arXiv subjects

Houra Mahmoudzadeh

Publications and source records attributed to Houra Mahmoudzadeh.

4 recordsLinked to original sources

arXiv2024

Expert-Guided Inverse Optimization for Convex Constraint Inference

Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted solutions are provided as input. In this paper, we propose an inverse optimization model that inputs several accepted and rejected solutions and recovers the underlying convex optimization model that can be used to generate such solutions. The novelty of our model is two-fold: First, we focus on inferring the parameters of the underlying convex feasible region. Second, the proposed model learns the convex constraint set from a set of past observations that are either accepted or rejected by an expert. The resulting inverse model is a mixed-integer nonlinear problem that is complex to solve. To mitigate the inverse problem complexity, we employ variational inequalities and the theoretical properties of the solutions to derive a reduced formulation that retains the complexity of its forward counterpart. Using realistic breast cancer patient data, we demonstrate that our inverse model can utilize a subset of past accepted and rejected treatment plans to infer clinical criteria that can lead to nearly guaranteed acceptable treatment plans for future patients.

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arXiv2022

Robust Direct Aperture Optimization for Radiation Therapy Treatment Planning

Intensity-modulated radiation therapy (IMRT) allows for the design of customized, highly-conformal treatments for cancer patients. Creating IMRT treatment plans, however, is a mathematically complex process, which is often tackled in multiple, simpler stages. This sequential approach typically separates radiation dose requirements from mechanical deliverability considerations, which may result in suboptimal treatment quality. For patient health to be considered paramount, holistic models must address these plan elements concurrently, eliminating quality loss between stages. This combined direct aperture optimization (DAO) approach is rarely paired with uncertainty mitigation techniques, such as robust optimization, due to the inherent complexity of both parts. This paper outlines a robust DAO (RDAO) model and discusses novel methodologies for efficiently integrating salient constraints. Because the highly-complex RDAO model is difficult to solve, an original candidate plan generation (CPG) heuristic is proposed. The CPG produces rapid, high-quality, feasible plans, which are immediately clinically viable, and can also be used to generate a feasible incumbent solution for warm starting the RDAO model. Computational results obtained using clinical patient datasets with motion uncertainty show the benefit of incorporating the CPG, both in terms of first incumbent solution and final output plan quality.

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arXiv2021

Effective Budget of Uncertainty for Classes of Robust Optimization

Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of conservatism in RO, one can use the well-known budget-of-uncertainty approach which limits the amount of uncertainty to be considered in the model. In this paper, we study a class of problems with resource uncertainty and propose a robust optimization methodology that produces solutions that are even less conservative than the conventional budget-of-uncertainty approach. We propose a new tractable two-stage robust optimization approach that identifies the "ineffective" parts of the uncertainty set and optimizes for the "effective" worst-case scenario only. In the first stage, we identify the effective range of the uncertain parameter, and in the second stage, we provide a formulation that eliminates the unnecessary protection for the ineffective parts, and hence, produces less conservative solutions and provides intuitive insights on the trade-off between robustness and solution conservatism. We demonstrate the applicability of the proposed approach using a power dispatch optimization problem with wind uncertainty. We also provide examples of other application areas that would benefit from the proposed approach.

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arXiv2020

Inferring Linear Feasible Regions using Inverse Optimization

Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear constraints that would render all the given observations feasible while making the preferred ones optimal for the cost (objective) function. By doing so, we infer the implicit feasible region of the linear programming problem. Providing such feasible regions (i) builds a baseline for categorizing future observations as feasible or infeasible, and (ii) allows for using sensitivity analysis to discern changes in optimal solutions if the objective function changes in the future. In this paper, we propose an inverse optimization framework to recover the constraints of a forward optimization problem using multiple past observations as input. We focus on linear models in which the objective function is known but the constraint matrix is partially or fully unknown. We propose a general inverse optimization methodology that recovers the complete constraint matrix and then introduce a tractable equivalent reformulation. Furthermore, we provide and discuss several generalized loss functions to inform the desirable properties of the feasible region based on user preference and historical data. Our numerical examples verify the validity of our approach, emphasize the differences among the proposed measures, and provide intuition for large-scale implementations. We further demonstrate our approach using a diet recommendation problem to show how the proposed models can help impute personalized constraints for each dieter.

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