arXiv subjects

Guzin Bayraksan

Publications and source records attributed to Guzin Bayraksan.

5 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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arXiv2026

Residuals-Based Contextual Distributionally Robust Optimization with Decision-Dependent Uncertainty: Theoretical Guarantees and Decomposition Algorithm

We consider a residuals-based distributionally robust optimization (DRO) model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt both parametric and nonparametric regression models to learn the latent decision dependency and construct a nominal distribution (thereby ambiguity sets) around the learned model using empirical residuals from the regressions. We formulate the ambiguity set via the Wasserstein distance, where the nominal distribution is both decision- and covariate-dependent. We provide conditions under which desired statistical properties such as asymptotic optimality, rate of convergence, and finite sample guarantees are satisfied. To solve the resulting DRO model, we develop a specialized Bender's decomposition algorithm with nonlinear cuts and prove its finite convergence. Through numerical experiments, we illustrate the effectiveness of our approach and the benefits of integrating decision dependency into a residuals-based DRO framework.

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arXiv2026

Multi-horizon optimization for domestic renewable energy system design under uncertainty

In this paper we address the challenge of designing optimal domestic renewable energy systems under multiple sources of uncertainty appearing at different time scales. Long-term uncertainties, such as investment and maintenance costs of different technologies, are combined with short-term uncertainties, including solar radiation, electricity prices, and uncontrolled load variations. We formulate the problem as a multistage multi-horizon stochastic Mixed Integer Linear Programming (MILP) model, minimizing the total cost of a domestic building complex's energy system. The model integrates long-term investment decisions, such as the capacity of photovoltaic panels and battery energy storage systems, with short-term operational decisions, including energy dispatch, grid exchanges, and load supply. To ensure robust operation under extreme scenarios, first- and second-order stochastic dominance risk-averse measures are considered preserving the time consistency of the solution. Given the computational complexity of solving the stochastic MILP for large instances, a rolling horizon-based matheuristic algorithm is developed. Additionally, various lower-bound strategies are explored, including wait-and-see schemes, expected value approximations, multistage grouping and clustering schemes. An extensive computational experiment validates the effectiveness of the proposed approach on a case study based on a building complex in South Germany. We tackle models with over 43 million constraints and 12 million binary, 700 hundred integer and 10 million continuous variables; they are solved with up to 0.32% optimality gap in reasonable computing time, where the value of the stochastic decisions as well as the benefit of the integrated risk-averse measures are quantified.

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arXiv2021

Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance

We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem. Recognizing that not all the realizations and scenario paths might have an "effect" on the optimal value, we investigate the question of how to define and identify critical scenarios for nested multistage DRO problems. Our analysis extends the work of Rahimian, Bayraksan, and Homem-de-Mello [Math. Program. 173(1--2): 393--430, 2019], which was in the context of a static/two-stage setting, to the multistage setting. To this end, we define the notions of effectiveness of scenario paths and the conditional effectiveness of realizations along a scenario path for a general class of multistage DRO problems. We then propose easy-to-check conditions to identify the effectiveness of scenario paths in the multistage setting when the distributional ambiguity is modeled via the total variation distance. Numerical results show that these notions provide useful insight on the underlying uncertainty of the problem.

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arXiv2020

A Multistage Distributionally Robust Optimization Approach to Water Allocation under Climate Uncertainty

This paper investigates a Multistage Distributionally Robust Optimization (MDRO) approach to water allocation under climate uncertainty. The MDRO is formed by creating sets of conditional distributions (called conditional ambiguity sets) on a finite scenario tree. The distributions in the conditional ambiguity sets remain close to a nominal conditional distribution according a $ϕ$-divergence (e.g., Kullback-Liebler divergence, Hellinger distance, Burg entropy, etc.). The paper discusses a decomposition algorithm to solve the resulting MDRO and applies the modeling and solution techniques to allocate water in a rapidly-developing area of Tucson, Arizona. Tucson, like many arid and semi-arid regions around the world, faces considerable uncertainty in its ability to provide water for its citizens in the future. The primary sources of uncertainty in the Tucson region include (1) unpredictable population growth, (2) the availability of water from the Colorado River, and (3) the effects of climate variability on water consumption. This paper integrates forecasts for all these sources of uncertainty into a single optimization model for robust and sustainable water allocation. Then, it uses this model to analyze the value of constructing additional treatment facilities to reduce future water shortages. The results indicate that the MDRO approach can be very valuable for water managers by providing insights to minimize their risks and help them plan for the future.

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