Engineering topics
Publications and source records attributed to Stinchfield, Georgia.
In this presentation, we show a quadratically constrained optimization model to assess how operational decisions in a produced water network can meet minimum Lithium recovery concentration requirements while minimizing operating costs. We also discuss the need for global optimization algorithmic tools and how we look to address such challenges.
Our most recent work expands the water desalination case study from 76 variants to 10,897 variants using the equation-oriented model built in Pyomo as part of the PARETO project. Using the discretization formulation presented in Stinchfield (2024a), rather than solving for all 10,897 variants simultaneously, we decompose the formulation into subproblems containing subsets of variants from the process family. We solve the overall problem with Progressive Hedging (PH) deployed in parallel on a distributed HPC cluster using the open-source Python package mpi-sppy (Knueven et al., 2023). This approach allowed us to solve this process family design problem to ~1.5% relative optimality gap in about 5 hours; in comparison, Gurobi reached ~50% relative optimality gap in about 6 hours (Stinchfield et al., 2024b). However, this approach still requires discretization of the common unit module design ranges; additionally, PH acts as a heuristic for MILP’s with gap-closing capabilities. Ideally, we would not have to use ML surrogates or discretization to solve this problem, instead solving the process family design problem with the equation-oriented model directly to achieve the most accurate results. However, recall that we did not consider solving the MINLP directly due to complexity and size. In this work, we aim to decompose and solve this large-scale MINLP using a Structured Nonlinear Global Optimization algorithm presented by Cao and Zavala (2019).
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This work builds on our optimization formulation for process family design and extends it to explicitly include the benefits of economies of numbers. Economies of numbers (sometimes referred to as economies of learning) is a well-documented cost saving phenomenon. It characterizes the manufacturing cost savings due to standardization; in particular, it is capturing the correlation between cost reduction and the number of times a particular product has been manufactured. Following an approach similar to that in Gazzaneo et al. (2022), we develop a costing expression that captures material costs and manufacturing costs as a function of the number of unit modules produced. If the platform has a small number of unit module designs, we will be manufacturing a large number of each of these designs and gaining increased benefits from economies of numbers. However, increasing the number of unit module designs in the platform gives each process variant more choices to consider (at the cost of reducing economies of numbers). The optimization formulation in Stinchfield et al. (2023) pre-specified the number of unit module designs to be included in the platform. Here, by including the economies of numbers explicitly, we allow the mathematical programming formulation to determine the optimal number of unit module designs to include in the platform. We demonstrate this approach on multiple case studies, including MEA-based carbon capture and water desalination.
Developing methods for rapid, large-scale deployment of carbon capture systems is critical for meeting climate change goals. Optimization-based decisions can be employed at the design and manufacturing phases to minimize costs of deployment and operation. Manufacturing standardization results in significant cost savings due to economies of numbers. Building off previous work, we present a process family design approach to design a set of carbon capture systems while explicitly including economies of numbers savings within the formulation. Our formulation optimizes both the number and characteristics of the common components in the platform and simultaneously designs the resulting set of carbon capture systems. Savings from economies of numbers are explicitly included in the formulation to determine the number of components in the platform. We show and discuss the savings we gain from economies of numbers.
Battery sizing and siting problems are computationally challenging due to the need to make long-term planning decisions that are cognizant of short-term operational decisions. This paper considers sizing, siting, and operating batteries in a power grid to maximize their benefits, including price arbitrage and load shed mitigation, during both normal operations and periods with high wildfire ignition risk. Here we formulate a multi-scenario optimization problem for long duration battery storage while considering the possibility of load shedding during Public Safety Power Shutoff (PSPS) events that de-energize lines to mitigate severe wildfire ignition risk. To enable a computationally scalable solution of this problem with many scenarios of wildfire risk and power injection variability, we develop a customized temporal decomposition method based on a progressive hedging framework. Extending traditional progressive hedging techniques, we consider coupling in both placement variables across all scenarios and state-of-charge variables at temporal boundaries. This enforces consistency across scenarios while enabling parallel computations despite both spatial and temporal coupling. The proposed decomposition facilitates efficient and scalable modeling of a full year of hourly operational decisions to inform the sizing and siting of batteries. With this decomposition, we model a year of hourly operational decisions to inform optimal battery placement for a 240-bus WECC model in under 70 min of wall-clock time.
