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Reviewing extensions and solution methods of the planar Weber single facility location problem

COMPUTERS & OPERATIONS RESEARCH 2025年 173卷

作者： Church, Richard L. Drezner, Zvi Plastria, Frank Tamir, Arie Univ Calif Santa Barbara Dept Geog Santa Barbara CA 93106 USA Calif State Univ Fullerton Coll Business & Econ Fullerton CA 92834 USA Vrije Univ Brussel BUTO Dept Business Technol & Operat Brussels Belgium Tel Aviv Univ Sch Math Sci Tel Aviv Israel

One of the classic foundational constructs of Location Science was proposed by Alfred Weber in 1909. His construct involved finding the location for a single production facility which minimized the sum of weighted distances of transporting the needed raw materials from localized sources along with the sum of weighted distances in delivering the final product to one or more markets. The first objective of this paper is to review the major advancements in this simple classic single facility location problem and its variations. One can find in the literature a very large number of algorithms to solve the standard Weber problem. Some are iterative and others are finite even for geometric Euclidean and rectilinear spaces. Moreover, some schemes are efficient (theoretically) and others are practically quite fast. The second goal of this paper is to show that many extensions of the standard Weber problem can be solved by solving a polynomial number of standard Weber problems. This unifying result implies, in particular, that all these extensions are polynomially solvable since the standard Weber problem can be solved in polynomial time. In addition, with this unifying approach we solve some important planar non-convex Euclidean location problems in polynomial time.

关键词： Location analysis Weber problem solution algorithm Non-linear programming

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Current development and future prospects of multi-target assignment problem:A bibliometric analysis review

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Defence Technology(防务技术) 2025年第1期43卷 44-59页

作者： Shuangxi Liu Zehuai Lin Wei Huang Binbin Yan College of Aerospace Science and Engineering National University of Defense TechnologyChangsha410073China Hypersonic Technology Laboratory National University of Defense of TechnologyChangsha410073China School of Astronautics Northwestern Polytechnical UniversityXi'an710072China

The multi-target assignment(MTA)problem,a crucial challenge in command control,mission planning,and a fundamental research focus in military operations,has garnered significant attention over the *** studied across various domains such as land,sea,air,space,and electronics,the MTA problem has led to the emergence of numerous models and *** delve deeper into this field,this paper starts by conducting a bibliometric analysis on 463 Scopus database papers using CiteSpace *** analysis includes examining keyword clustering,co-occurrence,and burst,with visual representations of the *** this,the paper provides an overview of current classification and modeling techniques for addressing the MTA problem,distinguishing between static multi-target assignment(SMTA)and dynamic multi-target assignment(DMTA).Subsequently,existing solution algorithms for the MTA problem are reviewed,generally falling into three categories:exact algorithms,heuristic algorithms,and machine learning ***,a development framework is proposed based on the"HIGH"model(high-speed,integrated,great,harmonious)to guide future research and intelligent weapon system development concerning the MTA *** framework emphasizes application scenarios,modeling mechanisms,solution algorithms,and system efficiency to offer a roadmap for future exploration in this area.

关键词： Multi-target assignment Offensive and defensive confrontation Cooperative operation Modeling mechanism solution algorithm CiteSpace analysis

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An improved algorithm for solving the Weber location problem

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4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 2025年第1期23卷 53-63页

作者： Drezner, Zvi Calif State Univ Fullerton Coll Business & Econ Fullerton CA 92834 USA

In this note we propose an improved algorithm for the solution of the Weber problem which is the most fundamental problem in location analysis. It is used as a building block in many algorithms for solving more complicated location problems. The algorithm is very simple to implement and the idea behind it can inspire solution approaches to other optimization problems as well. Computational experiments demonstrated the superior performance of the proposed algorithm. Such an improvement will assist in the solution of more complicated models that apply the solution to Weber problem repeatedly many times as part of their solution algorithms.

