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Solving scheduling problems under uncertainty using parametric programming

IFAC Proceedings Volumes 2001年第25期34卷 203-208页

作者： Jun-hyung Ryu Efstratios N. Pistikopoulos Centre for Process Systems Engineering Department of Chemical Engineering Imperial College London SW7 2BY U.K.

This work proposes a novel methodology to solve scheduling problems under uncertainty using parametric programming. Uncertainty, such as in processing times and equipment availabilities, is incorporated into scheduling models, which are then transformed into multi-parametric mixed integer linear programming (mp-MILP) problems. A solution procedure based upon recently proposed mp-MILP algorithms is then discussed. The key advantage of the proposed methodology is that the complete map of optimal schedules can be obtained as a function of varying parameters; rescheduling can thus be performed via simple function evaluations without any further optimization. Numerical examples are presented to illustrate the significance of the proposed methodology.

关键词： reactive scheduling uncertainty parametric programming

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The use of parametric programming and simulation-optimisation approaches for stochastic inventory control in the food markets under fuzzy deterioration rate

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年 168卷

作者： Sel, Cagri Karabuk Univ Dept Ind Engn Fac Engn TR-78050 Karabuk Turkey

In this study, we address the stochastic inventory control problem of green vegetables deteriorating in a fruit and vegetable wholesaler. The problem is to re-order green vegetables periodically to meet demand of the green markets. The aim is to decide the order quantity and the order-up-to level for each period minimising the total inventory cost. In the fruit and vegetable wholesaler, a staff separates the fresh and non-fresh products to sustain freshness in the green vegetable crates. The behaviour of the wholesaler staff on selecting the non-fresh green vegetables is personal reasoning that fuzzy logic can help to deal with the uncertainty. Accordingly, we introduce a stochastic integer linear programming model accounting for the uncertain demand. We represent the deterioration rate indicated in the model by fuzzy numbers and transform the resulting fuzzy model into an alpha-para-metric programming model. As a solution method, we propose a simulated annealing based simulation optimisation algorithm. The models and the heuristic algorithm are applied to a case study that reflects the real settings of a food market in Turkey. The numerical analysis is conducted on the case study to understand the effect of the fuzziness on the solution quality and time under varying cost parameters and deterioration rates. As a result, the numerical analyses demonstrate that the proposed models allow us better to estimate the total costs and the waste quantity. The heuristic algorithm yields near-optimal solutions. The solutions approach approximately 3% difference on average for the medium and long term decisions. The heuristic algorithm results in significantly shorter computation times compared to the proposed model.

关键词： Stochastic inventory control Fuzzy deterioration rate parametric programming Simulation-optimisation Simulated annealing algorithm

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Wind Farm Load Reduction via parametric programming Based Controller Design

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IFAC Proceedings Volumes 2011年第1期44卷 1704-1709页

作者： Vedrana Spudić Mato Baotić Nedjeljko Perić University of Zagreb Faculty of Electrical Engineering and Computing Unska 3 10000 Zagreb Croatia

Abstract We propose an optimization-based strategy for wind farm control. The objectives for the farm are to produce demanded power and to minimize the loads on mechanical parts of wind turbines that occur due to turbulent winds. The load reduction is achieved by dynamic adaptation of individual wind turbine power references to the current, turbulence induced, disturbances. However, the changes in operation of all wind turbines are coordinated to ensure that the wind farm produces power according to the grid operator demands. The pursued approach uses parametric programming to find the optimal control actions for the wind farm with respect to the constraints inherent to the system. The considered control design is also motivated by the need for efficient controller computation that will allow implementations on large wind farms.

关键词： wind farm control parametric programming constrained optimal control

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The Explicit Control Law for Hybrid Systems via parametric programming

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IFAC Proceedings Volumes 2001年第10期34卷 109-114页

作者： V. Sakizlis V. Dua N. Kakalis J.D. Perkins E.N. Pistikopoulos Centre for Process Systems Engineering Department of Chemical Engineering Imperial College London SW7 2BY U.K. Centre for Process Systems Engineering Department of Chemical Engineering Imperial College London SW7 2BY U.K. Tel: +44 20 7594 6620. Fax: +44 20 7594 6606.

