arXiv subjects

Milad Dehghani Filabadi

Publications and source records attributed to Milad Dehghani Filabadi.

3 recordsLinked to original sources

arXiv2024

Exponential Conic Relaxations for Signomial Geometric Programming

Signomial geometric programming (SGP) is a computationally challenging, NP-Hard class of nonconvex nonlinear optimization problems. SGP can be solved iteratively using a sequence of convex relaxations; consequently, the strength of such relaxations is an important factor to this iterative approach. Motivated by recent advances in solving exponential conic programming (ECP) problems, this paper develops a novel convex relaxation for SGP. Unlike existing work on relaxations, the base model in this paper does not assume bounded variables. However, bounded variables or monomial terms can be used to strengthen the relaxation by means of additional valid linear inequalities. We show how to embed the ECP relaxation in an iterative algorithm for SGP; leveraging recent advances in interior point method solvers, our computational experiments demonstrate the practical effectiveness of this approach.

math.OC↗

arXiv2022

Robust-and-Cheap Framework for Network Resilience: A Novel Mixed-Integer Formulation and Solution Method

Resilience and robustness are important properties in the reliability and attack-tolerance analysis of networks. In recent decades, various qualitative and heuristic-based quantitative approaches have made significant contributions in addressing network resilience and robustness. However, the lack of exact methods such as mixed-integer programming (MIP) models is sensible in the literature. In this paper, we contribute to the literature on the network resilience and robustness for targeted and random attacks and propose a MIP model considering graph-theoretical aspects of networks. The proposed MIP model consists of two stages where in the first stage the worst-case attack is identified. Then, the second-stage problem maximizes the network resilience under the worst-case attack by adding links considering a link addition financial budget. In addition, we propose a solution method that (i) provides a tight relaxation for the MIP formulation by relaxing some of the integrality restrictions, (ii) exploits the structure of the problem and reduces the second-stage problem to a less complex but equivalent problem, and (iii) identifies underlying knapsack constraints and generates lifted cover inequalities (LCI) for such constraints. We conclude numerical experiments for randomly-generated networks and then extend our results to power system networks. Numerical experiments demonstrate the applicability and computational efficiency of the proposed robust-and-cheap framework for network resilience.

math.OC↗

arXiv2021

Effective Budget of Uncertainty for Classes of Robust Optimization

Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of conservatism in RO, one can use the well-known budget-of-uncertainty approach which limits the amount of uncertainty to be considered in the model. In this paper, we study a class of problems with resource uncertainty and propose a robust optimization methodology that produces solutions that are even less conservative than the conventional budget-of-uncertainty approach. We propose a new tractable two-stage robust optimization approach that identifies the "ineffective" parts of the uncertainty set and optimizes for the "effective" worst-case scenario only. In the first stage, we identify the effective range of the uncertain parameter, and in the second stage, we provide a formulation that eliminates the unnecessary protection for the ineffective parts, and hence, produces less conservative solutions and provides intuitive insights on the trade-off between robustness and solution conservatism. We demonstrate the applicability of the proposed approach using a power dispatch optimization problem with wind uncertainty. We also provide examples of other application areas that would benefit from the proposed approach.

math.OC↗