关键词： Location analysis Weber problem solution algorithm Non-linear programming

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Efficient solution algorithms for thermomechanical contact problems based on a domain/boundary decomposition method

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INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2009年第6期44卷 610-622页

作者： Shin, Eui Sup Kim, Yong Uhn Jung, Sung Nam Chonbuk Natl Univ Dept Aerosp Engn Jeonju 561756 South Korea Konkuk Univ Dept Aerosp Engn Seoul 143701 South Korea

An efficient domain/boundary decomposition method is presented for fully coupled thermomechanical problems with contact boundaries. The whole domain is regarded as a union of subdomains, an interface, and contact interfaces. Penalized variational formulations are performed to connect the interface or contact interfaces with the neighboring subdomains that satisfy continuity constraints on the displacement and temperature fields. As a result, non-linear finite element computations due to the contact boundaries can be localized within a few subdomains or contact interfaces. Therefore, the computational efficiency can be enhanced considerably by devising suitable solution algorithms. A variety of numerical examples were tested to confirm the important features of the new algorithms presented. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Thermomechanical contact Domain/boundary decomposition Penalty method Finite element solution algorithm

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A COMPARISON OF DIFFERENT solution algorithmS FOR THE NUMERICAL ANALYSIS OF VEHICLE-BRIDGE INTERACTION

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2014年第2期14卷 1350065-1350081页

作者： Liu, K. Zhang, N. Xia, H. De Roeck, G. Beijing Normal Univ Acad Disaster Reduct & Emergency Management Beijing 100875 Peoples R China Katholieke Univ Leuven Dept Civil Engn B-3001 Louvain Belgium Beijing Jiaotong Univ Dept Civil Engn Beijing 100044 Peoples R China

The interaction between a bridge and a train moving on the bridge is a coupled dynamic problem. The equations of motion of the bridge and the vehicle are coupled by the time dependent contact forces. At each time step, the motion of the bridge influences the forces transferred to the vehicle and this, in turn, changes the forces acting on the bridge. In this paper, a comparison of three different time domain solution algorithms for the coupled equation of motion of the train-bridge system is presented. Guidelines are given for a good choice of the time step.

关键词： Train-bridge interaction solution algorithm time step

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IMPLICIT UPWIND solution algorithmS FOR 3-DIMENSIONAL UNSTRUCTURED MESHES

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AIAA JOURNAL 1993年第5期31卷 801-805页

作者： BATINA, JT NASA Langley Research Center Hampton Virginia 23681

The development of implicit upwind algorithms for the solution of the three-dimensional, time-dependent Euler equations on unstructured tetrahedral meshes is described. The implicit temporal discretization involves either a two-sweep Gauss-Seidel relaxation procedure, a two-sweep point-Jacobi relaxation procedure, or a single-sweep point-implicit procedure;the upwind spatial discretization is based on the flux-difference splitting of Roe. Detailed descriptions of the three implicit solution algorithms are given, and calculations for the Boeing 747 transport configuration are presented to demonstrate the algorithms. Advantages and disadvantages of the implicit algorithms are discussed. A steady-state solution for the 747 configuration, obtained at transonic flow conditions using a mesh of over 100,000 cells, required less than 1 h of CPU time on a Cray-2 computer, thus demonstrating the speed and robustness of the general capability.

关键词： solution algorithm Boeing 747 Primitive Variable Flow Conditions Aircraft Configurations Upwind Scheme Aerodynamic Simulation Pressure Coefficient Angle of Attack NASA Ames Research Center

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Development of an interval quadratic programming water quality management model and its solution algorithms

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JOURNAL OF CLEANER PRODUCTION 2020年 249卷 119319-000页

作者： Zhang, Qianqian Li, Zhong Chengdu Univ Informat Technol Sch Management Chengdu 610225 Peoples R China McMaster Univ Dept Civil Engn 1280 Main St West Hamilton ON L8S 4L7 Canada

