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A parametric programming technique for efficient CNC machining operations

COMPUTERS & INDUSTRIAL ENGINEERING 1998年第1-2期35卷 33-36页

作者： Djassemi, M Murray State Univ Dept Ind & Engn Technol Murray KY 42071 USA

In this paper the application of parametric programming to CNC machining is discussed. As one of the less frequently utilized features of CNC machines, parametric programming has the potential to increase the efficiency of CNC operations. This feature is particularly beneficial to companies with group technology manufacturing where parts with similar design or operational requirements are processed within a machine cell. Using two case studies, the capabilities of parametric programming for CNC machines are illustrated. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： parametric programming CNC machining group technology

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parametric programming to the analysis of fuzzy queues

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FUZZY SETS AND SYSTEMS 1999年第1期107卷 93-100页

作者： Kao, C Li, CC Chen, SP Natl Cheng Kung Univ Grad Sch Ind Management Tainan Taiwan Natl Tsing Hua Univ Dept Ind Engn Hsinchu Taiwan

This paper proposes a general procedure to construct the membership functions of the performance measures in queueing systems when the interarrival time and service time are fuzzy numbers. The basic idea is to reduce a fuzzy queue into a family of crisp queues by applying the alpha-cut approach. A pair of parametric programs is formulated to describe th at family of crisp queues, via which the membership functions of the performance measures are derived. To demonstrate the validity of the proposed procedure, four fuzzy queues, namely, M/F/1, F/M/1, F/F/1, and FM/FM/1, are exemplified. The discussion of this paper is confined to systems with one and two fuzzy variables: nevertheless, the procedure can be extended to systems with more than two fuzzy variables. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： queueing theory parametric programming membership functions

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parametric programming-based approximate selective inference for adaptive lasso, adaptive elastic net and group lasso

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2024年第11期94卷 2412-2435页

作者： Pirenne, Sarah Claeskens, Gerda ORStat Leuven Belgium Leuven Stat Res Ctr Leuven Belgium Katholieke Univ Leuven ORStat Naamsestr 69 B-3000 Leuven Belgium Katholieke Univ Leuven Leuven Stat Res Ctr Naamsestr 69 B-3000 Leuven Belgium

Conducting model selection on data gives rise to selection uncertainty which, when ignored, invalidates subsequent classical inference which assumes that the model is given before the analysis and is in all its aspects correctly specified. In selective inference, the randomness induced by selection is dealt with by conditioning confidence intervals and p-values on the subspace of the data which leads to the same model selection as the observed data. The main challenge is the characterization of this selection event. We develop an algorithm for conducting approximate post-selection inference for parameters after model selection events which may not be characterizable as polyhedrons. We apply this on the adaptive lasso, the adaptive elastic net and the group lasso. We conduct experiments on simulated and real data, illustrating that the algorithm can both successfully control the false-positive rate and is computationally efficient.

关键词： Post-selection inference selective inference adaptive lasso adaptive elastic net group lasso parametric programming

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HY-POP: Hyperparameter optimization of machine learning models through parametric programming

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COMPUTERS & CHEMICAL ENGINEERING 2020年 139卷 106902-106902页

作者： Tso, William W. Burnak, Baris Pistikopoulos, Efstratios N. Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA Texas A&M Univ Texas A&M Energy Inst College Stn TX 77843 USA Texas A&M Energy Inst 1617 Res Pkwy College Stn TX 77843 USA

Fitting a machine learning model often requires presetting parameter values (hyperparameters) that control how an algorithm learns from the data. Selecting an optimal model that minimizes error and generalizes well to unseen data becomes a problem of tuning or optimizing these hyperparameters. Typical hyperparameter optimization strategies involve discretizing the parameter space and implementing an iterative search procedure to approximate the optimal hyperparameter and model selection through cross-validation. Instead, for machine learning algorithms that are formulated as linear or quadratic programming (LP/QP) models, an exact solution to the hyperparameter optimization problem is obtainable through parametric programming without any approximation. First, the hyperparameter optimization problem is posed more naturally as a bilevel optimization. Second, using parametric programming theory, the bilevel optimization is reformulated into a single level problem. Exact solutions to the hyperparameter optimization problem for LASSO regression and LP L-1-norm support vector machine (SVM) are derived and validated on example data. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Machine learning Hyperparameter optimization parametric programming Bilevel optimization Model selection Regularization

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INFORMATIVE LAGRANGE MULTIPLIERS IN NONLINEAR parametric programming MODELS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2024年第4期20卷 1534-1560页

作者： Jie, Tao Yan, Gao Univ Shanghai Sci & Technol Business Sch Dept Syst Sci Shanghai Peoples R China

The minimum norm Lagrange multiplier, as a type of informative Lagrange multiplier, is proposed to replace the classical shadow price when the later fails to exist. This kind of multiplier expresses the rate of cost improvement when the right-hand side of the constraints are permitted to slightly violated. However, the minimum norm Lagrange multiplier may fail to be informative in fully parametric optimization problems. In this paper, we extend the classical constraint violation condition to a general formulation, which captures the characteristics of the problem structure of nonlinear parametric programming models. Based on the generalized constraint violation condition, we provide sufficient conditions for the minimum norm Lagrange multiplier to be informative. Furthermore, we propose a kind of penalty function method to derive the informative Lagrange multiplier in fully parametric programming models, which means that the perturbations are not only on the right-hand side of the constraints. Finally, we use examples to support our theoretic results.

