

作者： Ouyang, H. Richiedei, D. Trevisani, A. Zanardo, G. Univ Padua Dept Management & Engn DTG I-36100 Vicenza Italy Univ Liverpool Sch Engn Liverpool L69 3GH Merseyside England

The inverse eigenstructure assignment in structural dynamics and control aims at determining the mass and stiffness parameters to ensure the desired dynamic behavior expressed in terms of the prescribed eigenstructure. Several methods have been developed for the solution of this problem in the past. However, in the techniques proposed so far, all the design variables are assumed to be continuous. In practice, some design variables can only be changed through discrete modifications since either standard mass modules or springs are available. The determination of the discrete optimal solution of the structural modification problem cannot be performed by simply rounding the continuous optimal solution to the "nearest" integer, since rounded solutions can be considerably far from the optimality. On the other hand, the total enumeration as a solution method is infeasible for medium and large scale problems. To overcome this limitation, in this work, the eigenstructure assignment is formulated firstly as an inverse eigenvalue problem within the frame of constrained nonlinear integer programming, and then is solved by means of a partial enumeration technique with a reduced number of iterations. The experimental validation of the method on a five-degree-of-freedom lumped-parameter rig demonstrates its capability to compute effective modifications meeting the prescribed requirements and satisfying all the constraints. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Modal optimization Vibrating system design Inverse eigenvalue problem nonlinear integer programming

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An adaptive multimeme algorithm for designing HIV multidrug therapies

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2007年第2期4卷 264-278页

作者： Neri, Ferrante Toivanen, Jari Cascella, Giuseppe Leonardo Ong, Yew-Soon Agora Univ Dept Math Informat Technol FI-40014 Jyvaskyla Finland Politecn Bari Dipartimento Elettrotecn & Elettron I-70125 Bari Italy Nanyang Technol Univ Sch Comp Engn Singapore 639798 Singapore

This paper proposes a period representation for modeling the multidrug HIV therapies and an Adaptive Multimeme Algorithm (AMmA) for designing the optimal therapy. The period representation offers benefits in terms of flexibility and reduction in dimensionality compared to the binary representation. The AMmA is a memetic algorithm which employs a list of three local searchers adaptively activated by an evolutionary framework. These local searchers, having different features according to the exploration logic and the pivot rule, have the role of exploring the decision space from different and complementary perspectives and, thus, assisting the standard evolutionary operators in the optimization process. Furthermore, the AMmA makes use of an adaptation which dynamically sets the algorithmic parameters in order to prevent stagnation and premature convergence. The numerical results demonstrate that the application of the proposed algorithm leads to very efficient medication schedules which quickly stimulate a strong immune response to HIV. The earlier termination of the medication schedule leads to lesser unpleasant side effects for the patient due to strong antiretroviral therapy. A numerical comparison shows that the AMmA is more efficient than three popular metaheuristics. Finally, a statistical test based on the calculation of the tolerance interval confirms the superiority of the AMmA compared to the other methods for the problem under study.

关键词： HIV therapy design memetic algorithms adaptive algorithms nonlinear integer programming

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A solution method for optimal weight design problem of herical spring using genetic algorithms

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COMPUTERS & INDUSTRIAL ENGINEERING 1997年第1-2期33卷 71-76页

作者： Yokota, T Taguchi, T Gen, M Department of Industrial and Systems Engineering Ashikaga Institute of Technology Ashikaga 326 Japan

In this paper, we formulate an optimal weight design problem of herical spring for a constrained allowable shearing stress, number of active coils and coil's mean diameter as a nonlinear integer programming(NIP) problem and solve it directly by keeping the nonlinear constraint by using an improved genetic algorithm (GA). We discuss the efficency of the propose method. (C) 1997 Elsevier Science Ltd.

关键词： herical spring design problem nonlinear integer programming genetic algorithm

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