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integer nonlinear programming and optimized weighted-average approach for mobile hotel recommendation by considering travelers' unknown preferences

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OPERATIONAL RESEARCH 2018年第3期18卷 625-643页

作者： Lin, Yu-Cheng Chen, Toly Wang, Li-Chih Overseas Chinese Univ Dept Comp Aided Ind Design Taichung Taiwan Natl Chiao Tung Univ Dept Ind Engn & Management Hsinchu Taiwan Tunghai Univ Dept Ind Engn & Enterprise Informat Taichung Taiwan

The existing mobile hotel recommendation systems are usually subject to a difficult problem-travelers choose dominated hotels. This problem is difficult to resolve because there is no reason to recommend a hotel that is inferior to another in all aspects. To address this problem, an artificial dimension is added to each hotel to model unknown personal preferences. The possible values along the artificial dimension and the weight associated with it are derived by solving an integer nonlinear programming problem. Thus, the proposed methodology hybridizes objective and subjective weights. An illustrative example is provided to show the applicability of the proposed methodology. In addition, a field study was conducted in a small region of Seatwen District, Taichung City, Taiwan to evaluate the possible advantages of the proposed methodology over existing methods. The experimental results showed that the proposed methodology outperformed five existing methods in improving the successful recommendation rate, with the most significant advantage being up to 33 %. Furthermore, the recommendation results generated using the proposed methodology were found to be less risky.

关键词： Hotel Recommendation integer nonlinear programming Dominated solution

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Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第1期177卷 445-457页

作者： Chen, Shih-Pin Natl Chung Cheng Univ Dept Business Adm Chiayi 621 Taiwan

This paper proposes a mathematical programming method to construct the membership functions of the fuzzy objective value of the cost-based queueing decision problem with the cost coefficients and the arrival rate being fuzzy numbers. On the basis of Zadeh's extension principle, three pairs of mixed integer nonlinear programs (MINLP) parameterized by the possibility level alpha are formulated to calculate the lower and upper bounds of the minimal expected total cost per unit time at alpha, through which the membership function of the minimal expected total cost per unit time of the fuzzy objective value is constructed. To provide a suitable optimal service rate for designing queueing systems, the Yager's ranking index method is adopted. Two numerical examples are solved successfully to demonstrate the validity of the proposed method. Since the objective value is completely expressed by a membership function rather than by a crisp value, it conserves the fuzziness of the input information, thus more information is provided for designing queueing systems. The successful extension of queueing decision models to fuzzy environments permits queueing decision models to have wider applications in practice. (c) 2006 Elsevier B.V. All rights reserved.

关键词： queueing decision model fuzzy sets integer nonlinear programming

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LAGRANGEAN DECOMPOSITION FOR integer nonlinear-programming WITH LINEAR CONSTRAINTS

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MATHEMATICAL programming 1991年第2期52卷 303-313页

作者： MICHELON, P MACULAN, N FED UNIV RIO DE JANEIRO COPPEBR-21945 RIO DE JANEIROBRAZIL FED UNIV RIO DE JANEIRO INST MATEMATBR-21945 RIO DE JANEIROBRAZIL

We present a Lagrangean decomposition to study integer nonlinear programming problems. Solving the dual Lagrangean relaxation we have to obtain at each iteration the solution of a nonlinear programming with continuous variables and an integer linear programming. Decreasing iteratively the primal-dual gap we propose two algorithms to treat the integer nonlinear programming.

关键词： integer nonlinear programming LAGRANGEAN DECOMPOSITION LAGRANGEAN RELAXATION

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Exact Methods for Multi-Objective integer nonlinear programming

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CYBERNETICS AND SYSTEMS 2024年第7期55卷 1668-1701页

作者： Yu, Zixuan Sun, Wei Huang, Min Northeastern Univ Dept Intelligent Data & Syst Engn State Key Lab Synthet Automat Proc Ind Shenyang Peoples R China Liaoning Univ Business Sch Shenyang Peoples R China

Multi-objective integer nonlinear programming (MOINLP) problems are multi-objective integer programming problems with at least one nonlinear objective function or constraint. To date, MOINLP problem has not been exactly solved. Although traditional epsilon-constraint method can be used to solve MOINLP problem, the obtained solution may not be Pareto-optimal. To overcome this shortcoming, a basic epsilon-constraint method (BEM) is proposed to solve MOINLP problem exactly. However, the time complexity of BEM is as high as O((p-1)(MN)-N-2), where p, M, and N are the numbers of objectives, Pareto-optimal solutions, and feasible solutions, respectively. For this reason, an improved BEM (IBEM) is developed whose time complexity is O((MN)-N-2). That is, the time complexity of IBEM for solving MOINLP problem is equal to solving the single-objective one. Finally, to avoid using all the feasible solutions (N) in obtaining each Pareto-optimal solution, three methods to eliminate dominated solutions effectively are used before performing IBEM. The test results illustrate that our method can not only solve MOINLP problem exactly but also has high efficiency.

