The Experts below are selected from a list of 15456 Experts worldwide ranked by ideXlab platform

Efstratios N. Pistikopoulos - One of the best experts on this subject based on the ideXlab platform.

  • hy pop hyperparameter optimization of machine learning models through Parametric Programming
    Computers & Chemical Engineering, 2020
    Co-Authors: William W Tso, Baris Burnak, Efstratios N. Pistikopoulos
    Abstract:

    Abstract 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 L1-norm support vector machine (SVM) are derived and validated on example data.

  • a multi Parametric optimization approach for bilevel mixed integer linear and quadratic Programming problems
    Computers & Chemical Engineering, 2019
    Co-Authors: Styliani Avraamidou, Efstratios N. Pistikopoulos
    Abstract:

    Abstract Optimization problems involving two decision makers at two different decision levels are referred to as bi-level Programming problems. In this work, we present novel algorithms for the exact and global solution of two classes of bi-level Programming problems, namely (i) bi-level mixed-integer linear Programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic Programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-Parametric Programming theory, the main idea is to recast the lower level problem as a multi-Parametric Programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-Parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.

  • Adjustable robust optimization through multi-Parametric Programming
    Optimization Letters, 2019
    Co-Authors: Styliani Avraamidou, Efstratios N. Pistikopoulos
    Abstract:

    Adjustable robust optimization (ARO) involves recourse decisions (i.e. reactive actions after the realization of the uncertainty, ‘wait-and-see’) as functions of the uncertainty, typically posed in a two-stage stochastic setting. Solving the general ARO problems is challenging, therefore ways to reduce the computational effort have been proposed, with the most popular being the affine decision rules, where ‘wait-and-see’ decisions are approximated as affine adjustments of the uncertainty. In this work we propose a novel method for the derivation of generalized affine decision rules for linear mixed-integer ARO problems through multi-Parametric Programming, that lead to the exact and global solution of the ARO problem. The problem is treated as a multi-level Programming problem and it is then solved using a novel algorithm for the exact and global solution of multi-level mixed-integer linear Programming problems. The main idea behind the proposed approach is to solve the lower optimization level of the ARO problem Parametrically, by considering ‘here-and-now’ variables and uncertainties as parameters. This will result in a set of affine decision rules for the ‘wait-and-see’ variables as a function of ‘here-and-now’ variables and uncertainties for their entire feasible space. A set of illustrative numerical examples are provided to demonstrate the potential of the proposed novel approach.

  • On unbounded and binary parameters in multi-Parametric Programming: applications to mixed-integer bilevel optimization and duality theory
    Journal of Global Optimization, 2017
    Co-Authors: Richard Oberdieck, Styliani Avraamidou, Nikolaos A Diangelakis, Efstratios N. Pistikopoulos
    Abstract:

    In multi-Parametric Programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of strictly convex multi-Parametric quadratic Programming (mp-QP) problems with affine constraints to investigate problems where these conditions are not met. Based on the combinatorial solution approach for mp-QP problems featuring bounded and continuous parameters, we show that (i) for unbounded parameters, it is possible to obtain the multi-Parametric solution if there exists one realization of the parameters for which the optimization problem can be solved and (ii) for binary parameters, we present the equivalent mixed-integer formulations for the application of the combinatorial algorithm. These advances are combined into a new, generalized version of the combinatorial algorithm for mp-QP problems, which enables the solution of problems featuring both unbounded and binary parameters. This novel approach is applied to mixed-integer bilevel optimization problems and the Parametric solution of the dual of a convex problem.

  • process design and control optimization a simultaneous approach by multi Parametric Programming
    Aiche Journal, 2017
    Co-Authors: Nikolaos A Diangelakis, Baris Burnak, Justin Katz, Efstratios N. Pistikopoulos
    Abstract:

    We present a framework for the application of design and control optimization via multiParametric Programming through four case studies. We develop design dependent multi-Parametric model predictive controllers that are able to provide the optimal control actions as functions of the system state and the design of the process at hand, via our recently introduced PAROC framework1. The process and the design dependent explicit controllers undergo a Mixed Integer Dynamic Optimization (MIDO) step for the determination of the optimal design. The result of the MIDO is the optimal design of the process under optimal operation. We demonstrate the framework through case studies of a tank, a continuously stirred tank reactor, a binary distillation column and a residential cogeneration unit. This article is protected by copyright. All rights reserved.

