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binary programming formulations for the upper domination problem

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2023年第2期98卷 155-168页

作者： Burdett, Ryan Haythorpe, Michael Newcombe, Alex Flinders Univ S Australia South Rd Tonsley Pk SA 1284 Australia

We consider Upper Domination, the problem of finding the minimal dominating set of maximum cardinality. Very few exact algorithms have been described for solving Upper Domination. In particular, no binary programming formulations for Upper Domination have been described in literature, although such formulations have proved quite successful for other kinds of domination problems. We introduce two such binary programming formulations, and show that both can be improved with the addition of extra constraints which reduce the number of feasible solutions. We compare the performance of the formulations on various kinds of graphs, and demonstrate that (a) the additional constraints improve the performance of both formulations, and (b) the first formulation outperforms the second in most cases, although the second performs better for very sparse graphs. Also included is a short proof that the upper domination number of any generalized Petersen graph P(n, k) is equal to n.

关键词： Upper domination Minimal dominating set binary programming Formulation Graphs

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binary programming AND TEST DESIGN

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PSYCHOMETRIKA 1985年第4期50卷 411-420页

作者： THEUNISSEN, TJJM NATL INST EDUC MEASUREMENT CITOPOB 10346801 MG ARNHEMNETHERLANDS

An algorithmic approach to test design, using information functions, is presented. The approach uses a special branch of linear programming, i.e. binary programming. In addition, results of some benchmark problems are... 详细信息

关键词： linear programming binary programming information function test-design individualized testing item bank

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An efficient binary programming method for black-box optimization and its application in processor design

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Science China(Information Sciences) 2024年第12期67卷 140-156页

作者： Xiaoliang LV Qiaozhu ZHAI Jianchen HU Yuhang ZHU Jinhui LIU Xiaohong GUAN Faculty of Electronic and Information Engineering Xi'an Jiaotong University Department of Automation Tsinghua University

Optimizing the parameter settings in a large design space for the processor with limited simulation resources is a challenging task. The current black-box optimization algorithms for processor design space exploration(DSE) problems usually require a large amount of simulation resources for high-dimensional and discrete problems. Besides, the constraints handling techniques in these algorithms need to be improved. To address the issues, we propose an efficient binary integer programming(BIP) approach for the DSE of the processor with strictly guaranteed constraints. Our approach involves adopting the separability assumption to establish a surrogate objective function that is ordinal consistent, thus avoiding the complex non-linearity of the real objective function. Moreover, the design rules can be taken simply as constraints in BIP model to further reduce the design space. Thus, the efforts spent in the infeasible exploration space can be *** experimental results show that the proposed algorithm outperforms the state-of-the-art Bayesian optimization and evolutionary algorithms in terms of exploration efficiency, required simulation points and performance of the recommended points.

关键词： black-box optimization binary programming design space exploration processor design expensive simulation system

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Joint Empirical Mode Decomposition and Sparse binary programming for Underlying Trend Extraction

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2013年第10期62卷 2673-2682页

作者： Yang, Zhijing Ling, Bingo Wing-Kuen Bingham, Chris Guangdong Univ Technol Fac Comp Guangzhou 510006 Guangdong Peoples R China Guangdong Univ Technol Fac Informat Engn Guangzhou 510006 Guangdong Peoples R China Lincoln Univ Sch Engn Lincoln LN6 7TS England

This paper presents a novel methodology for extracting the underlying trends of signals via a joint empirical mode decomposition (EMD) and sparse binary programming approach. The EMD is applied to the signals and the corresponding intrinsic mode functions (IMFs) are obtained. The underlying trends of the signals are obtained by the sums of the IMFs where these IMFs are either selected or discarded. The total number of the selected IMFs is minimized subject to a specification on the maximum absolute differences between the denoised signals (signals obtained by discarding the first IMFs) and the underlying trends. Since the total number of the selected IMFs is minimized, the obtained solutions are sparse and only few IMFs are selected. The selected IMFs correspond to the components of the underlying trend of the signals. On the other hand, the L-infinity norm specification guarantees that the maximum absolute differences between the underlying trends and the denoised signals are bounded by an acceptable level. This forces the underlying trends to follow the global changes of the signals. As the IMFs are either selected or discarded, the coefficients are either zero or one. This problem is actually a sparse binary programming problem with an L-0 norm objective function subject to an L-infinity norm constraint. Nevertheless, the problem is nonconvex, nonsmooth, and NP hard. It requires an exhaustive search for solving the problem. However, the required computational effort is too heavy to be implemented practically. To address these difficulties, we approximate the L-0 norm objective function by the L-1 norm objective function, and the solution of the sparse binary programming problem is obtained by applying the zero and one quantization to the solution of the corresponding continuous-valued L-1 norm optimization problem. Since the isometry condition is satisfied and the number of the IMFs is small for most of practical signals, this approximation is valid and verified

