arXiv subjects

Miguel F. Anjos

Publications and source records attributed to Miguel F. Anjos.

17 recordsLinked to original sources

arXiv2026

Stochastic Capacity Accreditation: Incentivizing Resource Adequacy under Weather Uncertainty

High penetrations of variable renewable energy introduce significant resource adequacy challenges, particularly when weather-driven uncertainty affects renewable availability, electricity demand, and the effective capacity of thermal generators. Existing capacity credit accreditation methods often neglect these correlated weather effects, which may overstate firm capacity, distort long-term investment decisions, and weaken reliability outcomes in electricity market with price caps. This paper proposes a two-stage stochastic optimization framework for capacity accreditation that explicitly captures uncertainty in wind, solar, and temperature-dependent thermal derating. Using five years of ERCOT demand and renewable availability data, we compare the proposed stochastic capacity credit method with deterministic and average accreditation approaches, and quantify the impact of alternative accreditation methods on reliability, investment incentives, and the value of weather information. The results show that incorporating weather uncertainty yields more informative capacity credits and more reliable investment signals. In contrast, deterministic and averaged approaches can distort resource expansion decisions and produce materially worse reliability outcomes. These findings demonstrate the importance of explicitly accounting for weather uncertainty in capacity accreditation and long-term resource adequacy planning.

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arXiv2025

Decision-Focused Forecasting: A Differentiable Multistage Optimisation Architecture

Most decision-focused learning work has focused on single stage problems whereas many real-world decision problems are more appropriately modelled using multistage optimisation. In multistage problems contextual information is revealed over time, decisions have to be taken sequentially, and decisions now have an intertemporal effect on future decisions. Decision-focused forecasting is a recurrent differentiable optimisation architecture that expresses a fully differentiable multistage optimisation approach. This architecture enables us to account for the intertemporal decision effects of forecasts. We show what gradient adjustments are made to account for the state-path caused by forecasting. We apply the model to multistage problems in energy storage arbitrage and portfolio optimisation and report that our model outperforms existing approaches.

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arXiv2025

Multiple-Resolution Tokenization for Time Series Forecasting with an Application to Pricing

We propose a transformer architecture for time series forecasting with a focus on time series tokenisation and apply it to a real-world prediction problem from the pricing domain. Our architecture aims to learn effective representations at many scales across all available data simultaneously. The model contains a number of novel modules: a differentiated form of time series patching which employs multiple resolutions, a multiple-resolution module for time-varying known variables, a mixer-based module for capturing cross-series information, and a novel output head with favourable scaling to account for the increased number of tokens. We present an application of this model to a real world prediction problem faced by the markdown team at a very large retailer. On the experiments conducted our model outperforms in-house models and the selected existing deep learning architectures.

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arXiv2025

OPO: Making Decision-Focused Data Acquisition Decisions

We propose a model for making data acquisition decisions for variables in contextual stochastic optimisation problems. Data acquisition decisions are typically treated as separate and fixed. We explore problem settings in which the acquisition of contextual variables is costly and consequently constrained. The data acquisition problem is often solved heuristically for proxy objectives such as coverage. The more intuitive objective is the downstream decision quality as a result of data acquisition decisions. The whole pipeline can be characterised as an optimise-then-predict-then-optimise (OPO) problem. Analogously, much recent research has focused on how to integrate prediction and optimisation (PO) in the form of decision-focused learning. We propose leveraging differentiable optimisation to extend the integration to data acquisition. We solve the data acquisition problem with well-defined constraints by learning a surrogate linear objective function. We demonstrate an application of this model on a shortest path problem for which we first have to set a drone reconnaissance strategy to capture image segments serving as inputs to a model that predicts travel costs. We ablate the problem with a number of training modalities and demonstrate that the differentiable optimisation approach outperforms random search strategies.

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arXiv2024

Cuts and semidefinite liftings for the complex cut polytope

We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices $xx^{\mathrm{H}}$, where the elements of $x \in \mathbb{C}^n$ are $m$th unit roots. These polytopes have applications in ${\text{MAX-3-CUT}}$, digital communication technology, angular synchronization and more generally, complex quadratic programming. For ${m=2}$, the complex cut polytope corresponds to the well-known cut polytope. We generalize valid cuts for this polytope to cuts for any complex cut polytope with finite $m>2$ and provide a framework to compare them. Further, we consider a second semidefinite lifting of the complex cut polytope for $m=\infty$. This lifting is proven to be equivalent to other complex Lasserre-type liftings of the same order proposed in the literature, while being of smaller size. Our theoretical findings are supported by numerical experiments on various optimization problems.

