Related papers: Valid Cuts for the Design of Potential-based Flow …

We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…

The aim of this paper is a short survey of models and methods that developed by the authors. These models and methods are used to optimize general networks with nonlinear non-convex restrictions and objectives possessing mixed…

The existence of strictly positive lower bounds on voltage magnitude is taken for granted in optimal power flow problems. Nevertheless, it is not possible to rely on such bounds for a variety of real-world network optimization problems.…

Capacitated fixed-charge network flows are used to model a variety of problems in telecommunication, facility location, production planning and supply chain management. In this paper, we investigate capacitated path substructures and derive…

We study network design problems for nonlinear and nonconvex flow models without controllable elements under load scenario uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable…

Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety…

Due to their slow gas flow dynamics, natural gas pipelines function as short-term storage, the so-called linepack. By efficiently utilizing linepack, the natural gas system can provide flexibility to the power system through the flexible…

As a common practice, the direction of natural gas flow in every pipeline is determined ex-ante for simplification purposes, and treated as a given parameter within the scheduling problem. However, in integrated gas and electric power…

In this paper we study the min-cost flow problem in planar networks. We start with the min-cost flow problem and apply two transformations, one is based on geometric duality of planar graphs and the other on linear programming duality. The…

The maximum achievable capacity from source to destination in a network is limited by the min-cut max-flow bound; this serves as a converse limit. In practice, link capacities often fluctuate due to dynamic network conditions. In this work,…

Branch-price-and-cut algorithms play an important role in solving many vehicle routing problems (VRPs). Adding valid inequalities in this framework can impact the pricing subproblem, for which the literature distinguishes between 'robust'…

In potential flow networks, the equilibrium flow rates are usually not proportional to the demands and flow control elements are required to regulate the flow. The control elements can broadly be classified into two types - discrete and…

We examine the dynamic network flow problem under the assumption that the flow consists of discrete units. The dynamic network flow problem is commonly addressed in the context of developing evacuation plans, where the flow is typically…

The convex restriction of the power flow feasible sets identifies the convex subset of power injections where the solution for power flow is guaranteed to exist and satisfy the operational constraints. In contrast to convex relaxations, the…

We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of…

Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches. For this reason, we present further…

We consider a linear relaxation of a generalized minimum-cost network flow problem with binary input dependencies. In this model the flows through certain arcs are bounded by linear (or more generally, piecewise linear concave) functions of…

When the underlying physical network layer in optimal network flow problems is a large graph, the associated optimization problem has a large set of decision variables. In this paper, we discuss how the cycle basis from graph theory can be…

The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…

Non-convex, nonlinear gas network optimization models are used to determine the feasibility of flows on existing networks given constraints on network flows, gas mixing, and pressure loss along pipes. This work improves two existing gas…