In this paper an algorithm is presented for the derivation of the explicit optimal control policy for linear dynamic systems that also involve (i) discrete decisions and (ii) constraints on process inputs and outputs. The control actions are usually computed by solving regularly an on-line optimization problem based on a set of measurements that specify the current process state. The approach presented in this paper derives the optimal control law off-line as a function of the state of the process, thus eliminating the repetitive solution of on-line optimization problems. Hence, the on-line implementation is reduced to a sequence of simple function evaluations. The key advantageous features of the algorithm are demonstrated via an illustrative example.

关键词： Process control MPC quadratic programming parametric programming mixed integer optimization

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The Explicit Model-Based Tracking Control Law via parametric programming

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IFAC Proceedings Volumes 2004年第1期37卷 631-636页

作者： Vassilis Sakizlis John D. Perkins Efstratios N. Pistikopoulos Centre for Process Systems Engineering Department of Chemical Engineering Imperial College London South Kensington campus London SW7 2AZ U.K.

In this paper two methods are presented for deriving the explicit model-based tracking optimal control law for constrained linear dynamic systems subject to persistent disturbances. The first scheme augments explicitly the model dynamics with a set of integral states that are then readily incorporated with a positive definite penalty in the system performance measure. The second scheme employs a state observer for estimating the value of the disturbance and then computes the new state target. Then it shifts accordingly the state and control values to ensure asymptotic tracking. The underlying controller structure in both approaches is derived off-line via parametric programming before any actual process implementation takes place. The proposed control schemes guarantee steady-state offset elimination and optimal performance in the presence of unknown constant uncertainties.

关键词： Model predictive control parametric programming process control integral action observer

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More powerful conditional selective inference for generalized Lasso by parametric programming

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 13544-13580页

作者： Vo Nguyen Le Duy Ichiro Takeuchi Nagoya Institute of Technology and RIKEN Nagoya Aichi Japan Nagoya University and RIKEN Nagoya Aichi Japan

Conditional selective inference (SI) has been studied intensively as a new statistical inference framework for data-driven hypotheses. The basic concept of conditional SI is to make the inference conditional on the selection event, which enables an exact and valid statistical inference to be conducted even when the hypothesis is selected based on the data. Conditional SI has mainly been studied in the context of model selection, such as vanilla lasso or generalized lasso. The main limitation of existing approaches is the low statistical power owing to over-conditioning, which is required for computational tractability. In this study, we propose a more powerful and general conditional SI method for a class of problems that can be converted into quadratic parametric programming, which includes generalized lasso. The key concept is to compute the continuum path of the optimal solution in the direction of the selected test statistic and to identify the subset of the data space that corresponds to the model selection event by following the solution path. The proposed parametric programming-based method not only avoids the aforementioned major drawback of over-conditioning, but also improves the performance and practicality of SI in various respects. We conducted several experiments to demonstrate the effectiveness and efficiency of our proposed method.

关键词： generalized Lasso model selection selective inference parametric programming quadratic programming

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A parametric programming Method on Gaussian Type-2 Fuzzy Set and Its Application to a Multilevel Supply Chain

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INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 2016年第3期24卷 451-477页

作者： Jana, Dipak Kumar Pramanik, Sutapa Maiti, Manoranjan Haldia Inst Technol Dept Engn Sci Midna Pur 721657 W Bengal India Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore W Bengal India

The transportation problem is an important and relevant supply chain optimization problem in the traffic engineering. This paper minimizes shipping costs of a three channel distribution system comprised of plants, distribution centers, and customers. Plants manufacture several products that are delivered to distribution centers. If a distribution center is used then fixed cost is charged. Customers are replenished by an only one distribution center. To characterize the uncertainty that typically occurs in many practical decision environments, this paper considers the supply capacities, demands as Gaussian type-2 fuzzy variables. To provide a modelling framework for optimization problems with multi-fold uncertainty, different reduction methods are proposed to transform a Gaussian type-2 fuzzy variable into a type-1 fuzzy variable by mean reduction method. Then the transportation problem is reformulated as a chance-constrained expected value model enlightened by the credibility optimization method. The deterministic models are then solved using two different soft computing techniques (i) Generalized Reduced Gradient (Lingo-14.0), and (ii) modified Particle Swarm Optimization(PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. The numerical experiments illustrate the application and effectiveness of the proposed solution approaches.