Rapid, wide-scale deployment of green process systems, such as carbon capture or water desalination systems, is essential for combatting climate change. Methods relying on traditional design or modularity fail to capture the benefits of both economies of numbers and economies of scale. We have proposed process family design, which designs a family of processes simultaneously exploiting opportunities for common elements. In previous work, we explored different optimization formulations to solve this problem. In this work, we develop a decomposition approach to tackle larger problems efficiently. We solve a water desalination case study, which is too large to solve within a reasonable timeframe with the discretization formulation. We exploit the block angular structure of the discretization problem to decompose and solve using Progressive Hedging (PH). We use the open-source Python package mpi-sppy to execute PH which allows us to leverage parallelization and a HPC cluster to further improve solution time.
In previous work, we have introduced a mathematical model for solving a discretized version of the process family design problem. This involves two sets of decision variables. One set selects which unit module designs are included in the process platform out of a candidate set of options; the other set determines which of these unit module designs are assigned to each variant. In this work, we exploit a parallelized Progressive Hedging (PH) algorithm to solve even larger scale design problems. PH is a well-known algorithm traditionally used to solve stochastic programming problems. While our problem is not a two-stage stochastic programming problem, the structure is similar, and it can be directly mapped to the PH approach, which we employ here to solve this deterministic optimization problem. We decompose our problem by process variant. We treat the platform unit module design variables as first-stage and the assignment of unit module designs to variants as second-stage, solving the problem using mpi-sppy. We demonstrate this approach on case studies of CC, water desalination, and refrigeration.
Tackling climate change goals requires widespread deployment of process technology variants across many decentralized sites with different geographical, environmental, and operational requirements. Conventional engineering approaches focus on unique designs for each installation (process variant), while missing opportunities for manufacturing standardization. Here, instead we seek to optimize a process platform of common unit designs while simultaneously designing an entire family of process variants that make use of that platform. This reduces engineering effort, deployment timelines, and manufacturing costs. We propose a nonlinear generalized disjunctive programming formulation and convert this to an efficient mixed-integer linear programming (MILP) formulation through discretization of the design space. We formulate our optimization in Pyomo with costing from IDAES, and we demonstrate the computational performance and solution quality on a water treatment desalination system from the PARETO framework and a carbon capture system built in Aspen Plus as part of CCSI2.
Enabling rapid, widespread deployment of many process variants across a range of design requirements is key to ensuring the widespread availability of critical decentralized technologies such as carbon capture systems. Unfortunately, traditional process design methods are not efficient for designing many similar variations of a process rapidly across a wide range of system requirements. Rather than considering each process variant as a separate design task, we have proposed viewing the entire set of variants as a “family.” In our work, we present rigorous optimization formulations that simultaneously design each variant within the family from a platform of available unit modules, largely inspired by product family and platform design.
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Machine learning models are promising as surrogates in optimization when replacing difficult to solve equations or black-box type models. This work demonstrates the viability of linear model decision trees as piecewise-linear surrogates in decision-making problems. Linear model decision trees can be represented exactly in mixed-integer linear programming (MILP) and mixed-integer quadratic constrained programming (MIQCP) formulations. Furthermore, they can represent discontinuous functions, bringing advantages over neural networks in some cases. We present several formulations using transformations from Generalized Disjunctive Programming (GDP) formulations and modifications of MILP formulations for gradient boosted decision trees (GBDT). We then compare the computational performance of these different MILP and MIQCP representations in an optimization problem and illustrate their use on engineering applications. Importantly, we observe faster solution times for optimization problems with linear model decision tree surrogates when compared with GBDT surrogates using the Optimization and Machine Learning Toolkit (OMLT).
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The paper was presented at the 33rd European Symposium on Computer Aided Process Engineering (ESCAPE33) June 18-21, 2023, in Athens, Greece.
This work demonstrates the IDAES process family framework and the computational benefits of these formulations on a family of transcritical CO2 refrigeration cycles to meet a range of design criteria over both cooling capacity and outside air temperature.
This work presents a new framework for optimization of process families used for the design of modular systems. The framework has been applied to carbon capture systems.
This work presents a new framework for optimization of process families used to for the design of modular systems. The framework has been applied to carbon capture systems.
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