Transfer Learning in Information Criteria-based Feature Selection

This paper investigates the effectiveness of transfer learning based on Mallows' Cp. We propose a procedure that combines transfer learning with Mallows' Cp (TLCp) and prove that it outperforms the conventional Mallows' Cp criterion in terms of accuracy and stability. Our theoretical results indicate that, for any sample size in the target domain, the proposed TLCp estimator performs better than the Cp estimator by the mean squared error (MSE) metric in the case of orthogonal predictors, provided that i) the dissimilarity between the tasks from source domain and target domain is small, and ii) the procedure parameters (complexity penalties) are tuned according to certain explicit rules. Moreover, we show that our transfer learning framework can be extended to other feature selection criteria, such as the Bayesian information criterion. By analyzing the solution of the orthogonalized Cp, we identify an estimator that asymptotically approximates the solution of the Cp criterion in the case of non-orthogonal predictors. Similar results are obtained for the non-orthogonal TLCp. Finally, simulation studies and applications with real data demonstrate the usefulness of the TLCp scheme

A decomposition framework for gas network design

Gas networks are used to transport natural gas, which is an important resource for both residential and industrial customers throughout the world. The gas network design problem is a challenging nonlinear and non-convex optimization problem. In this paper, we propose a decomposition framework to solve this problem. In particular, we utilize a two-stage procedure that involves a convex reformulation of the original problem. We conduct experiments on a benchmark network to validate and analyze the performance of our framework

A Framework for Optimization and Quantification of Uncertainty and Sensitivity for Developing Carbon Capture Systems

AbstractUnder the auspices of the U.S. Department of Energy's Carbon Capture Simulation Initiative (CCSI), a Framework for Optimization and Quantification of Uncertainty and Sensitivity (FOQUS) has been developed. This tool enables carbon capture systems to be rapidly synthesized and rigorously optimized, in an environment that accounts for and propagates uncertainties in parameters and models. FOQUS currently enables (1) the development of surrogate algebraic models utilizing the ALAMO algorithm, which can be used for superstructure optimization to identify optimal process configurations, (2) simulation-based optimization utilizing derivative free optimization (DFO) algorithms with detailed black-box process models, and (3) rigorous uncertainty quantification through PSUADE. FOQUS utilizes another CCSI technology, the Turbine Science Gateway, to manage the thousands of simulated runs necessary for optimization and UQ. This computational framework has been demonstrated for the design and analysis of a solid sorbent based carbon capture system

Optimization under uncertainty: State-of-the-art and opportunities

A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, governs the prices of fuels, the availability of electricity, and the demand for chemicals. A key difficulty in optimization under uncertainty is in dealing with an uncertainty space that is huge and frequently leads to very large-scale optimization models. Decision-making under uncertainty is often further complicated by the presence of integer decision variables to model logical and other discrete decisions in a multi-period or multi-stage setting. This paper reviews theory and methodology that have been developed to cope with the complexity of optimization problems under uncertainty. We discuss and contrast the classical recourse-based stochastic programming, robust stochastic programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastic dynamic programming. The advantages and shortcomings of these models are reviewed and illustrated through examples. Applications and the state-of-the-art in computations are also reviewed. Finally, we discuss several main areas for future development in this field. These include development of polynomial-time approximation schemes for multi-stage stochastic programs and the application of global optimization algorithms to two-stage and chance-constraint formulations

An approximation scheme for stochastic integer programs arising in capacity expansion

Planning for capacity expansion forms a crucial part of the strategic level decision making in many applications. Consequently, quantitative models for economic capac-ity expansion planning have been the subject of intense research. However, much of the work in this area has been restricted to linear cost models and/or limited degree of uncertainty to make the problems analytically tractable. This paper addresses a stochastic capacity expansion problem where the economies-of-scale in expansion costs are handled via fixed-charge cost functions, and forecast uncertainties in the problem parameters are explicitly considered by specifying a set of scenarios. The resulting formulation is a multi-stage stochastic integer program. We develop a fast, linear pro-gramming based, approximation scheme that exploits the decomposable structure and is guaranteed to produce feasible solutions for this problem. Through probabilistic analysis tools, we prove that the optimality gap of the heuristic solution almost surely vanishes asymptotically as the problem size increases. 1