Publications

Laird, Carl D.; Nicholson, Bethany L.; Rodriguez, Jose S.

Abstract not provided.

Bynum, Michael L.; Klise, Katherine A.; Hart, David B.; Haxton, Terranna H.; Murray, Regan M.; Laird, Carl D.

Abstract not provided.

Haxton, Terranna H.; Laky, Daniel L.; Klise, Katherine A.; Laird, Carl D.; Burkhardt, Jonathan B.; Murray, Regan M.

Abstract not provided.

Laird, Carl D.

Abstract not provided.

Laird, Carl D.; Bynum, Michael L.; Castillo, Anya; Watson, Jean-Paul W.; Liu, Jianfeng L.

Abstract not provided.

Laird, Carl D.

Abstract not provided.

Laird, Carl D.

Abstract not provided.

IEEE Transactions on Power Systems

Liu, Jianfeng; Laird, Carl D.; Scott, Joseph K.; Watson, Jean-Paul W.; Castillo, Anya

We propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current (ac) model of the transmission network, which is a nonconvex mixed-integer nonlinear programming problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with ac power flow constraints and leverage second-order cone relaxations, piecewise outer approximations, and optimization-based bounds tightening to provide a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.

Nicholson, Bethany L.; Thierry, David T.; Parker, Robertl P.; Rodriguez, Jose S.; Laird, Carl D.; Biegler, Lorenz T.

Abstract not provided.

Processes

Laky, Daniel L.; Xu, Shu X.; Rodriguez, Jose S.; Vaidyaraman, Shankar V.; Munoz, Salvador G.; Laird, Carl D.

To increase manufacturing flexibility and system understanding in pharmaceutical development, the FDA launched the quality by design (QbD) initiative. Within QbD, the design space is the multidimensional region (of the input variables and process parameters) where product quality is assured. Given the high cost of extensive experimentation, there is a need for computational methods to estimate the probabilistic design space that considers interactions between critical process parameters and critical quality attributes, as well as model uncertainty. In this paper we propose two algorithms that extend the flexibility test and flexibility index formulations to replace simulation-based analysis and identify the probabilistic design space more efficiently. The effectiveness and computational efficiency of these approaches is shown on a small example and an industrial case study.

Nicholson, Bethany L.; Laird, Carl D.; Siirola, John D.

Abstract not provided.

Computer Aided Chemical Engineering

Seth, Arpan; Hackebeil, Gaberiel A.; Haxton, Terranna; Murray, Regan; Laird, Carl D.; Klise, Katherine A.

Drinking water utilities use booster stations to maintain chlorine residuals throughout water distribution systems. Booster stations could also be used as part of an emergency response plan to minimize health risks in the event of an unintentional or malicious contamination incident. The benefit of booster stations for emergency response depends on several factors, including the reaction between chlorine and an unknown contaminant species, the fate and transport of the contaminant in the water distribution system, and the time delay between detection and initiation of boosted levels of chlorine. This paper takes these aspects into account and proposes a mixed-integer linear program formulation for optimizing the placement of booster stations for emergency response. A case study is used to explore the ability of optimally placed booster stations to reduce the impact of contamination in water distribution systems.

Hart, William E.; Laird, Carl D.; Siirola, John D.; Rodriguez, Jose S.

Abstract not provided.

Computer Aided Chemical Engineering

Rodriguez, Jose S.; Hackebeil, Gabriel; Siirola, John D.; Zavala, Victor M.; Laird, Carl D.

There is a need for efficient optimization strategies to efficiently solve large-scale, nonlinear optimization problems. Many problem classes, including design under uncertainty are inherently structured and can be accelerated with decomposition approaches. This paper describes a second-order multiplier update for the alternating direction method of multipliers (ADMM) to solve nonlinear stochastic programming problems. We exploit connections between ADMM and the Schur-complement decomposition to derive an accelerated version of ADMM. Specifically, we study the effectiveness of performing a Newton-Raphson algorithm to compute multiplier estimates for the method of multipliers (MM). We interpret ADMM as a decomposable version of MM and propose modifications to the multiplier update of the standard ADMM scheme based on improvements observed in MM. The modifications to the ADMM algorithm seek to accelerate solutions of optimization problems for design under uncertainty and the numerical effectiveness of the approaches is demonstrated on a set of ten stochastic programming problems. Practical strategies for improving computational performance are discussed along with comparisons between the algorithms. We observe that the second-order update achieves convergence in fewer unconstrained minimizations for MM on general nonlinear problems. In the case of ADMM, the second-order update reduces significantly the number of subproblem solves for convex quadratic programs (QPs).

