Robust Modifier Adaptation via Worst-Case and Probabilistic Approaches

Speakman, Jack; François, Grégory

doi:10.1021/acs.iecr.1c03142

Cited by 3 publications

(1 citation statement)

References 31 publications

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“…For many problems, these assumptions are wrong and this may cause problems. For example, when implementing an optimal solution, a system may not give optimal output, because of the inaccurate equations used in the model, or because uncertainty breaks the equilibrium of any Karush-Kuhn-Tucker (KKT) conditions, thus destroying the optimality of the solution [16].…”

Section: Frame Of Referencementioning

confidence: 99%

An Adaptive Linear Programming Algorithm with Parameter Learning

Guo,

Nellippallil,

Smith

et al. 2024

Algorithms

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When dealing with engineering design problems, designers often encounter nonlinear and nonconvex features, multiple objectives, coupled decision making, and various levels of fidelity of sub-systems. To realize the design with limited computational resources, problems with the features above need to be linearized and then solved using solution algorithms for linear programming. The adaptive linear programming (ALP) algorithm is an extension of the Sequential Linear Programming algorithm where a nonlinear compromise decision support problem (cDSP) is iteratively linearized, and the resulting linear programming problem is solved with satisficing solutions returned. The reduced move coefficient (RMC) is used to define how far away from the boundary the next linearization is to be performed, and currently, it is determined based on a heuristic. The choice of RMC significantly affects the efficacy of the linearization process and, hence, the rapidity of finding the solution. In this paper, we propose a rule-based parameter-learning procedure to vary the RMC at each iteration, thereby significantly increasing the speed of determining the ultimate solution. To demonstrate the efficacy of the ALP algorithm with parameter learning (ALPPL), we use an industry-inspired problem, namely, the integrated design of a hot-rolling process chain for the production of a steel rod. Using the proposed ALPPL, we can incorporate domain expertise to identify the most relevant criteria to evaluate the performance of the linearization algorithm, quantify the criteria as evaluation indices, and tune the RMC to return the solutions that fall into the most desired range of each evaluation index. Compared with the old ALP algorithm using the golden section search to update the RMC, the ALPPL improves the algorithm by identifying the RMC values with better linearization performance without adding computational complexity. The insensitive region of the RMC is better explored using the ALPPL—the ALP only explores the insensitive region twice, whereas the ALPPL explores four times throughout the iterations. With ALPPL, we have a more comprehensive definition of linearization performance—given multiple design scenarios, using evaluation indices (EIs) including the statistics of deviations, the numbers of binding (active) constraints and bounds, the numbers of accumulated linear constraints, and the number of iterations. The desired range of evaluation indices (DEI) is also learned during the iterations. The RMC value that brings the most EIs into the DEI is returned as the best RMC, which ensures a balance between the accuracy of the linearization and the robustness of the solutions. For our test problem, the hot-rolling process chain, the ALP returns the best RMC in twelve iterations considering only the deviation as the linearization performance index, whereas the ALPPL returns the best RMC in fourteen iterations considering multiple EIs. The complexity of both the ALP and the ALPPL is O(n2). The parameter-learning steps can be customized to improve the parameter determination of other algorithms.

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Section: Frame Of Referencementioning

confidence: 99%

An Adaptive Linear Programming Algorithm with Parameter Learning

Guo,

Nellippallil,

Smith

et al. 2024

Algorithms

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Feasibility in real-time optimization under model uncertainty. The use of Lipschitz bounds

Marchetti¹

2022

Computers & Chemical Engineering

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A Multiple Solution Approach to Real-Time Optimization

Speakman

François

2022

Processes

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Modifier Adaptation (MA) is a method of real-time optimization (RTO) which modifies a single model to match the first order properties of the plant. Known uncertainties in the parameters of this model are discarded in favor of real-time measurements, but they can be used to quantify the mismatch between the plant and model. Using multi-model methods increases the computation time, but can improve rate of convergence of the RTO scheme. This article proposes a framework, known as multiple solution modifier adaptation (MSMA), which produces several models which are all modified in the same way as standard MA, each producing a potential solution to be applied to the plant. From this framework, three recommended schemes are proposed on how to select the operating point to be applied to the plant: (1) Selecting the solution based off the modifiers; (2) Selecting the mean solution from convex models; (3) Selecting the closest solution to the current operating point. Each of these methods have different advantages, including limiting the increase in computational complexity and improving the model adequacy conditions of the scheme. These recommended schemes are shown on three different case studies of varying complexity with all three schemes showing improvements over standard MA.

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Robust Modifier Adaptation via Worst-Case and Probabilistic Approaches

Cited by 3 publications

References 31 publications

An Adaptive Linear Programming Algorithm with Parameter Learning

An Adaptive Linear Programming Algorithm with Parameter Learning

Feasibility in real-time optimization under model uncertainty. The use of Lipschitz bounds

A Multiple Solution Approach to Real-Time Optimization

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