关键词： binary programming empirical mode decomposition intrinsic mode function L-0 norm optimization L-1 norm optimization nonconvex optimization nonsmooth optimization NP hard combinational optimization sparse optimization underlying trend extraction

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Fast and accurate solution for the SCUC problem in large-scale power systems using adapted binary programming and enhanced dual neural network

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ENERGY CONVERSION AND MANAGEMENT 2014年 78卷 477-485页

作者： Shafie-khah, M. Moghaddam, M. P. Sheikh-El-Eslami, M. K. Catalao, J. P. S. Univ Beira Interior P-6201001 Covilha Portugal Tarbiat Modares Univ Tehran 14115111 Iran INESC ID P-1000029 Lisbon Portugal Univ Lisbon IST P-1049001 Lisbon Portugal

This paper presents a novel hybrid method for solving the security constrained unit commitment (SCUC) problem. The proposed formulation requires much less computation time in comparison with other methods while assuring the accuracy of the results. Furthermore, the framework provided here allows including an accurate description of warmth-dependent startup costs, valve point effects, multiple fuel costs, forbidden zones of operation, and AC load flow bounds. To solve the nonconvex problem, an adapted binary programming method and enhanced dual neural network model are utilized as optimization tools, and a procedure for AC power flow modeling is developed for including contingency/security issues, as new contributions to earlier studies. Unlike classical SCUC methods, the proposed method allows to simultaneously solve the unit commitment problem and comply with the network limits. In addition to conventional test systems, a real-world large-scale power system with 493 units has been used to fully validate the effectiveness of the novel hybrid method proposed. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： AC power flow binary programming Dual neural network Security constrained unit commitment

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A methodology to optimally site and design municipal solid waste transfer stations using binary programming

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RESOURCES CONSERVATION AND RECYCLING 2012年 60卷 89-98页

作者： Chatzouridis, Constantinos Komilis, Dimitrios Democritus Univ Thrace Dept Environm Engn Lab Solid & Hazardous Waste Management GR-67100 Xanthi Greece

Mathematical programming has been often used to optimize municipal solid waste management and transfer systems. The objective of this work was to develop a practical methodology to aid in the optimal design of a solid waste collection network in regions with well-specified boundaries. The objective function was a non-linear equation that minimized total collection cost. The cost comprised the capital and operating costs of: (i) the waste transfer stations, (ii) the waste collection vehicles, (iii) the semitrailers and tractors as well as the waste collection within a community, and the cost to haul the wastes to the transfer stations or to the landfills. The adjustable (decision) variables were binary variables that designated whether a path between two nodes is valid or not. binary variables were also used to designate whether a transfer station should be constructed or not. In this methodology, the waste production nodes and their waste production rates were specified. The locations of all candidate waste transfer stations were designated using two alternative GIS-based siting methodologies;the locations of the final nodes (landfills) were precisely specified too. The actual travel distances and times among all nodes were the main input variables. The model was developed in an Excel (R) spreadsheet and was applied to a Hellenic region that has 53 municipalities. The candidate transfer stations sited in the region were 47 and one or two landfills were present in the system. The optimal solution suggested that 47 and 6 municipalities should direct their wastes to 12 transfer stations and to 2 landfills, respectively. The 12 transfer stations should then transfer their wastes to their adjacent landfills. The optimal collection cost was (sic)42.4 t(-1). A sensitivity analysis concluded that fuel cost was the most sensitive parameter in the model. (C) 2011 Elsevier B.V. All rights reserved.