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arXiv2024

Robust Bilevel Optimization for Near-Optimal Lower-Level Solutions

Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility from limited deviations from the optimal solution at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of general bilevel optimization problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of exact and heuristic methods and the impact of valid inequalities on the solution time.

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arXiv2023

Learning Deterministic Surrogates for Robust Convex QCQPs

Decision-focused learning is a promising development for contextual optimisation. It enables us to train prediction models that reflect the contextual sensitivity structure of the problem. However, there have been limited attempts to extend this paradigm to robust optimisation. We propose a double implicit layer model for training prediction models with respect to robust decision loss in uncertain convex quadratically constrained quadratic programs (QCQP). The first layer solves a deterministic version of the problem, the second layer evaluates the worst case realisation for an uncertainty set centred on the observation given the decisions obtained from the first layer. This enables us to learn model parameterisations that lead to robust decisions while only solving a simpler deterministic problem at test time. Additionally, instead of having to solve a robust counterpart we solve two smaller and potentially easier problems in training. The second layer (worst case problem) can be seen as a regularisation approach for predict-and-optimise by fitting to a neighbourhood of problems instead of just a point observation. We motivate relaxations of the worst-case problem in cases of uncertainty sets that would otherwise lead to trust region problems, and leverage various relaxations to deal with uncertain constraints. Both layers are typically strictly convex in this problem setting and thus have meaningful gradients almost everywhere. We demonstrate an application of this model on simulated experiments. The method is an effective regularisation tool for decision-focused learning for uncertain convex QCQPs.

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arXiv2023

Maximum flow-based formulation for the optimal location of electric vehicle charging stations

With the increasing effects of climate change, the urgency to step away from fossil fuels is greater than ever before. Electric vehicles (EVs) are one way to diminish these effects, but their widespread adoption is often limited by the insufficient availability of charging stations. In this work, our goal is to expand the infrastructure of EV charging stations, in order to provide a better quality of service in terms of user satisfaction (and availability of charging stations). Specifically, our focus is directed towards urban areas. We first propose a model for the assignment of EV charging demand to stations, framing it as a maximum flow problem. This model is the basis for the evaluation of user satisfaction with a given charging infrastructure. Secondly, we incorporate the maximum flow model into a mixed-integer linear program, where decisions on the opening of new stations and on the expansion of their capacity through additional outlets is accounted for. We showcase our methodology for the city of Montreal, demonstrating the scalability of our approach to handle real-world scenarios. We conclude that considering both spacial and temporal variations in charging demand is meaningful when solving realistic instances.

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arXiv2023

Optimising Electric Vehicle Charging Station Placement using Advanced Discrete Choice Models

We present a new model for finding the optimal placement of electric vehicle charging stations across a multi-period time frame so as to maximise electric vehicle adoption. Via the use of advanced discrete choice models and user classes, this work allows for a granular modelling of user attributes and their preferences in regard to charging station characteristics. Instead of embedding an analytical probability model in the formulation, we adopt a simulation approach and pre-compute error terms for each option available to users for a given number of scenarios. This results in a bilevel optimisation model that is, however, intractable for all but the simplest instances. Using the pre-computed error terms to calculate the users covered by each charging station allows for a maximum covering model, for which solutions can be found more efficiently than for the bilevel formulation. The maximum covering formulation remains intractable in some instances, so we propose rolling horizon, greedy, and GRASP heuristics to obtain good quality solutions more efficiently. Extensive computational results are provided, which compare the maximum covering formulation with the current state-of-the-art, both for exact solutions and the heuristic methods. Keywords: Electric vehicle charging stations, facility location, integer programming, discrete choice models, maximum covering

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arXiv2021

CONICOPF: Conic relaxations for AC optimal power flow computations

Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite relaxations for large-scale meshed networks in terms of optimality gap and computation time: the tight-and-cheap relaxation (TCR) and the quadratic convex relaxation (QCR). We compare these relaxations on 60 PGLib-OPF test cases with up to 1,354 buses under three operating conditions and show that TCR dominates QCR on all 20 typical (TYP) test cases, on 18 out of 20 active power increase (API), and 12 out of 20 small angle difference (SAD). Selected state-of-the-art conic relaxations are implemented in the new MATLAB-based package CONICOPF available on GitHub.

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arXiv2020

Complexity of near-optimal robust versions of multilevel optimization problems

Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where near-optimal robustness is modelled through additional adversarial decision-makers. Near-optimal robust versions of multilevel problems are shown to remain in the same complexity class as the problem without near-optimality robustness under general conditions.

