arXiv subjects

Parth Brahmbhatt

Publications and source records attributed to Parth Brahmbhatt.

4 recordsLinked to original sources

arXiv2026

Multi-Agent Receding Horizon Games Framework for Autonomous Market Participation

Electrochemical distributed energy resources (DERs), such as electrolyzers and battery energy storage systems, consume large amounts of electricity. Buying that power directly from wholesale markets can sharply reduce operating costs. Accessing these markets, however, requires a minimum bid size that individual small or medium-scale units struggle to meet. Grouping several units to bid as a single participant clears this barrier while letting each unit use its own low-cost renewable generation. The common remedy is to hire a third-party aggregator, but aggregators charge commissions and solve a centralized optimization that often favors certain units over others. A fairer alternative is peer-to-peer (P2P) participation, where units form a self-governing group and bid jointly with no central authority. Because each self-interested unit is unwilling to share private data, coordination is best posed as a game-theoretic distributed optimization problem. Existing P2P methods, however, address only single-round spot markets and ignore the two-stage structure of real wholesale markets, where participants commit a day ahead and continuously adjust in real time. We close this gap with a two-stage receding-horizon generalized Nash equilibrium (GNE) game. Each unit re-optimizes its strategy every five minutes over a rolling one-hour horizon, while the group satisfies both market stages collectively. Units exchange only publicly visible aggregate power, never private cost or production data. We apply the approach to a six-unit fleet on the PJM market. It delivers 37% higher profit, 29% lower electricity cost, and 92% less renewable curtailment than individual participation, with every unit better off.

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arXiv2026

Enhancing Interpretability of Stochastic Programming Solutions: A Multiparametric Approach

Stochastic programming (SP) is a powerful framework for decision-making under uncertainty, but its practical adoption in industry is often hindered by the difficulty in understanding the causal relationships that drive optimal solutions. In the two-stage SP, strategic first-stage decisions are coupled with operational second-stage recourse decisions. When the number of scenarios under consideration is large, understanding the direct link between the uncertainty realization and optimal recourse strategy becomes computationally and cognitively demanding. Common approaches to improve interpretability include trained classification trees or scenario reduction, replacing the large scenario set with a representative subset. This is often achieved through post-hoc clustering (e.g., k-means) based on uncertainty realizations or optimal recourse decisions. While useful, these methods only provide a statistical approximation of the solution space and may fail to reveal the underlying structural properties of the recourse problem that drive optimal first-stage decisions. This work introduces a novel, deterministic approach to explainability using multiparametric programming (mp) within a Benders decomposition framework. We reformulate the recourse subproblem as a multiparametric linear program, generating an explicit map of Critical Regions (CRs), which are polyhedral partitions of the uncertainty space. This allows us to cluster scenarios analytically rather than statistically. We demonstrate this methodology on a supply chain planning under demand uncertainty. Our results show that 100 stochastic scenarios map to exactly six critical region clusters. This mapping allows us to explain optimal capacity planning decisions as a precise trade-off between specific operational modes, providing a fully transparent interpretation of the stochastic solution.

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arXiv2026

Parametric Region Search: A Mixed-Integer Bilevel Optimization Problem Primal Heuristic

Bilevel optimization is a mathematical modeling formulation for hierarchical systems and two-player interactions, with wide-ranging applications in environmental, energy, and control engineering. Despite its utility, the mixed-integer bilevel optimization (MIBO) problem is exceptionally challenging to solve. While numerous exact and metaheuristic methods exist, the development of specialized primal heuristics for MIBO, aimed at quickly identifying high-quality feasible solutions, remains an underexplored area. This paper introduces the Parametric Region Search (PRS), a new primal heuristic for MIBO. The PRS method leverages insights from multi-parametric optimization by iteratively exploring regions defined by the lower-level problem's critical regions. We formally define the MIBO structure and the necessary parametric region formulations, and then detail the proposed heuristic's initialization and iterative search mechanism. Computational results demonstrate that the PRS heuristic consistently locates high-quality primal solutions compared to established derivative-free metaheuristics, including DOMINO-COBYLA and DOMINO-ISRES. Furthermore, we illustrate how the PRS can be effectively integrated with other heuristics like DOMINO-COBYLA to enhance the overall solution discovery process for MIBO.

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arXiv2025

Benders Decomposition using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition by embedding multi-parametric programming (mp) surrogates for optimization subproblems. Our approach leverages the OptiGraph abstraction in Plasmo$.$jl to model and decompose graph-structured problems. By solving the subproblems associated with the graph nodes once using mp, we can extract explicit piecewise affine mappings for primal and dual variables which replace the expensive subproblem solves with efficient look-ups and function evaluations during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution and implement this integration in the open-source PlasmoBenders$.$jl software package. We apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under uncertainty in product demand/prices and availability of raw materials. We evaluate single-cut and multi-cut variants of Benders and show that the mp surrogate approach achieves substantial speedups in subproblem solve time while preserving the convergence guarantees of Benders. Furthermore, we highlight advantages in the solution analysis and interpretability that is enabled by mp critical region tracking. Our results demonstrate that combining mp programming with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. By decomposing the problem into tractable subproblems, the proposed approach also aims to overcome scalability issues of mp, and the use of mp surrogates provides a unifying modeling framework to represent heterogeneous graph subproblems as common modeling objects.

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