Vivek Dua - One of the best experts on this subject based on the ideXlab platform.

  • multi Parametric mixed integer linear Programming under global uncertainty
    Computers & Chemical Engineering, 2018
    Co-Authors: Vassilis M Charitopoulos, Lazaros G Papageorgiou, Vivek Dua
    Abstract:

    Major application areas of the process systems engineering, such as hybrid control, scheduling and synthesis can be formulated as mixed integer linear Programming (MILP) problems and are naturally susceptible to uncertainty. Multi-Parametric Programming theory forms an active field of research and has proven to provide invaluable tools for decision making under uncertainty. While uncertainty in the right-hand side (RHS) and in the objective function's coefficients (OFC) have been thoroughly studied in the literature, the case of left-hand side (LHS) uncertainty has attracted significantly less attention mainly because of the computational implications that arise in such a problem. In the present work, we propose a novel algorithm for the analytical solution of multi-Parametric MILP (mp-MILP) problems under global uncertainty, i.e. RHS, OFC and LHS. The exact explicit solutions and the corresponding regions of the Parametric space are computed while a number of case studies illustrates the merits of the proposed algorithm.

  • nonlinear model based process operation under uncertainty using exact Parametric Programming
    Engineering, 2017
    Co-Authors: Vassilis M Charitopoulos, Lazaros G Papageorgiou, Vivek Dua
    Abstract:

    Abstract In the present work, two new, (multi-)Parametric Programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear Programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the Parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters.

  • approximate multi Parametric Programming based b b algorithm for minlps
    Computers & Chemical Engineering, 2012
    Co-Authors: Taoufiq Gueddar, Vivek Dua
    Abstract:

    In this work an improved B&B algorithm for MINLPs is proposed. The basic idea of the proposed algorithm is to treat binary variables as parameters and obtain the solution of the resulting multi-Parametric NLP (mp-NLP) as a function of the binary variables, relaxed as continuous variables, at the root node of the search tree. It is recognized that solving the mp-NLP at the root node can be more computationally expensive than exhaustively enumerating all terminal nodes of the tree. Therefore, only a local approximate Parametric solution, and not a complete map of the Parametric solution, is obtained and it is then used to guide the search in the tree.

  • multi Parametric Programming theory algorithms and applications
    2007
    Co-Authors: Efstratios N. Pistikopoulos, Michael C Georgiadis, Vivek Dua
    Abstract:

