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rs-Sparse principal component analysis: A mixed integer nonlinear programming approach with VNS

COMPUTERS & OPERATIONS RESEARCH 2014年第PartB期52卷 349-354页

作者： Carrizosa, Emilio Guerrero, Vanesa Univ Seville Inst Matemat Fac Matemat E-41012 Seville Spain

Principal component analysis is a popular data analysis dimensionality reduction technique, aiming to project with minimum error for a given dataset into a subspace of smaller number of dimensions. In order to improve interpretability, different variants of the method have been proposed in the literature, in which, besides error minimization, sparsity is sought. In this paper we formulate as a mixed integer nonlinear program the problem of finding a subspace with a sparse basis minimizing the sum of squares of distances between the points and their projections. Contrary to other attempts in the literature, with our model the user can fix the level of sparseness of the resulting basis vectors. Variable neighborhood search is proposed to solve the problem obtained this way. Our numerical experience on test sets shows that our procedure outperforms benchmark methods in the literature, both in terms of sparsity and errors. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Sparse principal component analysis Variable neighborhood search nonlinear mixed integer programming

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Fuzzy mathematical programming approaches for reverse supply chain optimization with disassembly line balancing problem

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2014年第4期26卷 1969-1985页

作者： Ozceylan, Eren Paksoy, Turan Selcuk Univ Dept Ind Engn Konya Turkey

Today, the requirement of reverse supply chain (RSC) optimization takes more attention due to environmental and competitive factors. However, increasing attention and existing uncertainty in RSC also increases the difficulties for decisions of production/distribution planning. Therefore, considering strategic and tactical decisions together under fuzziness is being essential. This paper presents a fuzzy programming approach to the integration of RSC optimization (strategic level) and disassembly line balancing (DLB) (tactical level) problems. The aim of this study is to apply fuzzy modeling to optimize a RSC that involves customers, collection/disassembly centers and plants while balancing the disassembly lines in disassembly centers, simultaneously. Two types of fuzzy mathematical programming models with different aggregation operators are used. Finally, accuracy and applicability of the model is illustrated and a comparison of fuzzy approaches is done via a hypothetical example.

关键词： Disassembly line balancing fuzzy mathematical programming nonlinear mixed integer programming reverse supply chain

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A joint supplier selection and order allocation model with disruption risks in centralized supply chain

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 127卷 734-748页

作者： Esmaeili-Najafabadi, Elham Nezhad, Mohammad Saber Fallah Pourmohammadi, Hamid Honarvar, Mahboobeh Vandatzad, Mohammad Ali Yazd Univ Ind Engn Dept Yazd Iran Calif State Univ Dominguez Hills Dept ISOM Carson CA USA

Supplier's coordination plays a vital role in managing a supply chain. Organizations have learned that selecting the right suppliers and allocating right orders are the keys to success. The presence of disruption risks in the supply chain creates more complexity in the supplier selection and order allocation process. This paper presents a mixed-integer nonlinear programming model to optimize supplier selection and order allocation simultaneously in centralized supply chains considering disruption risks. In order to reduce disruption effects, two protective policies are taken into account. Protection policy for the selected suppliers and emergency inventory allocation policy for the protected suppliers are utilized in this study. The presented model proves to be non convex, indicating that, conventional methods are not capable of solving such a complex problem. The proposed method is exemplified by numerical instances. The results indicate that with an increase in the disruption probability the factors which effect the decisions related to supplier selection and order allocation are altered. At the low disruption probability, the disruption risk plays a key role in the decisions, while at the higher disruption probability, wholesale price and disruption risk are the dominant factors to form the decisions.

关键词： Supplier selection Disruption risk Pre-position inventory Protected supplier Supply chain coordination nonlinear mixed integer programming

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An exact penalty function method for nonlinear mixed discrete programming problems

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OPTIMIZATION LETTERS 2013年第1期7卷 23-38页

作者： Yu, Changjun Teo, Kok Lay Bai, Yanqin Shanghai Univ Shanghai Peoples R China Curtin Univ Technol Perth WA Australia

In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. Then, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton methods. It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method.

关键词： nonlinear mixed integer programming Exact penalty function

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Automatic commercial aircraft-collision avoidance in free flight. The three-dimensional problem

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2006年第2期7卷 242-249页

作者： Christodoulou, Manolis A. Kodaxakis, Sifis G. Tech Univ Crete Dept Elect & Comp Engn Iraklion Greece

In this paper, optimal resolution of air-traffic (AT) conflicts were considered. Aircraft are assumed to cruise within a free altitude layer and are modeled in three dimensions with variable velocity and proximity bounds. Aircraft cannot get closer to each other than a predefined safety distance. The problem of solving conflicts arising among several aircraft that are assumed to move in a shared airspace were considered. For such systems of multiple aircraft, the total flight time by avoiding all possible conflicts were minimized. This paper proposes a formulation of the conflict avoidance problem as a mixed-integer nonlinear-programming problem. In the author's case, only velocity changes are admissible as maneuvers. Nevertheless, in subsequent work, simultaneous velocity and heading angle changes will be checked too. Simulation results for realistic aircraft conflict scenarios are provided.