关键词： Supply chain transportation problem particle swam optimization fuzzy type-2 variables parametric programming

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A logarithmic-time solution to the point location problem for parametric linear programming

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AUTOMATICA 2006年第12期42卷 2215-2218页

作者： Jones, C. N. Grieder, P. Rakovic, S. V. Univ Cambridge Dept Engn Control Grp Cambridge CB2 1PZ England Swiss Fed Inst Technol Automat Control Lab CH-8092 Zurich Switzerland Univ London Imperial Coll Sci Technol & Med London SW7 2BT England

The optimiser of a (multi) parametric linear program (pLP) is a piecewise affine function defined over a polyhedral subdivision of the set of feasible states. Once this affine function has been pre-calculated, the optimal solution can be computed for a particular parameter by determining the region that contains it. This is the so-called point location problem. In this paper, we show that this problem can be written as an additively weighted nearest neighbour search that can be solved in time linear in the dimension of the state space and logarithmic in the number of regions. It is well-known that linear model predictive control (MPC) problems based on linear control objectives (e.g., l- or infinity-norm) can be posed as pLPs, and on-line calculation of the control law involves the solution to the point location problem. Several orders of magnitude sampling speed improvement are demonstrated over traditional MPC and closed-form MPC schemes using the proposed scheme. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： predictive control parametric programming controller complexity

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Optimizing fuzzy portfolio selection problems by parametric quadratic programming

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FUZZY OPTIMIZATION AND DECISION MAKING 2012年第4期11卷 411-449页

作者： Wu, Xiao-Li Liu, Yan-Kui Hebei Univ Coll Math & Comp Sci Key Lab Machine Learning & Computat Intelligence Baoding 071002 Hebei Peoples R China

This paper develops a robust method to describe fuzzy returns by employing parametric possibility distributions. The parametric possibility distributions are obtained by equivalent value (EV) reduction methods. For common type-2 triangular and trapezoidal fuzzy variables, their reduced fuzzy variables are studied in the current development. The parametric possibility distributions of reduced fuzzy variables are first derived, then the second moment formulas for the reduced fuzzy variables are established. Taking the second moment as a new risk measure, the reward-risk and risk-reward models are developed to optimize fuzzy portfolio selection problems. The mathematical properties of the proposed optimization models are analyzed, including the analytical representations for the second moments of linear combinations of reduced fuzzy variables as well as the convexity of second moments with respect to decision vectors. On the basis of the analytical representations for the second moments, the reward-risk and risk-reward models can be turned into their equivalent parametric quadratic convex programming problems, which can be solved by conventional solution methods or general-purpose software. Finally, some numerical experiments are performed to demonstrate the new modeling ideas and the efficiency of solution method.

关键词： Portfolio selection Reduced fuzzy variable parametric possibility distribution Moment parametric programming

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OBSERVATIONS ON THE APPLICATION AND DEVELOPMENT OF parametric-programming TECHNIQUES

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COMPUTER-AIDED DESIGN 1992年第10期24卷 541-546页

作者： MCMAHON, CA LEHANE, K WILLIAMS, JHS WEBBER, G TRW STEERING SYST LTD CLEVEDON BS21 6NJAVONENGLAND UNIV BRISTOL DEPT ENGN MATHBRISTOL BS8 1TRAVONENGLAND

A parametric program may use rules and algorithms to define the relationships between dimensions and elements of designs, and it may thus generate variants of a design. Programs currently in use have technical limitations in their ability to handle time-varying and imprecise data, the search for suitable existing designs and their maintain-ability. The paper suggests how these and other limitations can be overcome to widen the field of application of parametric programs.

关键词： DESIGN AUTOMATION VARIANT DESIGN parametric programming parametric METHODS

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