关键词： parametric programming nonlinear programming informative lagrange multiplier shadow price penalty function method

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THE USE OF parametric programming IN FUZZY LINEAR-programming

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FUZZY SETS AND SYSTEMS 1983年第3期11卷 243-251页

作者： CHANAS, S Institute of Management Technical University Wrocław Poland

In this paper the possibility of the identification of a complete fuzzy decision (not only the maximizing alternative) in fuzzy linear programming by use of the parametric programming technique is presented. Also, it is shown that this fact can be useful in the Zimmermann approach to multiple objective linear programming. The presented remarks are illustrated by some numerical examples.

关键词： Fuzzy linear programming Multiple objective linear programming parametric programming

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Methodology of parametric programming for error compensation ora CNC centres

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2001年第8期17卷 570-574页

作者： Liu, ZQ Shandong Univ Technol Dept Mech Engn Jinan 250061 Peoples R China

Although work has been carried out on parametric programming on CNC centres, there have been few papers which focus on error compensation. parametric programming for error compensation is presented in this paper on the basis of a simple model of machining system deflections induced by the radial cutting force in CNC turning operations. The resulting errors are introduced as compensation values to the conventional tool movements along the programmed tool path. This can result in a complex tool path. parametric programming is applied to handle this complexity for error compensation.

关键词： error compensation machining error parametric programming turning

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Flexibility analysis and design using a parametric programming framework

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AICHE JOURNAL 2002年第12期48卷 2851-2868页

作者： Bansal, V Perkins, JD Pistikopoulos, EN Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2BY England

This article presents a new framework, based on parametric programming, that unifies the solution of the various flexibility analysis and design optimization problems that arise for linear, convex, and nonconvex, nonlinear systems with deterministic or stochastic uncertainties. This approach generalizes earlier work by Bansal et al. It allows (1) explicit information to be obtained on the dependence of the flexibility characteristics of a nonlinear system on the values of the uncertain parameters and design variables;(2) the critical uncertain parameter points to be identified a priori so that design optimization problems that do not require iteration between a design step and a flexibility analysis step can be solved;and (3) the nonlinearity to be removed from the optimization subproblems that need to be solved when evaluating the flexibility of systems with stochastic uncertainties.

关键词： .flexibility Design Optimization parametric programming uncertain parameters analysis and design upper bounds new framework based on parametric optimization subproblems

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Modeling fuzzy data envelopment analysis by parametric programming method

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EXPERT SYSTEMS WITH APPLICATIONS 2011年第7期38卷 8648-8663页

作者： Qin, Rui Liu, Yankui Liu, Zhi-Qiang Hebei Univ Coll Math & Comp Sci Baoding 071002 Peoples R China City Univ Hong Kong Sch Creat Media Hong Kong Hong Kong Peoples R China

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiency of decision making units (DMUs) consuming the same types of inputs and producing the same types of outputs. This paper studies the DEA models with type-2 data variations. In order to deal with the existed type-2 fuzziness, we propose the mean reduction methods for type-2 fuzzy variables. Based on the mean reductions of the type-2 fuzzy inputs and outputs, we formulate a new class of fuzzy generalized expectation DEA models. When the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we discuss the equivalent parametric forms for the constraints and the generalized expectation objective, where the parameters characterize the degree of uncertainty of the type-2 fuzzy coefficients so that the information cannot be lost via our reduction method. For any given parameters, the proposed model becomes nonlinear programming, which can be solved by standard optimization solvers. To illustrate the modeling idea and the efficiency of the proposed DEA model, we provide one numerical example. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Data envelopment analysis Type-2 fuzzy variable Reduction methods parametric programming

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Design of robust model-based controllers via parametric programming

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AUTOMATICA 2004年第2期40卷 189-201页

作者： Sakizlis, V Kakalis, NMP Dua, V Perkins, JD Pistikopoulos, EN Univ London Imperial Coll Sci Technol & Med Ctr Proc Syst Engn Dept Chem Engn London SW7 2AZ England

In this paper a method is presented for deriving the explicit robust model-based optimal control law for constrained linear dynamic systems. The controller is derived off-line via parametric programming before any actual process implementation takes place. The proposed control scheme guarantees feasible operation in the presence of bounded input uncertainties by (i) explicitly incorporating in the controller design stage a set of feasibility constraints and (ii) minimizing the nominal performance, or the expectation of the performance over the uncertainty space. An extension of the method to problems involving target point tracking in the presence of persistent disturbances is also discussed. The general concept is illustrated with two examples. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： model-based control parametric programming robust control feasibility analysis

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