    Preface-Volume 1: MultiParametric Programming. List of Authors. Related Titles. Part I Theory and Algorithms. 1 MultiParametric Linear and Quadratic Programming. 1.1 Introduction. 1.2 Methodology. 1.3 Numerical Examples. 1.3.1 Example 1: Crude Oil Refinery. 1.3.2 Example 2: Milk Surplus. 1.3.3 Example 3: Model-Based Predictive Control. 1.4 Computational Complexity. 1.5 Concluding Remarks. Acknowledgments. Appendix A. Redundancy Check for a Set of Linear Constraints. Appendix B. Definition of Rest of the Region. Literature. 2 MultiParametric Nonlinear Programming. 2.1 Introduction. 2.1.1 Motivating Example. 2.2 The mp-NLP Algorithm. 2.3 Example. 2.4 Global Optimization Issues. 2.4.1 Remarks and Observations on the Application of the mp-NLP Algorithm for Problem (2.8). 2.4.2 Algorithm for MultiParametric Nonlinear Programming. 2.4.3 Example (2.8) Solved with the New Algorithm. 2.4.4 Extension to Higher Order Spaces and Higher Order Objective Functions. 2.5 Concluding Remarks. Appendix A. Infeasibility of Corners. Appendix B. Comparison Procedure. Appendix C. Definition of the Rest of the Region. Appendix D. Redundancy Test. Appendix E. Vertices of a Critical Region. Acknowledgments. Literature. 3 MultiParametric Mixed-Integer Linear Programming. 3.1 Parametric Mixed-Integer Linear Programming. 3.2 MultiParametric Mixed-Integer Linear Programming. Branch and Bound Approach. 3.3 MultiParametric Mixed-Integer Linear Programming. Parametric and Integer Cuts. 3.3.1 Initialization. 3.3.2 MultiParametric LP Subproblem. 3.3.3 MILP Subproblem. 3.3.4 Comparison of Parametric Solutions. 3.3.5 MultiParametric MILP Algorithm. 3.4 Numerical Example. 3.5 Concluding Remarks. Appendix A. Definition of an Infeasible Region. Literature. 4 MultiParametric Mixed-Integer Quadratic and Nonlinear Programming. 4.1 Introduction. 4.2 Methodology. 4.3 The mp-MIQP Algorithm. 4.3.1 Initialization. 4.3.2 Primal Subproblem. 4.3.3 Master Subproblem. 4.3.4 Strategy for the Solution of the Master Subproblem. 4.3.5 Envelope of Solutions. 4.3.6 Redundant Profiles. 4.4 The mp-MINLP Algorithm. 4.4.1 Initialization. 4.4.2 Primal Subproblem. 4.4.3 Master Subproblem 82 4.4.4 Remarks and Summary of the Algorithm. 4.5 Examples. 4.5.1 Example on mp-MIQP. 4.5.2 Example on mp-MINLP. 4.6 Concluding Remarks. Acknowledgment. Literature. 5 Parametric Global Optimization. 5.1 Introduction. 5.2 Parametric Global Optimization. 5.2.1 B&B Algorithm. 5.2.2 MultiParametric Convex Nonlinear Programs. 5.3 MultiParametric Nonconvex Nonlinear Programming. 5.3.1 Motivating Examples. 5.3.2 An Algorithm for MultiParametric Nonconvex Nonlinear Programming. 5.4 MultiParametric Mixed-Integer Nonconvex Programming. 5.5 Numerical Examples. 5.5.1 Example 1. 5.5.2 Example 2. 5.6 Concluding Remarks. Acknowledgments. Appendix A. Comparison of Parametric Solutions. Appendix B. Definition of Rest of the Region. Literature. 6 Bilevel and Multilevel Programming. 6.1 Introduction. 6.1.1 Global Optimum of a Bilevel Programming Problem. 6.2 Quadratic Bilevel Programming. 6.2.1 LP|LP Bilevel Programming Problem. 