Ilias Mitrai

Jiyong Lee, Melody Agustin, Joanne Langsdorf et al.

In this paper, we consider the expansion of power grids under emerging large loads from data centers and electrified manufacturing. We develop a multi-period grid capacity expansion model to determine optimal investment profiles for power generation, storage, and transmission capacity while accounting for hourly power dispatch, such that electricity demand is satisfied and the total planning and operation cost is minimized. We also propose a new modeling approach regarding the spatial distribution of demand from large loads. The model is used to analyze the expansion of a synthetic grid that follows key characteristics of the ERCOT system over a seven-year planning horizon, under loads from data centers and electrified oil refining, which account for 17.5% and 4.7% of total annual electricity demand by the end of the planning horizon. The optimal investment policy leads to an 83.6% increase in generation capacity and exploits the short construction times of solar and storage as well as the operational flexibility of thermal generators. Finally, sensitivity analysis reveals that the construction time of grid assets substantially impacts investment timing, generation technology mix, and transmission capacity expansion. The proposed modeling framework is general and can be extended to other grid systems, enabling the exploration of diverse demand scenarios, policy assumptions, and regional characteristics.

Ilias Mitrai, Prodromos Daoutidis

The repeated solution of large-scale optimization problems arises frequently in process systems engineering tasks. Decomposition-based solution methods have been widely used to reduce the corresponding computational time, yet their implementation has multiple steps that are difficult to configure. We propose a machine learning approach to learn the optimal initialization of such algorithms which minimizes the computational time. Active and supervised learning is used to learn a surrogate model that predicts the computational performance for a given initialization. We apply this approach to the initialization of Generalized Benders Decomposition for the solution of mixed integer model predictive control problems. The surrogate models are used to find the optimal number of initial cuts that should be added in the master problem. The results show that the proposed approach can lead to a significant reduction in solution time, and active learning can reduce the data required for learning.

Bernard T. Agyeman, Zhe Li, Ilias Mitrai et al.

We propose a hybrid reinforcement and self-supervised learning framework for accelerating generalized Benders decomposition (GBD). In this framework, a graph based reinforcement learning agent operates on a bipartite representation of the master problem and, together with a verification mechanism, determines the integer variable assignments that solve the master problem. These assignments are then used as inputs to a KKT informed neural network, trained via self supervision to predict primal dual solutions that approximately satisfy the Karush Kuhn Tucker conditions of the subproblem. The predicted solutions are used to construct Benders cuts directly. The framework is evaluated on a mixed integer nonlinear programming case study, where it achieves a 57.5% reduction in solution time relative to classical GBD while consistently recovering optimal solutions across all test instances.

Ilias Mitrai, Prodromos Daoutidis

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures the structural and functional coupling among the variables and constraints of the problem via an appropriate set of features. Given this representation, a graph classifier is built to determine the best solution method for a given problem. The proposed approach is used to develop a classifier that determines whether a convex Mixed Integer Nonlinear Programming problem should be solved using branch and bound or the outer approximation algorithm. Finally, it is shown how the learned classifier can be incorporated into existing mixed integer optimization solvers.

Ilias Mitrai, Tongjia Liu, Gabriel E. Sanoja

Many chemical engineering systems are governed by mechanisms that switch across operating regimes, making the data-driven discovery of regime-dependent governing equations essential for predictive modeling, optimization, and control. We propose symbolic decision trees for the data-driven discovery of regime-dependent governing equations. The method simultaneously learns interpretable splitting conditions to partition the input domain and local governing equations that describe each regime. To improve tractability, both the splitting conditions and governing equations are parametrized using basis functions, resulting in a mixed-integer optimization learning problem. We use the proposed approach to learn hybrid dynamical models and a constitutive equation for the zero-shear viscosity of polymer melts. Symbolic decision trees identify physically interpretable regimes and local governing equations while improving predictive accuracy relative to approaches that learn a single global model or use existing decision tree models. This framework provides an interpretable and generalizable route for discovering regime-dependent models in chemical engineering systems.

Zhe Li, Ilias Mitrai

In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This modeling approach enables the discovery of both the dynamical model and a Lyapunov function in an interpretable form. The Lyapunov conditions for stability are enforced as constraints on the training data. The resulting learning task is a mixed-integer quadratically constrained optimization problem that can be solved to optimality using current state-of-the-art global optimization solvers. Application to two case studies shows that the proposed approach can discover the true model of the system and the associated Lyapunov function. Moreover, in the presence of noise, the model learned with the proposed approach achieves higher predictive accuracy than models learned with baselines that do not consider Lyapunov-related constraints.

Ilias Mitrai, Prodromos Daoutidis

Process control and optimization have been widely used to solve decision-making problems in chemical engineering applications. However, identifying and tuning the best solution algorithm is challenging and time-consuming. Machine learning tools can be used to automate these steps by learning the behavior of a numerical solver from data. In this paper, we discuss recent advances in (i) the representation of decision-making problems for machine learning tasks, (ii) algorithm selection, and (iii) algorithm configuration for monolithic and decomposition-based algorithms. Finally, we discuss open problems related to the application of machine learning for accelerating process optimization and control.

Bernard T. Agyeman, Zhe Li, Ilias Mitrai et al.

Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous subproblem. A key computational bottleneck is the repeated solution of increasingly complex master problems across iterations. In this paper, we propose a feasibility-aware imitation learning framework that predicts the values of the integer variables of the master problem at each iteration while accounting for feasibility with respect to constraints governing admissible integer assignments and the accumulated Benders feasibility cuts. The agent is trained using a two-stage procedure that combines behavioral cloning with a feasibility-based logit adjustment to bias predictions toward assignments that satisfy the evolving cut set. The agent is deployed within an agent-based Benders decomposition framework that combines explicit feasibility checks with a time-limited solver computation of a valid lower bound. The proposed approach retains finite convergence properties, as the lower bound is certified at each iteration. Application to a prototypical case study shows that the proposed method improves solution time relative to existing imitation learning approaches for accelerating Benders decomposition, while preserving solution accuracy.