关键词： Exact method integer nonlinear programming multi-objective reducing solution space

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Regulatory Networks of integer nonlinear programming(RNINLP): a Model to Analyze Gene Regulatory Networks of Breast Cancer Metastasis

Regulatory Networks of Integer Nonlinear Programming(RNINLP)...

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8th World Congress on Intelligent Control and Automation (WCICA)

作者： Luo, Wanchun Gong, Lihong Ren, Kaichun Yi, Dong Third Mil Med Univ Dept Med Stat Chongqing 400038 Peoples R China Third Mil Med Univ Coll Biomed Engn & Med Imaging Dept Math & Biomath Chongqing 400038 Peoples R China Chongqing Commun Coll Dept Machine & Elect Chongqing 400035 Peoples R China

ISBN: (纸本)9781424467129

There are more and more data from Human Genome Project that we need better methods to deal with. Some mathematical models have been presented to analyze gene regulatory networks, such as Boolean networks Bayesian networks, differential equation, weight matrices, etc. Some of the models could describe some rules of the genetic regulatory relations properly, such as Bayesian networks, differential equation, but the rest did not work very well. It is thus necessary to consider some new mathematical models to estimate the gene regulatory relations according to some experimental data. Here we have utilized the entropy information from gene data of breast cancer metastasis to get the weights of all the genes, and set up a RNINLP model in which minimum error is regarded as objective function to search for the regulatory relation in the genes, and then sieved regulatory genes by coefficient correlation model. Using the programs of LINGO8.0 and MATLAB7.0, we got a gene regulatory network of the 27 genes related to the breast cancer metastasis. We found that there were 25 pairs of genes exiting regulatory relation and 11 pairs of genes being mutual promotion effect. RNINLP utilizes almost all the information of the data, so it can describe the regulatory relation of genes with coefficient correlation model, and the model can be extended to even more complicated gene regulatory networks.

关键词： integer nonlinear programming gene regulatory networks breast cancer metastasis

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Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm

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APPLIED MATHEMATICS AND COMPUTATION 2011年第22期217卷 9234-9253页

作者： Taleizadeh, Ata Allah Niaki, Seyed Taghi Akhavan Barzinpour, Farnaz Sharif Univ Technol Dept Ind Engn Tehran *** Iran Iran Univ Sci & Technol Dept Ind Engn Tehran Iran

In this paper, a multi-buyer multi-vendor supply chain problem is considered in which there are several products, each buyer has limited capacity to purchase products, and each vendor has warehouse limitation to store products. In this chain, the demand of each product is stochastic and follows a uniform distribution. The lead-time of receiving products from a vendor to a buyer is assumed to vary linearly with respect to the order quantity of the buyer and the production rate of the vendor. For each product, a fraction of the shortage is backordered and the rest are lost. The ordered product quantities are placed in multiple of pre-defined packets and there are service rate constraints for the buyers. The goal is to determine the reorder points, the safety stocks, and the numbers of shipments and packets in each shipment of the products such that the total cost of the supply chain is minimized. We show that the model of this problem is of an integer nonlinear programming type and in order to solve it a harmony search algorithm is employed. To validate the solution and to compare the performance of the proposed algorithm, a genetic algorithm is utilized as well. A numerical illustration and sensitivity analysis are given at the end to show the applicability of the proposed methodology in real-world supply chain problems. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Supply chain management Multi-buyer Multi-vendor Partial back ordering Variable lead-time integer nonlinear programming Harmony search algorithm Genetic algorithsm

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A metaheuristic framework for nonlinear Capacitated Covering Problems

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OPTIMIZATION LETTERS 2016年第1期10卷 169-180页

作者： Malaguti, Enrico Medina Duran, Rosa Toth, Paolo Univ Bologna DEI I-40136 Bologna Italy Univ Concepcion Fac Ingn Dept Ingn Ind Concepcion Chile

Several relevant optimization problems can be formulated as generalizations of Capacitated Covering Problems, by considering a cost function that combines a linear term with a nonlinear one. In this paper we introduce the Staircase Capacitated Covering Problem, where the nonlinear term has a staircase shape, and we propose a framework based on a Metaheuristic algorithm for solving problems having this formulation. The performance of the Metaheuristic algorithm in solving the Staircase Capacitated Covering Problem is evaluated on a set of instances derived from an industrial application, and it is compared with a linearized formulation of the problem solved by CPLEX. In particular, the experiments show that the former produces better solutions in the same computing time.

