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Combining QCR and CHR for convex quadratic pure 0-1 programming problems with linear constraints

ANNALS OF OPERATIONS RESEARCH 2012年第1期199卷 33-49页

作者： Ahlatcioglu, Aykut Bussieck, Michael Esen, Mustafa Guignard, Monique Jagla, Jan-Hendrick Meeraus, Alexander Univ Penn Philadelphia PA 19104 USA Princeton Univ Princeton NJ 08544 USA GAMS Dev Corp Washington DC USA

The convex hull relaxation (CHR) method (Albornoz in Doctoral Dissertation, 1998, Ahlat double dagger A +/- oglu in Summer paper, 2007, Ahlat double dagger A +/- oglu and Guignard in OPIM Dept. Report, 2010) provides lower bounds and feasible solutions on convex 0-1 nonlinear programming problems with linear constraints. In the quadratic case, these bounds may often be improved by a preprocessing step that adds to the quadratic objective function terms that are equal to 0 for all 0-1 feasible solutions yet increase its continuous minimum. Prior to computing CHR bounds, one may use Plateau's quadratic convex reformulation (QCR) method (2006), or one of its weaker predecessors designed for unconstrained problems, the eigenvalue method of Hammer and Rubin (RAIRO 3:67-79, 1970) or the method of Billionnet and Elloumi (Math. Program, Ser. A 109:55-68, 2007). In this paper, we first describe the CHR method, and then present the QCR reformulation methods. We present computational results for convex GQAP problems.

关键词： nonlinear integer programming Bounds Relaxation Convex hull CHR QCR SDP GQAP

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nonlinear 0-1 programming .1. LINEARIZATION TECHNIQUES

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MATHEMATICAL programming 1984年第1期30卷 1-21页

作者： BALAS, E MAZZOLA, JB CARNEGIE MELLON UNIV PITTSBURGH PA 15213 USA UNIV N CAROLINA CHAPEL HILL NC 27514 USA

Any real-valued nonlinear function in 0–1 variables can be rewritten as a multilinear function. We discuss classes of lower and upper bounding linear expressions for multilinear functions in 0–1 variables. For any multilinear inequality in 0–1 variables, we define an equivalent family of linear inequalities. This family contains the well-known system of generalized covering inequalities, as well as other linear equivalents of the multilinear inequality that are more compact, i.e., of smaller cardinality. In a companion paper [7]. we discuss dominance relations between various linear equivalents of a multilinear inequality, and describe a class of algorithms for multilinear 0–1 programming based on these results.

关键词： Linearization of Multilinear Inequalities Multilinear Functions nonlinear integer programming

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MINIMIZING VARIATION OF PRODUCTION-RATES IN JUST-IN-TIME SYSTEMS - A SURVEY

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1993年第3期66卷 259-271页

作者： KUBIAK, W MEM UNIV NEWFOUNDLAND FAC BUSINESS ADM St John A1B 3X5 NEWFOUNDLAND CANADA

In the past several years, there has been growing interest in scheduling problems where jobs are penalized both for being early and for being tardy. This notable deviation from previous work, in which finishing early is generally regarded as being at least as desirable as finishing on time, is perceived to be the one that well captures the scheduling dimension of JIT production systems. A number of excellent surveys on these problems has appeared over the last four years. There is, however, another important scheduling objective in JIT production systems which is to minimize variation of rates at which processes supply their outputs. These scheduling problems are, for example, of primary concern in the Toyota JIT system. Thus far, most research efforts in this area have been focused on minimizing variation of the rate at which different products are being produced on the final, multi-model assembly line which itself is a supplying process. We shall review the results of this research, and relate them to the due date based scheduling problems. Extensions and open problems will also be reviewed. Schedules that minimize variation of the rate at which different products are being produced on the line do not necessarily minimize variation in the line demand for outputs of processes that supply it. Few heuristics for the problem of minimizing the variation are available and hardly anything is known on its complexity as wel as exact algorithms to tackle it. We shall review a mathematical programming model of the problem and open questions that result from it.