Interval quadratic programming (IQP) is one of the most popular programming techniques for addressing the uncertainties associated with nonlinear environmental management problems. However, efficient algorithms for solving IQP problems in water quality management (WQM) have not been well studied. In this study, an IQP model is developed for WQM under uncertainty. Three solution algorithms, including a piecewise linear approximation (PLA) method, a derivative algorithm (DEA) and a duality-based algorithm (DUA) are proposed for solving the IQP-WQM problem. The developed model and the corresponding solution algorithms are applied to a hypothetic WQM problem to demonstrate their applicability. The results show the lower bounds of the total cost obtained by three algorithms have a relationship of f(DUA)(-) = f(DEA)(-) <= f(PLA)(-), while that of the upper bounds is f(DEA)(+) <= f(PLA)(+) <= f(DUA)(+). Moreover, the sensitivity analysis shows that no matter how the IQP-WQM model is solved, the model response from the three solution algorithms is consistent. The results indicate that all of the three algorithms can efficiently deal with quadratic programming problems under uncertainties in the format of intervals. Comparison among the three algorithms shows that DUA provides interval solutions with wider ranges than the other two methods, and it requires less computational efforts than DEA. It is also found that PLA is more flexible and might require lower computational efforts for large scale problems. This study can provide useful technical support for effective WQM. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Interval quadratic programming Piecewise linear approximation Derivative algorithm Duality-based algorithm Water quality management solution algorithm

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On the solution of convex bilevel optimization problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第3期63卷 685-703页

作者： Dempe, S. Franke, S. Tech Univ Bergakad Freiberg D-09596 Freiberg Germany

An algorithm is presented for solving bilevel optimization problems with fully convex lower level problems. Convergence to a local optimal solution is shown under certain weak assumptions. This algorithm uses the optimal value transformation of the problem. Transformation of the bilevel optimization problem using the Fritz-John necessary optimality conditions applied to the lower level problem is shown to exhibit almost the same difficulties for solving the problem as the use of the Karush-Kuhn-Tucker conditions.

关键词： Bilevel programming Mathematical programs with equilibrium constraints Optimal value transformation KKT-transformation solution algorithm

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SHOCK SENSITIVITY IN PARABOLIZED NAVIER-STOKES solution OF HIGH ANGLE-OF-ATTACK SUPERSONIC-FLOW

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AIAA JOURNAL 1990年第3期28卷 406-413页

作者： CLINE, DD CAREY, GF UNIV TEXAS DPT AEROSP ENGN & MECH ENGNAUSTINTX 78712

Previous investigations with PNS/shock-fitting algorithms suggest that the lee-side shock profile is overly sensitive to the initial data when the angle of attack becomes large. The nature of this sensitivity is identified in the present work through an eigenvalue analysis of the coefficient matrices of the associated Euler system. These eigenvalues are evaluated along the evolving shock boundary and determine the relative amount of local numerical dissipation in the marching scheme. A significant disparity in the magnitude of the eigenvalues implies highly nonuniform damping of numerical errors along the shock boundary. Using eigenvalue estimates to deduce the PNS stepsize adaptively, and accounting for disparity in the eigenvalues, yields improved predictions of high angle-of-attack supersonic flow as demonstrated in the supporting numerical studies. Shock-profile anomalies encountered by previous investigators can therefore be attributed to an increase in the sensitivity of the PNS solution to the initial data as angle of attack is increased. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Angle of Attack Flow Conditions Bow Shock Freestream Conditions Rankine Hugoniot Relation Isotherms solution algorithm Viscosity Navier Stokes Equations Hypersonic Wind Tunnels

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Adaptive finite element solution of compressible turbulent flows

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AIAA JOURNAL 1998年第12期36卷 2187-2194页

作者： Ilinca, F Pelletier, D Ignat, L Natl Res Council Canada Inst Ind Mat Boucherville PQ Canada Ecole Polytech Dept Mech Engn Montreal PQ H3C 3A7 Canada

An adaptive finite element method for solving compressible turbulent Bows up to transonic regime is presented. Pressure-based methods previously developed for laminar compressible Bows and turbulent incompressible flows are combined to solve compressible turbulent Bows. Turbulence is incorporated via the k-epsilon model. The algorithm uses the logarithms of k and epsilon as computational variables to preserve positivity. solutions are obtained in primitive variables using quadratic finite elements on unstructured grids. The error is estimated by a local projection method. The solution algorithm and error estimation are validated on problems with known analytical solutions. The method is then applied to compressible subsonic and transonic Bows and predictions are compared with experimental measurements.

关键词： Transonic Flow Finite Element solution Compressibility Reynolds Averaged Navier Stokes Aerodynamics Turbulence Kinetic Energy solution algorithm Shear Layers Turbulence Models Computing

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