arXiv subjects

Bardhyl Miftari

Publications and source records attributed to Bardhyl Miftari.

5 recordsLinked to original sources

arXiv2026

Analyzing changes in optimal variables in linear programming with uncertain parameters

Linear problems often include many parameters that may be uncertain. Sensitivity analysis studies how these parameters impact optimal values. Instead of analyzing the objective function, we shift the focus to the optimal values of the variables. Three types of linear modifications are considered: on the cost vector, the right-hand side, and on the constraint matrix. Several theorems establish properties of these modifications, including conditions for continuity of optimal variable values, as well as local convexity and concavity properties.

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arXiv2026

Sensitivity analysis for linear changes of the constraint matrix of a (mixed-integer) linear program

Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly mixed-integer) linear optimisation problems in which the constraint matrix is subject to linear perturbations controlled by a scalar parameter that varies within a given interval. This is a largely unresolved question with the additional burden that the resulting value function may be largely irregular. We propose several bounding techniques that provide formal guarantees on the behaviour of the objective value across the entire parameter range. The proposed bounds rely on tools from robust optimisation, Lagrangian relaxation, and ad-hoc reformulations. Each method is assessed in terms of accuracy, precision, and computational performance. Experimental results on a large benchmark set show that the proposed bounding techniques effectively address this class of problems, delivering strong guarantees and good precision. In addition, we introduce a spatial branch-and-bound algorithm that incorporates these bounds to compute an anytime approximation of the value function within a given error tolerance, and we analyse its computational performance.

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arXiv2026

Efficient LP warmstarting for linear modifications of the constraint matrix

We consider the problem of computing the optimal solution and objective of a linear program under linearly changing linear constraints. The problem studied is given by $\min c^t x \text{ s.t } Ax + λDx \leq b$ where $λ$ belongs to a set of predefined values $Λ$. Based on the information given by a precomputed basis, we present three efficient LP warm-starting algorithms. Each algorithm is either based on the eigenvalue decomposition, the Schur decomposition, or a tweaked eigenvalue decomposition to evaluate the optimal solution and optimal objective of these problems. The three algorithms have an overall complexity $O(pm^2+pmn)$ where $m$ (resp. $n$) is the number of constraints (resp. variables) of the original problem and $p$ the number of values in $Λ$ after an initial preprocessing step. We also provide theorems related to the optimality conditions to verify when a basis is still optimal and a local bound on the objective.

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arXiv2025

Remote Renewable Energy Hubs: a Taxonomy

Serving the energy demand with renewable energy is hindered by its limited availability near load centres (i.e. places where the energy demand is high). To address this challenge, the concept of Remote Renewable Energy Hubs (RREH) emerges as a promising solution. RREHs are energy hubs located in areas with abundant renewable energy sources, such as sun in the Sahara Desert or wind in Greenland. In these hubs, renewable energy sources are used to synthetise energy molecules. To produce specific energy molecules, a tailored hub configuration must be designed, which means choosing a set of technologies that are interacting with each other as well as defining how they are integrated in their local environment. The plurality of technologies that may be employed in RREHs results in a large diversity of hubs. In order to characterize this diversity, we propose in this paper a taxonomy for accurately defining these hubs. This taxonomy allows to better describe and compare designs of hubs as well as to identify new ones. Thus, it may guide policymakers and engineers in hub design, contributing to cost efficiency and/or improving local integration.

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arXiv2023

Reinforcement Learning for Joint Design and Control of Battery-PV Systems

The decentralisation and unpredictability of new renewable energy sources require rethinking our energy system. Data-driven approaches, such as reinforcement learning (RL), have emerged as new control strategies for operating these systems, but they have not yet been applied to system design. This paper aims to bridge this gap by studying the use of an RL-based method for joint design and control of a real-world PV and battery system. The design problem is first formulated as a mixed-integer linear programming problem (MILP). The optimal MILP solution is then used to evaluate the performance of an RL agent trained in a surrogate environment designed for applying an existing data-driven algorithm. The main difference between the two models lies in their optimization approaches: while MILP finds a solution that minimizes the total costs for a one-year operation given the deterministic historical data, RL is a stochastic method that searches for an optimal strategy over one week of data on expectation over all weeks in the historical dataset. Both methods were applied on a toy example using one-week data and on a case study using one-year data. In both cases, models were found to converge to similar control solutions, but their investment decisions differed. Overall, these outcomes are an initial step illustrating benefits and challenges of using RL for the joint design and control of energy systems.

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