关键词： PRODUCTION SCHEDULING JUST-IN-TIME nonlinear integer programming MIXED-MODEL ASSEMBLY LINES ALGORITHMS COMPUTATIONAL COMPLEXITY

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Mathematical models to improve the current practice in a Home Healthcare Unit

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OR SPECTRUM 2020年第1期42卷 43-74页

作者： Quintanilla, Sacramento Ballestin, Francisco Perez, Angeles Univ Valencia Dept Matemat Econ & Empresa Valencia 46022 Spain

This paper addresses a home healthcare routing problem in which doctors and nurses visit patients at their homes to provide services. We consider a real-world home healthcare service arising in a particular hospital in Spain. Doctors and nurses are distributed in teams and travel by taxi;taxis transport a pre-defined set of workers who travel together the whole route. The objective is to minimise the transportation costs related to the total taxi journey time, including travelling and waiting costs. The paper presents a mathematical model that considers these current policies and permits the problem to be solved optimally. The paper also explores, after reviewing the hospital's current model, the benefits that can be obtained by changing some of the current policies of the hospital. In this way, a new model is proposed based on two sustainable strategies that can be extended to other home service fields: (1) workers can walk between houses and (2) the workers transported by a taxi may change during the route. A complex nonlinear mathematical model is presented, and a metaheuristic is designed to provide quality solutions. Computational tests on a set of instances based on real-world data estimate the gap between the solutions of both models.

关键词： Home healthcare problem Heuristics nonlinear integer programming Linear integer programming

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Lagrangean methods for the 0-1 Quadratic Knapsack Problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1996年第2期92卷 326-341页

作者： Michelon, P Veilleux, L COLL MIL ROYAL ST JEAN ST JEANPQ J0J 1R0CANADA

It is well known that the Lagrangean decomposition provides better bounds than the Lagrangean relaxation does. Nevertheless, the Lagrangean decomposition bound is harder to compute than the Lagrangean relaxation bound. Thus, one might wonder what is the best Lagrangean method to use in a branch-and-bound algorithm. In this paper, we give an answer to such a question for the 0-1 Quadratic Knapsack Problem. We first study the Lagrangean decomposition for this problem and give new necessary optimality conditions for the dual problem which allow us to elaborate a heuristic method for solving the Lagrangean decomposition dual problem. We then introduce this method in Chaillou-Hansen-Mahieu's branch-and-bound algorithm where upper bounds were computed by Lagrangean relaxation.

关键词： nonlinear integer programming Lagrangean methods branch-and-bound algorithm

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Fuzzy Portfolio Selection Including Cardinality Constraints and integer Conditions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2016年第1期170卷 343-355页

作者： Calvo, Clara Ivorra, Carlos Liern, Vicente Univ Valencia Valencia Spain

This paper is concerned with a fuzzy version of the portfolio selection problem, which includes diversification conditions and incorporates investor's subjective preferences. The inclusion of diversification conditions leads to mixed-integer models, which are computationally demanding. On the other hand, the consideration of integer conditions makes the solution very sensitive to investor's subjective preferences with regard to the trade-off between risk and expected return. These preferences are imprecise by their very nature. In this paper, we overcome these issues by proposing a solution method for a fuzzy quadratic portfolio selection model with integer conditions. The suitability of the proposed method is illustrated by means of two numerical examples.

关键词： Fuzzy optimization Portfolio selection Efficient frontier nonlinear integer programming

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A GRASP for simultaneously assigning and sequencing product families on flexible assembly lines

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ANNALS OF OPERATIONS RESEARCH 2013年第1期203卷 295-323页

作者： Heath, Susan K. Bard, Jonathan F. Morrice, Douglas J. USN Postgrad Sch Monterey CA 93943 USA Univ Texas Austin Grad Program Operat Res & Ind Engn Austin TX 78712 USA Univ Texas Austin McCombs Sch Business Austin TX 78712 USA

