Segment Routing (SR), a modern network architecture enhancing traffic engineering, offers flexibility by allowing traffic to be routed through intermediate nodes or links. This paper addresses the challenge of optimizing routing in uncertain traffic distribution scenarios. Rather than relying on a single traffic matrix for optimization, we take a unique approach, considering an infinite set of matrices defined by linear constraints. Our goal is to optimize routing strategies under the worst-case scenario within this set. Through novel formulations, we achieve significant improvements in optimization speed compared to traditional methods that explore all extreme points or use iterative constraint generation for these matrices. This research contributes to the field by enhancing the robustness of SR-based traffic engineering, an area previously explored using different methodologies. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

In this article we introduce a preprocessing technique to solve the Segment Routing Traffic Engineering Problem optimally using significantly fewer computational resources than previously introduced methods. Segment routing is a recently developed interior gateway routing protocol to be used on top of existing protocols that introduces more flexibility in traffic engineering. In practice, segment routing allows to deviate traffic from its original path by specifying a list of intermediate nodes or links, called segments, to visit before going to its destination. The issue we tackle in this article is that the number of segment paths scales exponentially with the maximum number of segments allowed leading to scalability issues in mathematical formulations. This article introduces the notion of dominated segment paths, these are paths that can be eliminated from the solution space when searching for an optimal solution. We propose a dynamic programming algorithm eliminating dominated paths for any number of segments. Numerical results show that respectively 50%, 90%, and 97% of paths are dominated when considering up to 2, 3, and 4 segments on benchmark network topologies.

Segment routing has recently received much attention in industry and academia for providing simple yet powerful and scalable traffic engineering, a most important concern for Internet Service Providers. However, the fundamental optimization problem underlying segment routing needs to be better understood today. This paper addresses this gap and presents a novel algorithmic approach to optimize traffic engineering in segment routing networks, accounting for demand uncertainty. In particular, we propose a stochastic approach to online segment routing which uses a conditional value at risk when accounting for the traffic matrix uncertainty. This approach can perform significantly better than the worst-case approach often considered in the literature. We also show that depending on the demand volatility, our stochastic approach can be further optimized in that it is sufficient to account for only a part of the demand without sacrificing traffic engineering quality.

With the emerging deregulated electricity markets, a part of the electricity trading takes place in day-ahead markets where producers and retailers place bids in order to maximize their profit. We present a price-maker model for strategic bidding from the perspective of a producer in Price Coupled Regions (PCR) considering a capacitated transmission network between local day-ahead markets. The aim for the bidder is to establish a production plan and set its bids taking into consideration the reaction of the market. We consider the problem as deterministic, that is, the bids of the competitors are known in advance. We are facing a bilevel optimization problem where the first level is a Unit Commitment problem, modeled as a Mixed Integer Linear Program (MILP), and the second level models a market equilibrium problem through a Linear Program. The problem is first reformulated as a single level problem. Properties of the optimal spot prices are studied to obtain an extended formulation that is linearized and tightened using new valid inequalities. Several properties of the spot prices allow to reduce significantly the number of binary variables. Two novel heuristics are proposed, the first applicable in PCR, the second for general formulations with Special Ordered Sets (SOS) of type 1. Our computational experiments highlights the risk of a loss for the bidder if some aspects usually not considered in the literature, such as Price Coupled Regions, or an accurate UC problem, are not taken into account. They also show that the reformulation techniques, combined with new valid inequalities, allow to solve much larger instances than the current state-of-the-art. Finally, our experiments also show that the proposed heuristics deliver very high quality solutions in a short computation time.

A distribution network is a system aiming to transfer a certain type of resource from feeders to customers. Feeders are producers of a resource and customers have a certain demand in this resource that must be satisfied. Distribution networks can be represented on graphs and be subject to constraints that limit the number of intermediate nodes between some elements of the network (hop constraints) because of physical constraints. This paper uses layered graphs for hop constrained problems to build extended formulations. Preprocessing techniques are also presented to reduce the size of the layered graphs used. The presented model is studied on the hop-constrained minimum margin problem in an electricity network. This problem consists of designing a connected electricity distribution network, and to assign customers to electricity feeders at a maximum number of hops H so as to maximize the minimum capacity margin over the feeders to avoid an overload for any feeder. Numerical results of our model are compared with those of state-of-the-art solution techniques of the minimum margin problem from Rossi, Aubry and facomino (2011). Variations of the initial problem are also presented, considering losses due to transportation or by replacing hop constraints by distance constraints, a variation arising in the context of multicast transmission in telecommunications. (C) 2017 Elsevier B.V. All rights reserved.

In this paper we consider energy management optimization problems in a future wherein an interaction with micro-grids has to be accounted for. We will model this interaction through a set of contracts between the generation companies owning centralized assets and the micro-grids. We will formulate a general stylized model that can, in principle, account for a variety of management questions such as unit commitment. The resulting model, a bilevel stochastic mixed integer program will be numerically tackled through a novel preprocessing procedure. As a result the solution for the bilevel (or single leader multiple follower) problem will be neither "optimistic" nor "pessimistic". We will numerically evaluate the difference of the resulting solution with the "optimistic" solution. We will also demonstrate the efficiency and potential of our methodology on a set of numerical instances. (C) 2018 Elsevier By. All rights reserved.