6.2.2 LP|QP Bilevel Programming Problem. 6.2.3 QP|QP Bilevel Programming Problem. 6.3 Bilevel Programming with Uncertainty. 6.4 Mixed-Integer Bilevel Programming. 6.5 Other Multilevel Optimization Problems. 6.5.1 Three-Level Programming Problem. 6.5.2 Bilevel Multifollower Programming Problem. 6.6 Concluding Remarks. Acknowledgments. Appendix A. Literature. 7 Dynamic Programming. 7.1 Introduction. 7.2 Constrained Dynamic Programming. 7.3 Illustrative Examples. 7.4 Complexity Analysis. 7.5 Concluding Remarks. Acknowledgments. Literature. Part II Applications. 8 Flexibility Analysis via Parametric Programming. 8.1 Introduction. 8.2 Flexibility Test and Index for Linear Systems. 8.2.1 Parametric Programming Approach. 8.2.2 Algorithm 8.1. 8.2.3 Illustrative Example. 8.2.4 Remarks on Algorithm 8.1. 8.2.5 Design Optimization of Linear Systems. 8.3 Stochastic Flexibility of Linear Systems. 8.3.1 Parametric Programming Approach. 8.3.2 Algorithm 8.2. 8.3.3 Illustrative Example. 8.3.4 Remarks on Algorithm 8.2. 8.4 Expected Stochastic Flexibility of Linear Systems. 8.5 Process Example 8.1: Chemical Complex. 8.5.1 Flexibility Test and Index. 8.5.2 Design with Optimal Degree of Flexibility. 8.5.3 Expected Stochastic Flexibility. 8.6 Process Example 8.2: HEN with 2 Hot, 2 Cold Streams. 8.6.1 Flexibility Test and Index. 8.6.2 Stochastic Flexibility. 8.7 Process Example 8.3: HEN with 4 Hot, 3 Cold Streams. 8.7.1 Flexibility Test and Index. 8.7.2 Stochastic Flexibility. 8.8 Incorporation of Discrete Decisions. 8.9 Extension to Multipurpose Processes. 8.10 Flexibility Test and Index for Convex Nonlinear Systems. 8.10.1 Parametric Programming Approach. 8.10.2 Algorithm 8.3. 8.10.3 Illustrative Example. 8.10.4 Remarks on Algorithm 8.3. 8.11 Design Optimization of Nonlinear Convex Systems. 8.12 Stochastic Flexibility of Nonlinear Convex Systems. 8.12.1 Algorithm 8.4. 8.12.2 Illustrative Example. 8.13 Flexibility Test and Index for Nonlinear Nonconvex Systems. 8.13.1 Parametric Programming Approach. 8.13.2 Algorithm 8.5. 8.13.3 Process Example 8.4. 8.14 Summary and Conclusions. Literature. 9 Planning and Material Design Under Uncertainty. 9.1 Introduction. 9.2 Process Planning Under Uncertainty. 9.3 Supply Chain Planning Under Uncertainty. 9.4 Hierarchical Decision Planning. 9.5 Material Design Under Uncertainty. 9.5.1 Material Design Example. 9.6 Concluding Remarks. Acknowledgments. Literature. 10 Multiobjective Energy and Environmental Analysis. 10.1 Introduction. 10.2 Review of Hydrogen Infrastructure Studies. 10.3 Motivation. 10.4 Methodology and Model Overview. 10.5 Model Formulation. 10.5.1 Centralized Production Sites and Technologies. 10.5.2 Distribution Network. 10.5.3 Forecourt Markets. 10.5.4 Net Present Value Objective Function. 10.5.5 Greenhouse Gas Emissions Objective Function. 10.5.6 Model Summary. 10.6 Solution Method. 10.6.1 Model Decomposition Algorithm. 10.6.2 Solution Time Comparison. 10.7 Illustrative Example. 10.7.1 Problem Formulation. 10.7.2 Trade-Off Analysis Results. 10.7.3 Constrained Roadmap Comparisons. 10.8 Conclusions. Literature. Index.