This paper introduces a new model and solution methodology for a real-world production scheduling problem arising in the electronics industry. The production environment is a high volume, just-in-time, make-to-order facility with volatile demand over many product families that are assembled on flexible lines. A distinguishing characteristic of the problem is the presence of non-traditional sequence-dependant setup costs, which complicate our ability to find high-quality solutions. The scheduling problem arose when product variety exceeded the mix that the existing lines could accommodate. A nonlinear integer programming formulation is presented for the problem of minimizing setup costs, and a greedy randomized adaptive search procedure (GRASP) is developed to find solutions. To select the GRASP parameter values, an efficient, space-filling experimental design method is used based on nearly orthogonal Latin hypercubes. The proposed methodology is tested on actual factory data and compared to a prior heuristic presented in the literature;our heuristic provides a cost savings in 7 out of the 10 cases examined, and an average improvement of 17.39 % which is shown to be highly statistically significant. This improvement is due in part to the introduction of a pre-processing step to determine preferential and non-preferential line assignment information.

关键词： GRASP Production sequencing Nearly orthogonal Latin hypercubes nonlinear integer programming

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Reliability optimal design problem with interval coefficients using Hybrid Genetic Algorithms

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COMPUTERS & INDUSTRIAL ENGINEERING 1998年第1-2期35卷 373-376页

作者： Taguchi, T Yokota, T Gen, M Ashikaga Inst Technol Dept Ind & Syst Engn Ashikaga 3268558 Japan

In this paper, we formulate an optimal design of system reliability problem as nonlinear integer programming (NIP) problem with interval coefficients! transform it into single objective NIP problem without interval coefficients, and solve it directly keeping the nonlinearity of the objective function based on Hybrid Genetic Algorithms (HGAs). Also, we demonstrate the efficiency of this method with Optimal Selection and Allocation problem of a System Reliability. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： nonlinear integer programming interval coefficient Hybrid Genetic Algorithm reliability optimization

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A solution method for a resistance circuit network design with optimal power consumption problem by using genetic algorithms

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COMPUTERS & INDUSTRIAL ENGINEERING 1998年第1-2期35卷 377-380页

作者： Zheng, LX Yokota, T Gen, M Huaqiao Univ Dept Elect Tech Fujian 362011 Peoples R China Ashikaga Inst Technol Dept Ind & Syst Engn Ashikaga 326 Japan

In this paper, we formulate a resistance circuit network design problem with optimal power consumption for a constrained electric current as a nonlinear integer programming (NIP) problem and solve it directly by keeping the nonlinear constraint based on genetic algorithms (GA). We discuss the efficency between the proposed method and Kuhn-Tucker discretized optimality criteria methods. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： resistance circuit network nonlinear integer programming genetic algorithm

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Cooperative green supply chain management with greenhouse gas emissions and fuzzy demand

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JOURNAL OF CLEANER PRODUCTION 2019年 208卷 1421-1435页

作者： Noh, Jiseong Kim, Jong Soo Hanyang Univ Dept Ind & Management Engn Erica Campus Ansan 15588 South Korea

Concerns about environmentally sustainable supply chain management have increased widely in recent years. As a consequence, supply chain members have cooperated with one another to make efficient contracts, frequently called green supply-chain management contracts. The purpose of this paper is to investigate one such contract between a single manufacturer and multiple retailers with limited resources for several types of products under greenhouse-gas emission regulations. Each retailer orders the products regularly within a limited budget and warehouse capacity. In response to orders, the manufacturer produces products and ships them after inspections. Demand for the products can be either known or have some uncertainty, which can best be represented using fuzzy number demand. To reflect demand properties, this paper introduces two nonlinear integer programming models, a crisp model and a fuzzy model. A genetic algorithm (GA) and hybrid genetic algorithm-pattern search (HGAS) are developed to solve the models. Numerical experiments evaluating the efficiency of the algorithms showed that the HGAS method performed better than the GA. Also observed is that the crisp model's average total costs were lower than those of the fuzzy model. The results as a whole indicate that the models can evaluate the performance of contracts and optimize cooperative green supply chain management. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Green supply chain management Greenhouse gas nonlinear integer programming Intelligent algorithm

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