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Packing unit spheres into the smallest sphere using VNS and NLP

COMPUTERS & OPERATIONS RESEARCH 2013年第2期40卷 603-615页

作者： M'Hallah, R. Alkandari, A. Mladenovic, N. Kuwait Univ Stat & Operat Res Dept Safat 13060 Kuwait Publ Author Appl Educ & Training Dept Appl Sci Safat 13092 Kuwait Brunel Univ Dept Math Sci Uxbridge UB8 3PH Middx England

This paper addresses the NP hard optimization problem of packing identical spheres of unit radii into the smallest sphere (PSS). It models PSS as a non-linear program (NIP) and approximately solves it using a hybrid heuristic which couples a variable neighborhood search (VNS) with a local search (LS). VNS serves as the diversification mechanism whereas LS acts as the intensification one. VNS investigates the neighborhood of a feasible local minimum u in search for the global minimum, where neighboring solutions are obtained by shaking one or more spheres of u and the size of the neighborhood is varied by changing the number of shaken spheres, the distance and the direction each sphere is moved. LS intensifies the search around a solution u by subjecting its neighbors to a sequential quadratic algorithm with non-monotone line search (as the NIP solver). The computational investigation highlights the role of LS and VNS in identifying (near) global optima, studies their sensitivity to initial solutions, and shows that the proposed hybrid heuristic provides more precise results than existing approaches. Most importantly, it provides computational evidence that the multiple-start strategy of non-linear programming solvers is not sufficient to solve PSS. Finally, it gives new upper bounds for 29 out of 48 benchmark instances of PSS. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Three-dimensional packing Unit-sphere packing non-linear programming Variable neighborhood search

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Stability Analysis of Uncertainty linear Systems Described by Fuzzy Characteristic Equations

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ASIAN JOURNAL OF CONTROL 2013年第1期15卷 193-202页

作者： Hallaji, Majid Zare, Assef Kamyad, Ali Vahidian Islamic Azad Univ Dept Elect Engn Neyshabur Branch Sama Coll Neyshabur Iran Islamic Azad Univ Dept Elect Engn Gonabad Branch Gonabad Iran Ferdowsi Univ Mashhad Dept Appl Math Fac Math Mashhad Iran Islamic Azad Univ Dept Elect Gonabad Branch Gonabad Iran

This paper uses Kharitonov's theorem to present a new idea for assessment of the stability of linear systems that are described by fuzzy differential equations, while system uncertainty is expressed as fuzzy convex sets for coefficients of the characteristic equation. The paper then deals with determination of stability margins and the design of classical robust controllers of fuzzy type for those systems. In each part, illustrative examples and simulation results are provided.

关键词： Fuzzy differential equations (FDE) Kharitonov's theory fuzzy convex sets non-linear programming

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Deterministic and stochastic global optimization techniques for planar covering with ellipses problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第1期224卷 23-40页

作者： Andretta, M. Birgin, E. G. Univ Sao Paulo Inst Math & Stat Dept Comp Sci BR-05508090 Sao Paulo Brazil Univ Sao Paulo Inst Math & Comp Sci Dept Appl Math & Stat BR-13566590 Sao Carlos SP Brazil

Problems of planar covering with ellipses are tackled in this work. Ellipses can have a fixed angle or each of them can be freely rotated. Deterministic global optimization methods are developed for both cases, while a stochastic version of the method is also proposed for large instances of the latter case. Numerical results show the effectiveness and efficiency of the proposed methods. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Global optimization non-linear programming Planar covering with ellipses Algorithms

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A column generation heuristic for congested facility location problem with clearing functions

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2013年第12期64卷 1780-1789页

作者： Kim, S. No Illinois Univ De Kalb IL 60115 USA

nonlinear clearing functions, an idea initially suggested to reflect congestion effects in production planning, are used to express throughput of facilities prone to congestion in a facility location problem where each demand site is served by exactly one facility. The traditional constant capacity constraint for a facility is replaced with the nonlinear clearing function. The resulting nonlinear integer problem is solved by a column generation heuristic in which initial columns for the restricted master problem are generated by known existing algorithms and additional columns by a previously developed dynamic programming algorithm. Computational experimentation in terms of dual gap and CPU time based on both randomly generated and published data sets show not only clear dominance of the column generation over a Lagrangian heuristic previously developed, but also the high quality of results from the suggested heuristic for large problems.