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arXiv2020

Design and implementation of a modular interior-point solver for linear optimization

This paper introduces the algorithmic design and implementation of Tulip, an open-source interior-point solver for linear optimization. It implements a regularized homogeneous interior-point algorithm with multiple centrality corrections, and therefore handles unbounded and infeasible problems. The solver is written in Julia, thus allowing for a flexible and efficient implementation: Tulip's algorithmic framework is fully disentangled from linear algebra implementations and from a model's arithmetic. In particular, this allows to seamlessly integrate specialized routines for structured problems. Extensive computational results are reported. We find that Tulip is competitive with open-source interior-point solvers on the H. Mittelmann's benchmark of barrier linear programming solvers. Furthermore, we design specialized linear algebra routines for structured master problems in the context of Dantzig-Wolfe decomposition. These routines yield a tenfold speedup on large and dense instances that arise in power systems operation and two-stage stochastic programming, thereby outperforming state-of-the-art commercial interior point method solvers. Finally, we illustrate Tulip's ability to use different levels of arithmetic precision by solving problems in extended precision.

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arXiv2020

Control of Two Energy Storage Units with Market Impact: Lagrangian Approach and Horizons

Energy storage and demand-side response will play an increasingly important role in the future electricity system. We extend previous results on a single energy storage unit to the management of two energy storage units cooperating for the purpose of price arbitrage. We consider a deterministic dynamic programming model for the cooperative problem, which accounts for market impact. We develop the Lagrangian theory and present a new algorithm to identify pairs of strategies. While we are not able to prove that the algorithm provides optimal strategies, we give strong numerical evidence in favour of it. Furthermore, the Lagrangian approach makes it possible to identify decision and forecast horizons, the latter being a time beyond which it is not necessary to look in order to determine the present optimal action. In practice, this allows for real-time reoptimization, with both horizons being of the order of days. Index Terms-control, two storage units, arbitrage, pricemaker, market impact, energy, Lagrangian.

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arXiv2019

A Bilevel Approach to Optimal Price-Setting of Time-and-Level-of-Use Tariffs

Time-and-Level-of-Use (TLOU) is a recently proposed pricing policy for energy, extending Time-of-Use with the addition of a capacity that users can book for a given time frame, reducing their expected energy cost if they respect this self-determined capacity limit. We introduce a variant of the TLOU defined in the literature, aligned with the supplier interest to prevent unplanned over-consumption. The optimal price-setting problem of TLOU is defined as a bilevel, bi-objective problem anticipating user choices in the supplier decision. An efficient resolution scheme is developed, based on the specific discrete structure of the lower-level user problem. Computational experiments using consumption distributions estimated from historical data illustrate the effectiveness of the proposed framework.

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arXiv2019

Tight-and-cheap conic relaxation for the AC optimal power flow problem

The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite optimization is lower than for second-order cone optimization. We propose a conic relaxation obtained by combining semidefinite optimization with the reformulation-linearization technique, commonly known as RLT. The proposed relaxation is stronger than the second-order cone relaxation and nearly as tight as the standard semidefinite relaxation. Computational experiments using standard test cases with up to 6515 buses show that the time to solve the new conic relaxation is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks.

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arXiv2019

Tight-and-cheap conic relaxation for the optimal reactive power dispatch problem

The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The ORPD problem is modelled as a mixed-integer nonlinear optimization problem and its complexity is increased compared to the ACOPF problem, which is highly nonconvex and generally hard to solve. Recently, convex relaxations of the ACOPF problem have attracted a significant interest since they can lead to global optimality. We propose a tight conic relaxation of the ORPD problem and show that a round-off technique applied with this relaxation leads to near-global optimal solutions with very small guaranteed optimality gaps, unlike with the nonconvex continuous relaxation. We report computational results on selected MATPOWER test cases with up to 3375 buses.

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arXiv2019

A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow

Many optimization problems in power transmission networks can be formulated as polynomial problems with complex variables. A polynomial optimization problem with complex variables consists in optimizing a real-valued polynomial whose variables and coefficients are complex numbers subject to some complex polynomial equality or inequality constraints. These problems are usually directly converted to real variables, either using the polar form or the rectangular form. In this work, we propose a Julia module allowing the representation of polynomial problems in their original complex formulation. This module is applied to power systems optimization and its generic design enables the description of several variants of power system problems. Results for the Optimal Power Flow in Alternating Current problem and for the Preventive-Security Constrained Optimal Power Flow problem are presented.

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