arXiv subjects

Roberto Mínguez

Publications and source records attributed to Roberto Mínguez.

5 recordsLinked to original sources

arXiv2019

On the convergence of cutting-plane methods for robust optimization with ellipsoidal uncertainty sets

Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral uncertainty sets guarantees convergence, finite termination when using ellipsoidal uncertainty sets is not theoretically guaranteed. This paper demonstrates that the cutting-plane algorithm set out for ellipsoidal uncertainty sets in its more general form also converges in a finite number of steps.

math.OC↗

arXiv2019

Robust Transmission Network Expansion Planning under Correlated Uncertainty

This paper addresses the transmission network expansion planning problem under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby the worst-case operating cost is accounted for under a given user-defined uncertainty set. This work differs from previously reported robust solutions in two respects. First, the typically disregarded correlation of uncertainty sources is explicitly considered through an ellipsoidal uncertainty set relying on their variance-covariance matrix. In addition, we describe the analogy between the corresponding second-stage problem and a certain class of mathematical programs arising in structural reliability. This analogy gives rise to a relevant probabilistic interpretation of the second stage, thereby revealing an undisclosed feature of the worst-case setting characterizing robust optimization with ellipsoidal uncertainty sets. More importantly, a novel nested decomposition approach based on results from structural reliability is devised to solve the proposed robust counterpart, which is cast as an instance of mixed-integer trilevel programming. Numerical results from several case studies demonstrate that the effect of correlated uncertainty can be captured by the proposed robust approach.

cs.CE↗

arXiv2017

Robust solutions of uncertain mixed-integer linear programs using decomposition techniques

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii) binary decisions and iii) hard constraints within an ellipsoidal uncertainty set, this paper provides a different interpretation of their robust counterpart (RC) inspired from decomposition techniques. This new interpretation allows the proposal of an ad-hoc decomposition technique to solve the RC problem with the following advantages: i) it improves tractability, specially for large-scale problems, and ii) it provides the exact probability of constraint violation in case the probability distribution of uncertain parameters are completely defined by using first and second-order probability moments. An attractive aspect of our method is that it decomposes the second-order cone programming problem, associated with the robust counterpart, into a linear master problem and different quadratically constrained problems (QCP) of considerable lower size. The optimal solution is achieved through the solution of these master and subproblems within an iterative scheme based on cutting plane approximations of the second-order cone constraints. In addition, proof of convergence of the iterative method is given.

math.NA↗

arXiv2017

Robust Dynamic Transmission and Renewable Generation Expansion Planning: Walking Towards Sustainable Systems

Nowadays, the transition from a conventional generation system to a renewable generation system is one of the most difficult challenges for system operators and companies. There are several reasons: the long-standing impact of investment decisions, the proper integration of renewable sources into the system, the present and future uncertainties, and the convenience to consider an integrated year-by-year representation of both uncertainties and investment decisions. However, recent breakthroughs in Dynamic Transmission Network Expansion Planning (DTNEP) have demonstrated that the use of robust optimization might render this problem computationally tractable for real systems. This paper intends to consider not only the capacity expansion of lines, but the construction and/or dismantling of renewable and conventional generation facilities as well. The Dynamic Transmission Network and Renewable Generation Expansion Planning (DTNRGEP) problem is formulated as an adaptive robust optimization problem with three levels. First level minimizes the investment costs of transmission network and generation expansion planning, the second level maximizes system operational costs with respect to uncertain parameters, while the third level minimizes those operational costs with respect to operational decisions. The method is tested for two cases: i) an illustrative example based on Garver IEEE system and ii) a case study using the IEEE 118-bus system. Numerical results from these examples demonstrate that the proposed model allows making optimal decisions towards reaching a sustainable power system, while overcoming problem size limitations and computational intractability for realistic cases.

math.OC↗

arXiv2016

On the Solution of Large-Scale Robust Transmission Network Expansion Planning under Uncertain Demand and Generation Capacity

Two-stage robust optimization has emerged as a relevant approach to deal with uncertain demand and generation capacity in the transmission network expansion planning problem. Unfortunately, available solution methodologies for the resulting trilevel robust counterpart are unsuitable for large-scale problems. In order to overcome this shortcoming, this paper presents an alternative column-and-constraint generation algorithm wherein the max-min problem associated with the second stage is solved by a novel coordinate descent method. As a major salient feature, the proposed approach does not rely on the transformation of the second-stage problem to a single-level equivalent. As a consequence, bilinear terms involving dual variables or Lagrange multipliers do not arise, thereby precluding the use of computationally expensive big-M-based linearization schemes. Thus, not only is the computational effort reduced, but also the typically overlooked non-trivial tuning of bounding parameters for dual variables or Lagrange multipliers is avoided. The practical applicability of the proposed methodology is confirmed by numerical testing on several benchmarks including a case based on the Polish 2383-bus system, which is well beyond the capability of the robust methods available in the literature.

cs.CE↗