关键词： facility location non-linear programming integer programming congestion column generation

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Univariate parameterization for global optimization of mixed-integer polynomial problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第3期229卷 613-625页

作者： Teles, Joao P. Castro, Pedro M. Matos, Henrique A. Lab Nacl Energia & Geol Unidade Modelacao & Optimizacao Sistemas Energet P-1649038 Lisbon Portugal Inst Super Tecn DEQ Ctr Proc Quim P-1049001 Lisbon Portugal

This paper presents a new relaxation technique to globally optimize mixed-integer polynomial programming problems that arise in many engineering and management contexts. Using a bilinear term as the basic building block, the underlying idea involves the discretization of one of the variables up to a chosen accuracy level (Teles, J.P., Castro, P.M., Matos, H.A. (2013). Multiparametric disaggregation technique for global optimization of polynomial programming problems. J. Glob. Optim. 55, 227-251), by means of a radix-based numeric representation system, coupled with a residual variable to effectively make its domain continuous. Binary variables are added to the formulation to choose the appropriate digit for each position together with new sets of continuous variables and constraints leading to the transformation of the original mixed-integer non-linear problem into a larger one of the mixed-integer linear programming type. The new underestimation approach can be made as tight as desired and is shown capable of providing considerably better lower bounds than a widely used global optimization solver for a specific class of design problems involving bilinear terms. (c) 2013 Elsevier B.V. All rights reserved.

关键词： Global optimization non-linear programming Integer programming Mixed-integer non-linear programming

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AN EFFICIENT HYBRID LP-LP METHOD FOR THE OPTIMAL UTILIZATION OF CONFINED AQUIFERS

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IRRIGATION AND DRAINAGE 2013年第1期62卷 120-128页

作者： Khadem, M. Afshar, M. H. Iran Univ Sci & Technol Sch Civil Engn Tehran Iran Iran Univ Sci & Technol Envirohydroinformat Ctr Excellence Tehran Iran

This paper presents an efficient hybrid methodology for solution of the groundwater management problem. The problem to be addressed is the minimization of the pumping cost of a predefined number of wells of fixed position in a two-dimensional (2D) confined aquifer. The solution of the problem is defined by the pumping rate of the wells which satisfy downstream demand, the lower/upper bound on the pumping rates, and the upper bound on the water level drawdown in the wells. This problem is one of non-linear optimization which can be solved using conventional non-linear programming (NLP) and modern heuristic algorithms with their corresponding advantages and shortcomings. In the proposed method, the problem is formulated as one of optimization in terms of pumping rates and water level drawdown in the wells by embedding the discretized version of the differential equation governing the aquifer in the problem formulation. The resulting constrained non-linear optimization problem is then decomposed into two linear optimization problems with different sets of decision variables, namely pumping rates and water level drawdown. The newly formed linear problems are solved iteratively using a simplex method leading to a highly efficient hybrid method. The ability and efficiency of the proposed method are tested against three test examples and the results presented and compared to other methods. The results indicate the superiority of the proposed method over others available in the literature such as NLP and GA in both accuracy and computational effort. While the performance of the available methods is shown to deteriorate with the size of the problem, when the number of wells to be operated are increased, the proposed method is shown to be insensitive to problem size, offering a robust method for solving real-life groundwater management problems. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： groundwater optimization genetic algorithm linear programming non-linear programming decomposition

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Deterministic global optimization in ab-initio quantum chemistry

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第2期56卷 537-558页

作者： Janes, Pete P. Rendell, Alistair P. Australian Natl Univ Res Sch Comp Sci Canberra ACT 0200 Australia

A large number of problems in ab-initio quantum chemistry involve finding the global minimum of the total system energy. These problems are traditionally solved by numerical approaches equivalent to local optimization. While these approaches are relatively efficient, they do not provide guarantees of global optimality unless a starting point sufficiently close to the global minimum is known apriori. Due to the enormous amount of computational effort required to solve these problems, more mathematically rigorous alternatives have so far received very little attention. Taking the above issue into consideration, this paper explores the use of deterministic global optimization in the context of Hartree-Fock theory, an important mathematical model applied in many quantum chemistry methods. In particular, it presents a general purpose approach for generating linear relaxations for problems arising from Hartree-Fock theory. This was then implemented as an extension to the (Convex Over and Under ENvelopes for nonlinear Estimation) branch and bound mixed integer non-linear programs solver. Proof of concept calculations that simultaneously optimise the orbital coefficients and the location of the nuclei in closed-shell Hartree-Fock calculations are presented and discussed.