关键词： binary programming Collection Municipal solid wastes Mathematical optimization Waste transfer stations Cost minimization

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A robust design for a Colombian dairy cooperative's milk storage and refrigeration logistics system using binary programming

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2017年第PartC期183卷 710-720页

作者： Tordecilla-Madera, Rafael Polo, Andres Munoz, Dairo Gonzalez-Rodriguez, Leonardo Fdn Univ Agr Colombia Ind Engn Program Innovar Tecnol Res Grp Calle 170 54A-10 Bogota Colombia Univ La Sabana Fac Engn Logist Syst Res Grp Grp Invest Sistemas Logist Chia Colombia

This article describes a robust design for a milk storage and refrigeration logistics system for a dairy cooperative located in the Ubate region of Colombia using a binary programming model. Such design included cooling tank location, assigning producers to the tanks and calculating system capacity. This research was aimed at identifying the most robust and cost-efficient configuration (given the design's parameters). Perturbation parameters, robustness requirements and performance features were thus qualitatively and quantitatively identified;the perturbation parameters' impact on robustness requirements and performance features was also determined. A supply chain involves a variety of configurations, along with variations in milk supply (perturbation parameter). The most robust configuration and associated costs were thus identified through robustness-cost characterization and used for designing the dairy cooperative's logistical Storage and refrigeration system. A tactical plan was also drawn up for optimizing cooling tank use. Our main theoretical conclusion regarding this matter (depending on how robustness requirements and perturbation parameters are defined and calculated) suggested that the most robust system does not necessarily represent higher costs because the most robust configurations were in fact the least costly concerning high milk supply values.

关键词： Robustness Cost binary programming Milk cooling tanks Location

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On the use of binary programming for sensor scheduling

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2007年第6期55卷 2826-2839页

作者： Chhetri, Amit S. Morrell, Darryl Papandreou-Suppappola, Antonia Arizona State Univ Dept Elect Engn Tempe AZ 85287 USA Arizona State Univ Dept Engn Tempe AZ 85287 USA

In this paper, we propose two myopic sensor scheduling algorithms for target tracking scenarios in which there is a tradeoff between tracking performance and sensor-usage costs.. Specifically, we consider the problem of activating the lowest cost combination of at most L sensors that maintains a desired squared-error accuracy in the target's position estimate. For sensors that provide position information only, we develop a binary (0-1) mixed integer programming formulation for the scheduling problem and solve it using a linear programming relaxation-based branch-and-bound technique. For sensors that provide both position and velocity information, we pose the scheduling problem as a binary convex programming problem and solve it using the outer approximation algorithm. We apply our scheduling procedures in a network of sensors where the sensor-usage costs correspond to network energy consumption. Our simulation results demonstrate that scheduling using binary programming allows us to obtain optimal solutions to scheduling involving up to 50-70 sensors typically in the order of seconds.

关键词： binary programming resource management sensor scheduling target tracking

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A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2012年第12期92卷 1026-1043页

作者： Browne, P. A. Budd, C. Gould, N. I. M. Kim, H. A. Scott, J. A. Univ Bath Dept Math Sci Bath BA2 7AY Avon England STFC Rutherford Appleton Lab Numer Anal Grp Didcot OX11 0QX Oxon England Univ Bath Dept Mech Engn Bath BA2 7AY Avon England

We present a method for finding solutions of large-scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analytic expression for the derivative of the stress stiffness matrix with respect to the density of an element in the finite-element setting. Results are presented for a number of two-dimensional test *** (c) 2012 John Wiley & Sons, Ltd.

关键词： topology optimization buckling eigenvalue structural optimization binary programming

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binary programming for Allocation of Players in Soccer Competitions by a Canadian Sports Event Management Company 1

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29th International Joint Conference on Industrial Engineering and Operations Management, IJCIEOM 2023

作者： Santos, Leandro José Tranzola Moreira, Miguel Ângelo Lellis de Araújo Costa, Igor Pinheiro dos Santos, Marcos da Silva, Ricardo Franceli SP São Paulo Brazil Fluminense Federal University RJ Niterói Brazil Naval System Analysis Center RJ Rio de Janeiro Brazil Military Institute of Engineering RJ Rio de Janeiro Brazil FIA Business School SP São Paulo Brazil

ISBN: (数字)9783031470585

ISBN: (纸本)9783031470578

The resource allocation problem becomes more complex as resources and activities are added to the scenario as the possibility of combinations grows exponentially, since by adding only one resource or activity, the number of variables increases as a function of the product of available resources per activity. With that complexity factor in mind, this work develops a binary programming model with the objective of allowing a Canadian sports event management company to optimize the allocation of individually enrolled players in 14 different soccer competitions. The problem considers constraints such as players’ availability on different days of the week, teams mix, minimum and maximum number of players per team, player skill level and different competitions on the same day. The aim of the model was to maximize the number of competitions each player will participate in, and although not all competitions had enough players allocated to them, the result was satisfactory as all players were allocated to at least one competition. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： binary programming Competition Resource allocation Soccer

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