•We present novel algorithms for the exact and global solution of two classes of bi-level programming problems:(i)Bi-level mixed-integer linear programming problems (B-MILP).(ii)Bi-level ...mixed-integer convex quadratic programming problems (B-MIQP).•The bi-level problems concidered can containing both integer and bounded continuous variables at both optimization levels.•Extensions of the developed approaches for bi-level problems with right hand side uncertainty are also presented.
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.
•p-ARGONAUT is extended towards constrained multi-objective optimization problems.•Data-driven approach is followed to optimize an energy market design problem.•The accuracy and consistency of the ...method is evaluated under equality constraints.•Computational results are compared with a number of available software.
The (global) optimization of energy systems, commonly characterized by high-fidelity and large-scale complex models, poses a formidable challenge partially due to the high noise and/or computational expense associated with the calculation of derivatives. This complexity is further amplified in the presence of multiple conflicting objectives, for which the goal is to generate trade-off compromise solutions, commonly known as Pareto-optimal solutions. We have previously introduced the p-ARGONAUT system, parallel AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems, which is designed to optimize general constrained single-objective grey-box problems by postulating accurate and tractable surrogate formulations for all unknown equations in a computationally efficient manner. In this work, we extend p-ARGONAUT towards multi-objective optimization problems and test the performance of the framework, both in terms of accuracy and consistency, under many equality constraints. Computational results are reported for a number of benchmark multi-objective problems and a case study of an energy market design problem for a commercial building, while the performance of the framework is compared with other derivative-free optimization solvers.
Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic ...interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed‐integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed‐loop implementation. We use multi‐parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base‐2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.
•A novel data-driven framework using nonlinear Support Vector Machine-based feature selection is proposed for fault detection and diagnosis in batch processes.•The proposed framework is applied on a ...comprehensive benchmark dataset comprising of 22,600 batches with 15 faults, and normal operation.•Fault and time-specific models are trained for simultaneous fault detection and diagnosis with three distinct time horizon approaches: one-step rolling, two-step rolling and evolving.
This paper presents a novel data-driven framework for process monitoring in batch processes, a critical task in industry to attain a safe operability and minimize loss of productivity and profit. We exploit high dimensional process data with nonlinear Support Vector Machine-based feature selection algorithm, where we aim to retrieve the most informative process measurements for accurate and simultaneous fault detection and diagnosis. The proposed framework is applied to an extensive benchmark data set which includes process data describing 22,200 batches with 15 faults. We train fault and time-specific models on the pre-aligned batch data trajectories via three distinct time horizon approaches: one-step rolling, two-step rolling, and evolving which varies the amount of data incorporation during modeling. The results show that two-step rolling and evolving time horizon approaches perform superior to the other. Regardless of the approach, proposed framework provides a promising decision support tool for online simultaneous fault detection and diagnosis for batch processes.
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.
Smart manufacturing and energy systems Edgar, Thomas F.; Pistikopoulos, Efstratios N.
Computers & chemical engineering,
06/2018, Letnik:
114, Številka:
C
Journal Article
Recenzirano
Odprti dostop
•Advances in smart manufacturing are covered in the context of PSE tool application.•Systems interface with smart manufacturing apps through a vendor agnostic platform.•Smart manufacturing apps ...employ high fidelity models, cybersecurity, and optimization algorithms.•Smart manufacturing can increase energy productivity and maintain product quality.•Goals are described for newly established Department of Energy manufacturing institute.
While many U.S. manufacturing operations utilize optimization for individual unit processes, smart manufacturing (SM) systems that integrate manufacturing intelligence in real time across an entire production operation are not pervasive in industry. A vendor-agnostic SM platform is under development that integrates information technology, models, and simulations driven by real-time plant data and performance metrics. By utilizing existing process control and automation systems, manufacturing organizations can manage systems at a much lower cost, optimizing process knowledge and improving energy productivity. Three case studies are presented: steam methane reforming to make hydrogen, optimization of a heat treatment furnace for metals processing, and a fuel cell system, all of which utilize high fidelity models as a starting point for optimization and control. The Smart Manufacturing Leadership Coalition has led the national effort in SM, and the recently established National Manufacturing Innovation Institute funded by DOE, private industry, and state governments will be described.
A unified theory and framework for the integration of process design, control, and scheduling based on a single high fidelity model is presented. The framework features (i) a mixed-integer dynamic ...optimization (MIDO) formulation with design, scheduling, and control considerations, and (ii) a multiparametric optimization strategy for the derivation of offline/explicit maps of optimal receding horizon policies. Explicit model predictive control schemes are developed as a function of design and scheduling decisions, and similarly design dependent scheduling policies are derived accounting for the closed-loop dynamics. Inherent multi-scale gap issues are addressed by an offline design dependent surrogate model. The proposed framwork is illustrated by two example problems, a system of two continuous stirred tank reactor, and a small residential combined heat and power (CHP) network.
► The optimal design of distributed energy systems under uncertainty is studied. ► A stochastic model is developed using genetic algorithm and Monte Carlo method. ► The proposed system possesses ...inherent robustness under uncertainty. ► The inherent robustness is due to energy storage facilities and grid connection.
A distributed energy system is a multi-input and multi-output energy system with substantial energy, economic and environmental benefits. The optimal design of such a complex system under energy demand and supply uncertainty poses significant challenges in terms of both modelling and corresponding solution strategies. This paper proposes a two-stage stochastic programming model for the optimal design of distributed energy systems. A two-stage decomposition based solution strategy is used to solve the optimization problem with genetic algorithm performing the search on the first stage variables and a Monte Carlo method dealing with uncertainty in the second stage. The model is applied to the planning of a distributed energy system in a hotel. Detailed computational results are presented and compared with those generated by a deterministic model. The impacts of demand and supply uncertainty on the optimal design of distributed energy systems are systematically investigated using proposed modelling framework and solution approach.
Flux balance analysis (FBA) is an optimization based approach to find the optimal steady state of a metabolic network, commonly of microorganisms such as yeast strains and Escherichia coli. However, ...the resulting solution from an FBA is typically not unique, as the optimization problem is, more often than not, degenerate. Flux variability analysis (FVA) is a method to determine the range of possible reaction fluxes that still satisfy, within some optimality factor, the original FBA problem. The resulting range of reaction fluxes can be utilized to determine metabolic reactions of high importance, amongst other analyses. In the literature, this has been done by solving Formula: see text linear programs (LPs), with n being the number of reactions in the metabolic network. However, FVA can be solved with less than Formula: see text LPs by utilizing the basic feasible solution property of bounded LPs to reduce the number of LPs that are needed to be solved. In this work, a new algorithm is proposed to solve FVA that requires less than Formula: see text LPs. The proposed algorithm is benchmarked on a problem set of 112 metabolic network models ranging from single cell organisms (iMM904, ect) to a human metabolic system (Recon3D). Showing a reduction in the number of LPs required to solve the FVA problem and thus the time to solve an FVA problem.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
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