关键词： Convex relaxation Deterministic global optimization Branch and bound non-linear programming Quantum chemistry Hartree-Fock

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Design of discrete Dutch auctions with an uncertain number of bidders

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ANNALS OF OPERATIONS RESEARCH 2013年第1期211卷 255-272页

作者： Li, Zhen Kuo, Ching-Chung Middle Tennessee State Univ Jones Coll Business Dept Management & Mkt Murfreesboro TN 37132 USA Univ N Texas Coll Business Dept Management Denton TX 76203 USA

The focus of this paper is on Dutch auctions where the bidding prices are restricted to a finite set of values and the number of bidders follows a Poisson distribution. The goal is to determine what the discrete bid levels should be to maximize the auctioneer's expected revenue, which is the same as the average selling price of the object under consideration. We take a new approach to the problem by formulating the descending-price competitive bidding process as a nonlinear program. The optimal solution indicates that the interval between two successive bids should be wider as the Dutch auction progresses. Moreover, the auctioneer's maximum expected revenue increases with the number of bid levels to be set as well as the expected number of bidders. Numerical examples are provided to illustrate the key results from this study and their managerial implications are discussed.

关键词： Dutch auction Discrete bid Poisson arrival Revenue maximization non-linear programming

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CONSOLIDATED AUTOMATED SUPPORT SYSTEM (CASS) EFFICIENCY AND ALLOCATION COST IMPROVEMENT

CONSOLIDATED AUTOMATED SUPPORT SYSTEM (CASS) EFFICIENCY AND ...

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作者： James L. Rorer Luis F. Asifuinagomez Naval Postgraduate School

学位级别：硕士

In this research project, we provide a method in which we incorporated a nonlinear model to allocate consolidated automated support system (CASS) stations utilizing real demand. In reviewing available literature, we frame the allocation of CASS stations as a problem of discrete capacity allocation with stochastic demand, and note that similar problems exist in the allocation of other types of service capacity (e. g., hospital beds). We employed a nonlinear model to present a better method for allocation. Currently, NAVAIR PMA 260 uses an algebraic formula to determine CASS station allocation. The nonlinear model takes into account factors that the algebraic formula does not, such as aircraft readiness and CASS station utilization. With the model, we generated an optimized allocation of CASS stations based on average demand from aircraft maintenance action forms received at a Fleet Readiness Center over a given period of time. Then, we demonstrate that the optimized allocation can account for monthly, non- stationary demand inputs, as potentially seen in a fleet response plan. Compared to the current allocation of the Fleet Readiness Center analyzed, the optimized allocation improves CASS station utilization rates with a decreased overall number of CASS stations, without an adverse change in aircraft readiness.

关键词： Consolidated automated support system CASS eCASS non-linear programming resource allocation discrete stochastic capacity allocation queuing congestion utilization operational availability readiness

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Lower-bound limit analysis by using the EFG method and non-linear programming

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2008年第3期74卷 391-415页

作者： Chen, Shenshen Liu, Yinghua Cen, Zhangzhi Tsinghua Univ Dept Engn Mech Beijing 100084 Peoples R China

Intended to avoid the complicated computations of elasto-plastic incremental analysis, limit analysis is an appealing direct method for determining the load-carrying capacity of structures. On the basis of the static limit analysis theorem, a solution procedure for lower-bound limit analysis is presented firstly, making use of the element-free Galerkin (EFG) method rather than traditional numerical methods such as the finite element method and boundary element method. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration. The reduced-basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. The self-equilibrium stress field is expressed by a linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve these non-linear programming sub-problems and determine the maximal load amplifier. Numerical examples show that it is feasible and effective to solve the problems of limit analysis by using the EFG method and non-linear programming. Copyright (C) 2007 John Wiley & Sons, Ltd.

关键词： limit analysis EFG method self-equilibrium stress non-linear programming Complex method

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