  • a bilevel Programming framework for enterprise wide process networks under uncertainty
    Computers & Chemical Engineering, 2004
    Co-Authors: Junhyung Ryu, Vivek Dua, Efstratios N. Pistikopoulos
    Abstract:

    Abstract Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a multi-level decision network structure can be mathematically represented by using multi-level Programming principles. In this paper, we specifically address bilevel decision-making problems under uncertainty in the context of enterprise-wide supply chain optimization with one level corresponding to a plant planning problem, while the other to a distribution network problem. We first describe how such problems can be modelled as bilevel Programming problems and then we present an effective solution strategy based on Parametric Programming techniques. An attractive feature of the proposed strategy is the fact that it transforms the bilevel problem into a family of single Parametric optimization problems, which can be solved to global optimality. A numerical example is presented to illustrate the proposed framework.

Richard Oberdieck - One of the best experts on this subject based on the ideXlab platform.

  • On unbounded and binary parameters in multi-Parametric Programming: applications to mixed-integer bilevel optimization and duality theory
    Journal of Global Optimization, 2017
    Co-Authors: Richard Oberdieck, Styliani Avraamidou, Nikolaos A Diangelakis, Efstratios N. Pistikopoulos
    Abstract:

    In multi-Parametric Programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of strictly convex multi-Parametric quadratic Programming (mp-QP) problems with affine constraints to investigate problems where these conditions are not met. Based on the combinatorial solution approach for mp-QP problems featuring bounded and continuous parameters, we show that (i) for unbounded parameters, it is possible to obtain the multi-Parametric solution if there exists one realization of the parameters for which the optimization problem can be solved and (ii) for binary parameters, we present the equivalent mixed-integer formulations for the application of the combinatorial algorithm. These advances are combined into a new, generalized version of the combinatorial algorithm for mp-QP problems, which enables the solution of problems featuring both unbounded and binary parameters. This novel approach is applied to mixed-integer bilevel optimization problems and the Parametric solution of the dual of a convex problem.

  • on multi Parametric Programming and its applications in process systems engineering
    Chemical Engineering Research & Design, 2016
    Co-Authors: Styliani Avraamidou, Nikolaos A Diangelakis, Richard Oberdieck, Ioana Nascu, Maria M Papathanasiou, Efstratios N. Pistikopoulos
    Abstract:

    Abstract In multi-Parametric Programming, an optimization problem is solved for a range and as a function of multiple parameters. In this review, we discuss the main developments of multi-Parametric Programming over the last two decades from a theoretical, algorithmic and application perspective. In addition, we provide an opinionated view of the future research directions in multi-Parametric Programming.

  • multi objective optimization with convex quadratic cost functions a multi Parametric Programming approach
    Computers & Chemical Engineering, 2016
    Co-Authors: Richard Oberdieck, Efstratios N. Pistikopoulos
    Abstract:

    Abstract In this note we present an approximate algorithm for the explicit calculation of the Pareto front for multi-objective optimization problems featuring convex quadratic cost functions and linear constraints based on multi-Parametric Programming and employing a set of suitable overestimators with tunable suboptimality. A numerical example as well as a small computational study highlight the features of the novel algorithm.

  • parallel computing in multi Parametric Programming
    Computer-aided chemical engineering, 2016
    Co-Authors: Richard Oberdieck, Efstratios N. Pistikopoulos
    Abstract:

    Abstract In multi-Parametric Programming, an optimization problem is solved as a function of certain bounded parameters. Hence it requires the exploration of the corresponding parameter space, a procedure which inherently leads to independent subproblems to be solved for each part of the parameter space. This characteristic is used to develop a parallelization strategy for many classes of multi-Parametric Programming algorithms. The trade-off between information overhead and independence of each machine is addressed explicitly through the introduction of a user-defined parameter. This novel approach is applied to a geometrical multi-Parametric quadratic Programming algorithm; a computational study as well as the application to a combined heat and power heat recovery subsystem show the benefits of the developed approach.

  • paroc an integrated framework and software platform for the optimisation and advanced model based control of process systems
    Chemical Engineering Science, 2015
    Co-Authors: Efstratios N. Pistikopoulos, Nikolaos A Diangelakis, Richard Oberdieck, Maria M Papathanasiou, Ioana Nascu
    Abstract:

    Abstract In this paper we present the main foundations and features of an integrated framework and software platform that enables the use of model-based tools in design, operational optimisation and advanced control studies. A step-wise procedure is outlined involving (i) the development of a high-fidelity dynamic model, and its validation and model analysis, (ii) a model approximation step, including system identification, model reduction and global sensitivity analysis, (iii) a receding horizon modelling step for model-predictive control (MPC) and reactive scheduling, (iv) a suite of multi-Parametric Programming techniques for optimisation under uncertainty, explicit/multi-Parametric MPC and state-estimation and (v) an ‘in-silico’ validation step for the derived optimisation, control and/or scheduling strategies to be analysed within the original high-fidelity model. The proposed software platform, PAROC, is also introduced and demonstrated in three different classes of process systems engineering applications; a combined heat and power energy system, a distillation column and a periodic purification process for biopharmaceuticals.

