Convex Relaxations for Gas Expansion Planning

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal soluutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solutions

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Hybrid simulation-optimization based approach for the optimal design of single-product biotechnological processes

In this work, we present a systematic method for the optimal development of bioprocesses that relies on the combined use of simulation packages and optimization tools. One of the main advantages of our method is that it allows for the simultaneous optimization of all the individual components of a bioprocess, including the main upstream and downstream units. The design task is mathematically formulated as a mixed-integer dynamic optimization (MIDO) problem, which is solved by a decomposition method that iterates between primal and master sub-problems. The primal dynamic optimization problem optimizes the operating conditions, bioreactor kinetics and equipment sizes, whereas the master levels entails the solution of a tailored mixed-integer linear programming (MILP) model that decides on the values of the integer variables (i.e., number of equipments in parallel and topological decisions). The dynamic optimization primal sub-problems are solved via a sequential approach that integrates the process simulator SuperPro Designer® with an external NLP solver implemented in Matlab®. The capabilities of the proposed methodology are illustrated through its application to a typical fermentation process and to the production of the amino acid L-lysine.Support from the Spanish Ministry of Education and Science (projects DPI2008-04099 and CTQ2009-14420-C02) and the Spanish Ministry of External Affairs (projects A/023551/09, A/031707/10 and HS2007-0006)

Data Analytics and Machine Learning to Enhance the Operational Visibility and Situation Awareness of Smart Grid High Penetration Photovoltaic Systems

Electric utilities have limited operational visibility and situation awareness over grid-tied distributed photovoltaic systems (PV). This will pose a risk to grid stability when the PV penetration into a given feeder exceeds 60% of its peak or minimum daytime load. Third-party service providers offer only real-time monitoring but not accurate insights into system performance and prediction of productions. PV systems also increase the attack surface of distribution networks since they are not under the direct supervision and control of the utility security analysts. Six key objectives were successfully achieved to enhance PV operational visibility and situation awareness: (1) conceptual cybersecurity frameworks for PV situation awareness at device, communications, applications, and cognitive levels; (2) a unique combinatorial approach using LASSO-Elastic Net regularizations and multilayer perceptron for PV generation forecasting; (3) applying a fixed-point primal dual log-barrier interior point method to expedite AC optimal power flow convergence; (4) adapting big data standards and capability maturity models to PV systems; (5) using K-nearest neighbors and random forests to impute missing values in PV big data; and (6) a hybrid data-model method that takes PV system deration factors and historical data to estimate generation and evaluate system performance using advanced metrics. These objectives were validated on three real-world case studies comprising grid-tied commercial PV systems. The results and conclusions show that the proposed imputation approach improved the accuracy by 91%, the estimation method performed better by 75% and 10% for two PV systems, and the use of the proposed forecasting model improved the generalization performance and reduced the likelihood of overfitting. The application of primal dual log-barrier interior point method improved the convergence of AC optimal power flow by 0.7 and 0.6 times that of the currently used deterministic models. Through the use of advanced performance metrics, it is shown how PV systems of different nameplate capacities installed at different geographical locations can be directly evaluated and compared over both instantaneous as well as extended periods of time. The results of this dissertation will be of particular use to multiple stakeholders of the PV domain including, but not limited to, the utility network and security operation centers, standards working groups, utility equipment, and service providers, data consultants, system integrator, regulators and public service commissions, government bodies, and end-consumers

User Association in 5G Networks: A Survey and an Outlook

26 pages; accepted to appear in IEEE Communications Surveys and Tutorial

Mathematical Models and Algorithms for Network Flow Problems Arising in Wireless Sensor Network Applications

We examine multiple variations on two classical network flow problems, the maximum flow and minimum-cost flow problems. These two problems are well-studied within the optimization community, and many models and algorithms have been presented for their solution. Due to the unique characteristics of the problems we consider, existing approaches cannot be directly applied. The problem variations we examine commonly arise in wireless sensor network (WSN) applications. A WSN consists of a set of sensors and collection sinks that gather and analyze environmental conditions. In addition to providing a taxonomy of relevant literature, we present mathematical programming models and algorithms for solving such problems. First, we consider a variation of the maximum flow problem having node-capacity restrictions. As an alternative to solving a single linear programming (LP) model, we present two alternative solution techniques. The first iteratively solves two smaller auxiliary LP models, and the second is a heuristic approach that avoids solving any LP. We also examine a variation of the maximum flow problem having semicontinuous restrictions that requires the flow, if positive, on any path to be greater than or equal to a minimum threshold. To avoid solving a mixed-integer programming (MIP) model, we present a branch-and-price algorithm that significantly improves the computational time required to solve the problem. Finally, we study two dynamic network flow problems that arise in wireless sensor networks under non-simultaneous flow assumptions. We first consider a dynamic maximum flow problem that requires an arc to transmit a minimum amount of flow each time it begins transmission. We present an MIP for solving this problem along with a heuristic algorithm for its solution. Additionally, we study a dynamic minimum-cost flow problem, in which an additional cost is incurred each time an arc begins transmission. In addition to an MIP, we present an exact algorithm that iteratively solves a relaxed version of the MIP until an optimal solution is found

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more