关键词： conflict resolution free flight nonlinear mixed integer programming

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A mathematical programming approach for improving the robustness of least sum of absolute deviations regression

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NAVAL RESEARCH LOGISTICS 2006年第4期53卷 261-271页

作者： Giloni, A Sengupta, B Simonoff, JS Yeshiva Univ Sy Syms Sch Business New York NY 10033 USA ExxonMobile Res & Engn Annandale NJ 08801 USA NYU Leonard N Stern Sch Business New York NY 10012 USA

This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least-sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. (C) 2006 Wiley Periodicals, Inc.

关键词： algorithms breakdown point knapsack problem nonlinear mixed integer programming robust regression

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Optimal design of degradation tests in presence of cost constraint

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2002年第2期76卷 109-115页

作者： Wu, SJ Chang, CT Tamkang Univ Dept Stat Taipei 251 Taiwan

Degradation test is a useful technique to provide information about the lifetime of highly reliable products. We obtain the degradation measurements over time in such a test. In general, the degradation data are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the failure time distribution can be estimated. However, in order to obtain a precise estimate of the percentile of failure time distribution, one needs to design an optimal degradation test. Therefore. this study proposes an approach to determine the number of units to test, inspection frequency, and termination time of a degradation test under a determined cost of experiment such that the variance of estimator of percentile of failure time distribution is minimum. The method will be applied to a numerical example and the sensitivity analysis will be discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： degradation data nonlinear mixed integer programming nonlinear mixed-effect model reliability

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Supply chain network design with direct and indirect production costs: Hybrid gradient and local search based heuristics

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2018年 203卷 203-215页

作者： Alzaman, Chaher Zhang, Zhi-Hai Diabat, Ali Concordia Univ Dept Supply Chain & Business Technol Management John Molson Sch Business Montreal PQ H3H 0A1 Canada Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China New York Univ Abu Dhabi Div Engn Abu Dhabi 129188 U Arab Emirates NYU Tandon Sch Engn Dept Civil & Urban Engn Brooklyn NY 11201 USA

Many works in the area of Supply Chain Network Design (SCND) have integrated production costs as one lumped cost. However, production costs embody indirect (overhead) and direct costs. This work brings a model that integrates these two production costs along with inventory and transportation costs. In particular, the work looks at the tradeoff between the shortening of the production duration (Pd) and the consequent increase in direct production costs. The work implicitly incorporates direct production costs that are the result of applying additional production resources to shorten Pd. Integrating both costs results in a nonlinear mathematical model. The overall objective function also includes binary variables to govern the selection of production plants resulting in a nonlinear mixed integer mathematical model. In this work, we prove the convexity of the objective function and we introduce a combination of a gradient and a local search heuristic to solve the resulting model. For practical implications, the paper presents four different scenarios to cover a wide range of supply chain settings. Principally, our results demonstrate promising benefits of reduced overall production costs, reduced production lead time, freed-up production capacity, and improved supply chain throughput.

关键词： Supply chains Hybrid heuristics Gradient search nonlinear mixed integer programming

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Identifying target green 3C customers in Taiwan using multiattribute utility theory

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EXPERT SYSTEMS WITH APPLICATIONS 2009年第10期36卷 12562-12569页

作者： Wang, Miao-Ling Kuo, Tsai-Chi Liu, Jia-Wen Ming Hsin Univ Sci & Technol Dept Ind Engn & Management Hsinchu 304 Taiwan Ming Hsin Univ Sci & Technol Inst Engn Management Hsinchu 304 Taiwan

Issues of environmental protection have become more and more important. Consumers are increasingly concerned about how their behaviors impact the earth. Therefore, with the emergence of a customer-oriented market, identifying consumers' behaviors has become an important issue for businesses. Determining how to identify target customers who are satisfied and willing to pay more, is an important issue. In this study, we applied data mining techniques to cope with this problem;a list of questionnaires was used to determine the preferences of customers with respect to a green 3C product in Taiwan. in order to tell the differences between the heterogeneous customers, clustering analysis is needed. Behavior variables, psychological variables, geographic variables. demographic variables, environmental knowledge, attitudes toward environmental protection and non-purchasing environmental behaviors were used to profile customers. Step-wise regression and ANOVA analysis were used to obtain the suitable segmentation variables. After clustering analysis, customers were segmented into different groups. The promoter or passive one in each cluster, as indicated by the net promoter score technology, is the satisfied customer in the corresponding cluster. A bi-objective nonlinear mixed integer problem is constructed with multiattribute utility theory;optimal price and promotion strategies can be provided as the foundation for marketing for satisfying both supplier and customer with a win-win concept. Then, business can really transmit the selling information to the users and improve the satisfaction of detractors to increase sales and profit. Crown Copyright (C) 2009 Published by Elsevier Ltd. All rights reserved.

关键词： Green product Cluster analysis NPS MAUT nonlinear mixed integer programming

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Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: nonlinear integer programming models with linear constraints

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2015年 76卷 117-135页

作者： Niu, Huimin Zhou, Xuesong Gao, Ruhu Lanzhou Jiaotong Univ Sch Traff & Transportat Lanzhou 730070 Peoples R China Arizona State Univ Sch Sustainable Engn & Built Environm Tempe AZ 85287 USA

This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin-destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Train timetable Passenger waiting time Time-varying demand Skip-stop pattern nonlinear mixed integer programming

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