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non-linear integer programming - SENSITIVITY ANALYSIS FOR BRANCH AND BOUND

OPERATIONS RESEARCH LETTERS 1987年第6期6卷 269-274页

作者： SKORINKAPOV, J GRANOT, F Faculty of Commerce and Business Administration The University of British Columbia 2053 Main Hall Vancouver B.C. Canada V6T 1Y8

We consider in this paper the non-linear integer programming problem with varying right hand side and objective function coefficients. We establish what additional information to keep in the implicit enumeration tree, when solving the original problem, in order to provide us with bounds on the optimal value of a perturbed problem. The results obtained are extensions of the results given by Schrage and Wolsey [10] for linear integer programs.

关键词： non-linear integer programming sensitivity analysis brand and bound

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non-linear integer programming by Darwin and Boltzmann mixed strategy

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1998年第1期105卷 224-235页

作者： Tian, P Ma, J Zhang, DM City Univ Hong Kong Dept Informat Syst Kowloon Hong Kong Shanghai Jiao Tong Univ Dept Comp Sci & Engn Shanghai 200030 Peoples R China

non-linear integer programming (NIP) is a NP-complete problem with extensive theoretical and practical backgrounds. Based on our proposed Darwin and Boltzmann mixed strategy, this paper presents a general stochastic iterative algorithm for the NIP problems. The algorithm synthesizes the advantages of the Darwin strategy and the Boltzmann annealing strategy. It converges asymptotically to the global optimums and has shown to be polynomial in complexity. The experimental evaluations also show that the proposed algorithm is more efficient than the simulated annealing algorithm. (C) 1998 Elsevier Science B.V.

关键词： optimization non-linear integer programming Darwin and Boltzmann mixed strategy global convergence polynomial algorithm

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A novel optimal configuration of sensor and actuator using a non-linear integer programming genetic algorithm for active vibration control

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JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES 2017年第15期28卷 2074-2081页

作者： Zhang, Chunyou Wang, Lihua Wu, Xiaoqiang Gao, Weijin Inner Mongolia Univ Nationalities Coll Mech Engn Tongliao Peoples R China Beihang Univ Dept Automat Sci & Elect Engn 37 Xueyuan Rd Beijing 100191 Peoples R China

Due to widespread applications of a large number of flexible structures, to obtain the best dynamic control performance of a system, optimal locations of the actuators and sensors are necessary to be determined. This article proposes a novel optimal criterion for the actuators or sensors ensuring good controllability or observability of a structure, and also considering the remaining modes to control the spillover effect. Based on the proposed optimization criteria, a non-linear integer programming genetic algorithm is employed to achieve the optimal configurations. Active vibration control is investigated for a cantilever plate with the actuators in optimal positions to suppress the specified modes utilizing linear quadratic regulator controller. Several simulation results validate the efficiency and feasibility of the proposed optimal criteria.

关键词： flexible structures optimization criteria non-linear integer programming active vibration control

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Integrated analytical hierarch process and mathematical programming to supplier selection problem with quantity discount

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APPLIED MATHEMATICAL MODELLING 2009年第3期33卷 1417-1429页

作者： Kokangul, Ali Susuz, Zeynep Cukurova Univ Dept Ind Engn TR-01330 Adana Turkey Alize Design & Graph Adana Turkey

In this article an integration of analytical hierarchy process and non-linear integer and multi-objective programming under some constraints such as quantity discounts, capacity, and budget is applied to determine the best suppliers and to place the optimal order quantities among them. This integration-based multi-criteria decision making methodology takes into account both qualitative and quantitative factors in supplier selection. While the analytical hierarchy process matches item characteristics with supplier characteristics, non-linear integer programming model analytically determines the best suppliers and the optimal order quantities among the determined suppliers. The objectives of the mathematical models constructed are maximizing the total value of purchase (TVP), minimizing the total cost of purchase (TCP) or maximizing TVP and minimizing TCP simultaneously. In addition, several "what if" scenarios are facilitated and the quality of the resulting models is evaluated on real-life data. (C) 2008 Elsevier Inc. All rights reserved.

关键词： Supplier selection Discounted cost AHP non-linear integer programming

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The multi-hour service system design problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第3期128卷 625-638页

作者： Amiri, A Oklahoma State Univ Coll Business Adm Dept Management Stillwater OK 74078 USA

This paper studies the multi-hour service system design problem that involves locating service facilities, determining their number and capacities and assigning user nodes to those facilities under time varying demand conditions. The goal is to minimize total costs made of the costs of accessing facilities by users and waiting for service at these facilities as well as the cost of setting up and operating the facilities. A unified model is proposed for the problem to exploit the benefits of the non-coincidence of demand across busy-hours. To Lagrangean relaxation-based heuristic solution procedures are developed and the results of extensive computational experiments are reported. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： service system design time varying demand response time non-linear integer programming Lagrangean relaxation heuristics

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A simulated annealing algorithm for designing cellular manufacturing systems with productivity consideration

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PRODUCTION PLANNING & CONTROL 2000年第6期11卷 589-597页

作者： Abduelmola, AI Taboun, SM Univ Windsor Dept Ind & Mfg Syst Engn Windsor ON N9B 3P4 Canada

In this paper, we propose a productivity model for solving the machine-part grouping problem in cellular manufacturing (CM) systems. First, a non-linear 0-1 integer programming model is developed to identify machine groups and part families simultaneously. This model aims to maximize the system productivity defined as the ratio of total output to the total material handling cost. Second, an efficient simulated annealing (SA) algorithm is developed to solve large-scale problems. This algorithm provides several advantages over the existing algorithms. It forms part families and machine cells simultaneously. It also considers production volume, sales price, and maximum number of machines in each cell and total material handling cost. The proposed SA also has the ability to determine the optimum number of manufacturing cells. The performance of the developed models is tested on eight problems of different size and complexity selected from the literature. The results show the superiority of the SA algorithm over the mathematical programming model in both productivity and computational time.