Tor Arne Johansen - One of the best experts on this subject based on the ideXlab platform.

  • further results on the exploration of combinatorial tree in multi Parametric quadratic Programming
    European Control Conference, 2016
    Co-Authors: Parisa Ahmadimoshkenani, Sorin Olaru, Tor Arne Johansen
    Abstract:

    A combinatorial approach has been recently proposed for multi-Parametric quadratic Programming and has shown to be more effective in finding the complete solution than existing geometric methods for higher-order systems. In this paper, we propose a method for exploring the combinatorial tree which exploits some of the underlying geometric properties of adjacent critical regions as the supplementary information in combinatorial approach to exclude a noticeable number of feasible candidate active sets from combinatorial tree. This method is particularly well-suited for cases where many combinations of active constraints are feasible but not optimal. Results indicate that this method can find all critical regions corresponding to non-degenerate multi-Parametric Programming. A postprocessing algorithm can be applied to complete the proposed method in the cases in which some critical regions might not be enumerated due to degeneracies in the problem.

  • brief paper using hash tables to manage the time storage complexity in a point location problem application to explicit model predictive control
    Automatica, 2011
    Co-Authors: Farhad Bayat, Tor Arne Johansen, Ali Akbar Jalali
    Abstract:

    The online computational burden of linear model predictive control (MPC) can be moved offline by using multi-Parametric Programming, so-called explicit MPC. The solution to the explicit MPC problem is a piecewise affine (PWA) state feedback function defined over a polyhedral subdivision of the set of feasible states. The online evaluation of such a control law needs to determine the polyhedral region in which the current state lies. This procedure is called point location; its computational complexity is challenging, and determines the minimum possible sampling time of the system. A new flexible algorithm is proposed which enables the designer to trade off between time and storage complexities. Utilizing the concept of hash tables and the associated hash functions, the proposed method solves an aggregated point location problem that overcomes prohibitive complexity growth with the number of polyhedral regions, while the storage-processing trade-off can be optimized via scaling parameters. The flexibility and power of this approach is supported by several numerical examples.

  • fault tolerant control allocation for a thruster controlled floating platform using Parametric Programming
    Conference on Decision and Control, 2009
    Co-Authors: J Spjotvold, Tor Arne Johansen
    Abstract:

    The task in control allocation is to allocate a specified generalized force to a redundant set of control effectors where the associated actuator control inputs are constrained, and other physical and operational constraints and objectives should be met. In this paper we consider a convex quadratic approximation to a control allocation problem for a thruster-controlled floating platform with eight rotatable azimuth thrusters where the high level controller is assumed to specify three generalized forces; surge, sway and yaw. The optimization problem is solved explicitly by viewing the generalized forces as a vector of parameters and utilizing Parametric Programming techniques, leading to a continuous piecewise affine (PWA) function implementing the optimal control allocation. Experimental results from a test basin with a 1∶100 scale model of a platform are presented. It is shown how thruster and machinery failure scenarios can be handled by automatic reconfiguration of the control allocation, exploiting symmetry of the thruster configuration.

  • hardware synthesis of explicit model predictive controllers
    IEEE Transactions on Control Systems and Technology, 2007
    Co-Authors: Tor Arne Johansen, W B Jackson, R Schreiber, P Tondel
    Abstract:

    The general solution to constrained linear and piecewise linear model predictive control (MPC) has recently been explicitly characterized in terms of piecewise-linear (PWL) state feedback control. This means that a PWL controller can be precomputed using Parametric Programming, and the exact explicit MPC implementation amounts to the evaluation of a PWL function in the control unit. It has recently been shown that PWL function evaluation can be accelerated by searching a binary tree data structure, leading to highly efficient, accurate, and verifiable software implementation in low-cost embedded control units. In this work, we report hardware synthesis results for this type of PWL control, and show that explicit MPC solutions can be implemented in an application specific integrated circuit (ASIC) with about 20 000 gates, leading to computation times in the microsecond scale. This opens the way for the use of highly advanced control designs such as constrained MPC in small-scale industrial and consumer electronics application areas that are characterized by fast sampling or low cost, including mechatronics, microelectromechanical systems (MEMS), automotive control, power electronics, and acoustics. The main limitation of the approach is that the memory requirements increase rapidly with the problem dimensions

Styliani Avraamidou - One of the best experts on this subject based on the ideXlab platform.

