arXiv subjects

V Varagapriya

Publications and source records attributed to V Varagapriya.

3 recordsLinked to original sources

arXiv2026

Bounds for multi-horizon stochastic optimization with application to power generation and transmission expansion planning

This paper investigates computationally efficient methods for deriving bounds on the optimal value of multi-horizon stochastic optimization problems, with a particular focus on applications in power generation and transmission expansion planning. Multi-horizon stochastic programs capture sequential decision-making under uncertainty across multiple time scales---e.g., strategic (long-term) and operational (short-term)---jointly. Due to their inherent complexity, especially when uncertainties span several time horizons, solving these problems directly becomes computationally prohibitive. To address this, the paper develops and analyzes various novel bounding techniques, based on the dissection of scenario trees. We investigate systematically dissecting (i) only the operational, (ii) only the strategic, or (iii) both scenario trees simultaneously, and we devise two ways to recombine them to obtain valid bounds. Each method leads to a monotonic chain of inequalities that approximate the optimal value of the original problem from below. One of these methods results in a significantly smaller number of subgroups to recombine in the operational and simultaneous dissections, leading to substantial computational savings. Numerical results on a multi-horizon mixed-integer generation and transmission expansion planning problem show the efficiency of the proposed approach through different dissection and recombination strategies.

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arXiv2025

Convex Approximations of Random Constrained Markov Decision Processes

Constrained Markov decision processes (CMDPs) are used as a decision-making framework to study the long-run performance of a stochastic system. It is well-known that a stationary optimal policy of a CMDP problem under discounted cost criterion can be obtained by solving a linear programming problem when running costs and transition probabilities are exactly known. In this paper, we consider a discounted cost CMDP problem where the running costs and transition probabilities are defined using random variables. Consequently, both the objective function and constraints become random. We use chance constraints to model these uncertainties and formulate the uncertain CMDP problem as a joint chance-constrained Markov decision process (JCCMDP). Under random running costs, we assume that the dependency among random constraint vectors is driven by a Gumbel-Hougaard copula. Using standard probability inequalities, we construct convex upper bound approximations of the JCCMDP problem under certain conditions on random running costs. In addition, we propose a linear programming problem whose optimal value gives a lower bound to the optimal value of the JCCMDP problem. When both running costs and transition probabilities are random, we define the latter variables as a sum of their means and random perturbations. Under mild conditions on the random perturbations and random running costs, we construct convex upper and lower bound approximations of the JCCMDP problem. We analyse the quality of the derived bounds through numerical experiments on a queueing control problem for random running costs. For the case when both running costs and transition probabilities are random, we choose randomly generated Markov decision problems called Garnets for numerical experiments.

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arXiv2025

Transition Uncertainties in Constrained Markov Decision Models: A Robust Optimization Approach

We examine a constrained Markov decision process under uncertain transition probabilities, with the uncertainty modeled as deviations from observed transition probabilities. We construct the uncertainty set associated with the deviations using polyhedral and second-order cone constraints and employ a robust optimization framework. We demonstrate that each inner optimization problem of the robust model can be equivalently transformed into a second-order cone programming problem. Using strong duality arguments, we show that the resulting robust problem can be equivalently reformulated into a second-order cone programming problem with bilinear constraints. In the numerical experiments, we study a machine replacement problem and explore potential sources of uncertainty in the transition probabilities. We examine how the optimal values and solutions differ as we vary the feasible region of the uncertainty set, considering only polyhedral constraints and a combination of polyhedral and second-order cone constraints. Furthermore, we analyze the impact of the number of states, the discount factor, and variations in the feasible region of the uncertainty set on the optimal values.

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