关键词： productivity cellular manufacturing non-linear integer programming simulated annealing material handling

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An improved test set approach to nonlinear integer problems with applications to engineering design

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2015年第2期62卷 565-588页

作者： Gago-Vargas, J. Hartillo, I. Puerto, J. Ucha, J. M. Univ Seville Dept Algebra E-41080 Seville Spain Univ Seville Dept Matemat Aplicada 1 ETS Ingn Informat E-41012 Seville Spain Univ Seville Fac Matemat Dept Estadist & Invest Operat E-41012 Seville Spain

Many problems in engineering design involve the use of nonlinearities and some integer variables. Methods based on test sets have been proposed to solve some particular problems with integer variables, but they have not been frequently applied because of computation costs. The walk-back procedure based on a test set gives an exact method to obtain an optimal point of an integer programming problem with linear and nonlinear constraints, but the calculation of this test set and the identification of an optimal solution using the test set directions are usually computationally intensive. In problems for which obtaining the test set is reasonably fast, we show how the effectiveness can still be substantially improved. This methodology is presented in its full generality and illustrated on two specific problems: (1) minimizing cost in the problem of scheduling jobs on parallel machines given restrictions on demands and capacity, and (2) minimizing cost in the series parallel redundancy allocation problem, given a target reliability. Our computational results are promising and suggest the applicability of this approach to deal with other problems with similar characteristics or to combine it with mainstream solvers to certify optimality.

关键词： non-linear integer programming Test set Grobner basis Chance constrained programming

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Competitive facility location and design problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第1期182卷 40-62页

作者： Aboolian, Robert Berman, Oded Krass, Dmitry Calif State Univ San Marcos Coll Business Adm San Marcos CA 92096 USA Univ Toronto Rotman Sch Management Toronto ON M5S 3E6 Canada

We develop a spatial interaction model that seeks to simultaneously optimize location and design decisions for a set of new facilities. The facilities compete for customer demand with pre-existing competitive facilities and with each other. The customer demand is assumed to be elastic, expanding as the utility of the service offered by the facilities increases. Increases in the utility can be achieved by increasing the number of facilities, design improvements, or locating facilities closer to the customer. We show that our model is able to capture some of the principal trade-offs involved in facility location and design decisions, including demand cannibalization, market expansion, and design/location trade-offs. Managerial insights are obtained through sensitivity analysis of the model and through several illustrative examples. An efficient near-optimal solution approach, with adjustable error bound, is developed for the special case where only a finite number of design alternatives are available. Several heuristic approaches capable of handling large instances are also presented. (c) 2006 Elsevier B.V. All rights reserved.

关键词： competitive facility location models facility design problems non-linear integer programming greedy heuristics worst-case bounds approximation

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Merging bus routes in Hong Kong's central business district: Analysis and models

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TRANSPORTATION RESEARCH PART A-POLICY AND PRACTICE 2006年第10期40卷 918-935页

作者： Hwe, Slu Kei Cheung, Raymond K. Wan, Yat-wah Natl Dong Hwa Univ Inst Global Operat Strategy & Logist Management Hualien Taiwan Hong Kong Univ Sci & Technol Dept Ind Engn & Logist Management Kowloon Hong Kong Peoples R China

A significant portion of the 200,000 people working in Hong Kong's central business district (CBD) relies on buses as their primary means of transport. During peak hours, nearly a thousand double-decker buses pour into a tiny area of 150 ha. This causes traffic congestion and air pollution. Moreover, given that the flow is uni-directional (into the CBD in the morning and out of the CBD in the afternoon), the occupancy of buses in the CBD is actually low. In this paper, we propose to reduce traffic congestion and to increase bus occupancy by merging bus routes. We describe the peculiar situation of the CBD in Hong Kong and explain the necessary conditions for the possible success of merging routes. Our analysis shows that merging will lead to an overall benefit for all parties, including government, bus operators, and passengers. The actual merging decisions, which routes to merge and at what frequencies buses should run, are determined by a mathematical model. The model also shows quantitatively the benefits of merging routes and the impacts of other factors. The procedure that we follow and the model that we adopt can be applied to other CBD. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： merging bus routes central business district non-linear integer programming

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Multi-impact optimization to reduce aviation noise and emissions

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TRANSPORTATION RESEARCH PART D-TRANSPORT AND ENVIRONMENT 2010年第2期15卷 82-93页

作者： Zachary, Daniel S. Gervais, Jessica Leopold, Ulrich Ctr Rech Publ Henri Tudor Ctr Ressources Technol Environm L-4421 Esch Sur Alzette Luxembourg ArcelorMittal Esch Belval L-4008 Esch Belval Luxembourg

This paper describes a multi-indicator assessment and minimization problem focused on aviation "Community" noise. The model explores a combined noise and emission objective for airfreight movements at Luxembourg's Findel Airport. Community noise is evaluated via four population impact indicators emissions are tabulated from in-flight segments in the proximity of the airport and from the contribution of taxiing. A set of scenarios based on trajectory, aircraft scheduling, fleet composition, operational procedures are implemented in software. An integer programming methodology is used to search for minimal environmental impact. An on/off switch allows for an evaluation of each indicator in the objective. Different impacts on the population are explored in a case study involving the Cargolux Airlines International S.A. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Aviation noise Geospatial mapping Day-evening-night penalty non-linear integer programming

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