  • a multi Parametric optimization approach for bilevel mixed integer linear and quadratic Programming problems
    Computers & Chemical Engineering, 2019
    Co-Authors: Styliani Avraamidou, Efstratios N. Pistikopoulos
    Abstract:

    Abstract Optimization problems involving two decision makers at two different decision levels are referred to as bi-level Programming problems. In this work, we present novel algorithms for the exact and global solution of two classes of bi-level Programming problems, namely (i) bi-level mixed-integer linear Programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic Programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-Parametric Programming theory, the main idea is to recast the lower level problem as a multi-Parametric Programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-Parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.

  • Adjustable robust optimization through multi-Parametric Programming
    Optimization Letters, 2019
    Co-Authors: Styliani Avraamidou, Efstratios N. Pistikopoulos
    Abstract:

    Adjustable robust optimization (ARO) involves recourse decisions (i.e. reactive actions after the realization of the uncertainty, ‘wait-and-see’) as functions of the uncertainty, typically posed in a two-stage stochastic setting. Solving the general ARO problems is challenging, therefore ways to reduce the computational effort have been proposed, with the most popular being the affine decision rules, where ‘wait-and-see’ decisions are approximated as affine adjustments of the uncertainty. In this work we propose a novel method for the derivation of generalized affine decision rules for linear mixed-integer ARO problems through multi-Parametric Programming, that lead to the exact and global solution of the ARO problem. The problem is treated as a multi-level Programming problem and it is then solved using a novel algorithm for the exact and global solution of multi-level mixed-integer linear Programming problems. The main idea behind the proposed approach is to solve the lower optimization level of the ARO problem Parametrically, by considering ‘here-and-now’ variables and uncertainties as parameters. This will result in a set of affine decision rules for the ‘wait-and-see’ variables as a function of ‘here-and-now’ variables and uncertainties for their entire feasible space. A set of illustrative numerical examples are provided to demonstrate the potential of the proposed novel approach.

  • On unbounded and binary parameters in multi-Parametric Programming: applications to mixed-integer bilevel optimization and duality theory
    Journal of Global Optimization, 2017
    Co-Authors: Richard Oberdieck, Styliani Avraamidou, Nikolaos A Diangelakis, Efstratios N. Pistikopoulos
    Abstract:

    In multi-Parametric Programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of strictly convex multi-Parametric quadratic Programming (mp-QP) problems with affine constraints to investigate problems where these conditions are not met. Based on the combinatorial solution approach for mp-QP problems featuring bounded and continuous parameters, we show that (i) for unbounded parameters, it is possible to obtain the multi-Parametric solution if there exists one realization of the parameters for which the optimization problem can be solved and (ii) for binary parameters, we present the equivalent mixed-integer formulations for the application of the combinatorial algorithm. These advances are combined into a new, generalized version of the combinatorial algorithm for mp-QP problems, which enables the solution of problems featuring both unbounded and binary parameters. This novel approach is applied to mixed-integer bilevel optimization problems and the Parametric solution of the dual of a convex problem.

  • on multi Parametric Programming and its applications in process systems engineering
    Chemical Engineering Research & Design, 2016
    Co-Authors: Styliani Avraamidou, Nikolaos A Diangelakis, Richard Oberdieck, Ioana Nascu, Maria M Papathanasiou, Efstratios N. Pistikopoulos
    Abstract:

    Abstract In multi-Parametric Programming, an optimization problem is solved for a range and as a function of multiple parameters. In this review, we discuss the main developments of multi-Parametric Programming over the last two decades from a theoretical, algorithmic and application perspective. In addition, we provide an opinionated view of the future research directions in multi-Parametric Programming.