关键词： integer nonlinear programming Capacitated Covering Problems Metaheuristic algorithm

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Solving a nonlinear non-convex trim loss problem with a genetic hybrid algorithm

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COMPUTERS & OPERATIONS RESEARCH 1999年第6期26卷 623-635页

作者： Östermark, R Abo Akad Univ Dept Business Adm FIN-20500 Turku Finland

In the present paper, we invoke a newly developed genetic hybrid algorithm (GHA) to solve the trim loss problem of a paper-converting mill. The genetic algorithm was specifically designed for nonconvex mixed integer nonlinear programming problems. The current problem is an integer non-convex nonlinear programming (INLP) problem involving bilinear constraints. As shown elsewhere, the problem can be written in expanded linear form and solved either as an integer linear programming (ILP) or as a mixed integer linear programming (MILP) problem. In each case, the formulation is a special case of MINLP and, therefore, directly solvable by the genetic hybrid algorithm. The example considered is taken from the family of real daily trim optimization problems encountered at a Finnish paper-converting mill with a yearly capacity of 100 000 t. In this paper, we present the genetic hybrid algorithm, the INLP-problem to be solved and compare the results with those obtained by a classical optimization method. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： optimization integer nonlinear programming trim loss problems evolutionary programming

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Controlling posterior producer and consumer risks in lot reinspection

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APPLIED MATHEMATICAL MODELLING 2016年第23-24期40卷 10760-10770页

作者： Fernandez, Arturo J. Univ La Laguna Dept Matemat Estadist & Invest Operat Tenerife 38071 Canary Islands Spain

Assuming that maximum tolerable posterior risks are specified for both producer and consumer, an integer nonlinear programming problem is formulated and solved in order to determine the optimal defects-per-unit acceptance sampling plan when lots found unacceptable may be resubmitted for reinspection. The number of nonconformities per inspected item follows a Poisson distribution. A computational algorithm is proposed to solve the underlying constrained minimization problem. The suggested procedure simplifies and quickens the determination of the inspection scheme for resubmitted lot acceptance with limited posterior risks that minimizes the expected number of sampled items per lot. An application to the manufacturing of paper is considered to illustrate the methodology developed. The generalized truncated gamma distribution is used to describe the prior uncertainty about the incoming defect rate per unit. The degree of similarity between the available previous information and the current study is 'also evaluated. Suitable ways are provided to assume a reduced parameter space for the defect rate and to update the prior model using past performance of the acceptance plan. The incorporation of lot resubmissions, as well as previous defect count data and expert opinions, into the decision process often yields appreciable savings in sampling effort. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Constrained optimization Generalized truncated gamma model Quality control integer nonlinear programming Poisson defect rate

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Differential evolution algorithm for static and multistage transmission expansion planning

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IET GENERATION TRANSMISSION & DISTRIBUTION 2009年第4期3卷 365-384页

作者： Sum-Im, T. Taylor, G. A. Irving, M. R. Song, Y. H. Brunel Univ Brunel Inst Power Syst Sch Engn & Design Uxbridge UB8 3PH Middx England Univ Liverpool Dept Elect Engn & Elect Liverpool L69 3GJ Merseyside England

A novel differential evolution algorithm (DEA) is applied directly to the DC power flow-based model in order to efficiently solve the problems of static and multistage transmission expansion planning (TEP). The purpose of TEP is to minimise the transmission investment cost associated with the technical operation and economical constraints. Mathematically, long-term TEP using the DC model is a mixed integer nonlinear programming problem that is difficult to solve for large-scale real-world transmission networks. In addition, the static TEP problem is considered both with and without the resizing of power generation in this research. The efficiency of the proposed method is initially demonstrated via the analysis of low, medium and high complexity transmission network test cases. The analysis is performed within the mathematical programming environment of MATLAB using both DEA and conventional genetic algorithm and a detailed comparative study is presented.

关键词： DC power flow-based model power transmission planning Power transmission, distribution and supply Power system planning and layout Power system management, operation and economics Optimisation techniques nonlinear programming integer programming large-scale transmission network DEA investment cost power transmission economics integer nonlinear programming evolutionary computation MATLAB environment multistage transmission expansion planning load flow static TEP economical constraint costing differential evolution algorithm

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