Bynum, Michael L.; Liu, Jianfeng L.; Zhen, Todd Z.; Klise, Katherine A.; Laird, Carl D.

Abstract not provided.

Bynum, Michael L.; Castillo, Anya; Laird, Carl D.; Watson, Jean-Paul W.

Abstract not provided.

Journal of Water Resources Planning and Management

Hart, David B.; Rodriguez, J.S.; Burkhardt, Jonathan; Borchers, Brian; Laird, Carl D.; Murray, Regan; Klise, Katherine A.; Haxton, Terranna

Sampling of drinking water distribution systems is performed to ensure good water quality and protect public health. Sampling also satisfies regulatory requirements and is done to respond to customer complaints or emergency situations. Water distribution system modeling techniques can be used to plan and inform sampling strategies. However, a high degree of accuracy and confidence in the hydraulic and water quality models is required to support real-time response. One source of error in these models is related to uncertainty in model input parameters. Effective characterization of these uncertainties and their effect on contaminant transport during a contamination incident is critical for providing confidence estimates in model-based design and evaluation of different sampling strategies. In this paper, the effects of uncertainty in customer demand, isolation valve status, bulk reaction rate coefficient, contaminant injection location, start time, duration, and rate on the size and location of the contaminant plume are quantified for two example water distribution systems. Results show that the most important parameter was the injection location. The size of the plume was also affected by the reaction rate coefficient, injection rate, and injection duration, whereas the exact location of the plume was additionally affected by the isolation valve status. Uncertainty quantification provides a more complete picture of how contaminants move within a water distribution system and more information when using modeling results to select sampling locations.

Zhen, Todd Z.; Klise, Katherine A.; Cunningham, Sean C.; Marszal, Edward M.; Laird, Carl D.

Abstract not provided.

Seth, Arpan S.; Hackebeil, Gaberiel H.; Haxton, Terranna H.; Murray, Regan M.; Laird, Carl D.; Klise, Katherine A.

Abstract not provided.

Computers and Chemical Engineering

Rodriguez, Jose S.; Nicholson, Bethany L.; Laird, Carl D.; Zavala, Victor M.

We study connections between the alternating direction method of multipliers (ADMM), the classical method of multipliers (MM), and progressive hedging (PH). The connections are used to derive benchmark metrics and strategies to monitor and accelerate convergence and to help explain why ADMM and PH are capable of solving complex nonconvex NLPs. Specifically, we observe that ADMM is an inexact version of MM and approaches its performance when multiple coordination steps are performed. In addition, we use the observation that PH is a specialization of ADMM and borrow Lyapunov function and primal-dual feasibility metrics used in ADMM to explain why PH is capable of solving nonconvex NLPs. This analysis also highlights that specialized PH schemes can be derived to tackle a wider range of stochastic programs and even other problem classes. Our exposition is tutorial in nature and seeks to to motivate algorithmic improvements and new decomposition strategies

Bynum, Michael L.; Laird, Carl D.; Castillo, Anya; Watson, Jean-Paul W.

Abstract not provided.

Rodriguez, Jose S.; Nicholson, Bethany L.; Zavala, Victor M.; Laird, Carl D.

Abstract not provided.

Rodriguez, Josde S.; Nicholson, Bethany L.; Siirola, John D.; Laird, Carl D.

Abstract not provided.

Computers and Chemical Engineering

Liu, Jianfeng; Bynum, Michael L.; Castillo, Anya; Watson, Jean-Paul W.; Laird, Carl D.

Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. Furthermore, this approach opens the door for global solution of MINLP problems with AC power flow equations.

Klise, Katherine A.; Laird, Carl D.; Nicholson, Bethany L.; Staid, Andrea S.; Woodruff, David L.

Abstract not provided.