Speeding up Energy System Models - a Best Practice Guide

Background Energy system models (ESM) are widely used in research and industry to analyze todays and future energy systems and potential pathways for the European energy transition. Current studies address future policy design, analysis of technology pathways and of future energy systems. To address these questions and support the transformation of today’s energy systems, ESM have to increase in complexity to provide valuable quantitative insights for policy makers and industry. Especially when dealing with uncertainty and in integrating large shares of renewable energies, ESM require a detailed implementation of the underlying electricity system. The increased complexity of the models makes the application of ESM more and more difficult, as the models are limited by the available computational power of today’s decentralized workstations. Severe simplifications of the models are common strategies to solve problems in a reasonable amount of time – naturally significantly influencing the validity of results and reliability of the models in general. Solutions for Energy-System Modelling Within BEAM-ME a consortium of researchers from different research fields (system analysis, mathematics, operations research and informatics) develop new strategies to increase the computational performance of energy system models and to transform energy system models for usage on high performance computing clusters. Within the project, an ESM will be applied on two of Germany’s fastest supercomputers. To further demonstrate the general application of named techniques on ESM, a model experiment is implemented as part of the project. Within this experiment up to six energy system models will jointly develop, implement and benchmark speed-up methods. Finally, continually collecting all experiences from the project and the experiment, identified efficient strategies will be documented and general standards for increasing computational performance and for applying ESM to high performance computing will be documented in a best-practice guide

Optimal lines in public rail transport

This thesis deals with the line planning problem for public transportation networks based on periodic schedules. The models and algorithms represented in this thesis take care of peculiarities of public rail transport. A line consists of a route in the network and a cycle time. The line planning problem consists of choosing a set of operating lines that complies with the passenger demand and optimizes a given objective. An important frame work for line planning is based on a hierarchical decomposition of this complex problem. The most challenging task is the line optimization problem. Algorithms for the line optimization problem described in the literature focus on heuristics with one major drawback: the lack of a performance guarantee for generated solutions. The models for the line planning problem considered in this monograph are integer linear programs. These programs provide a convenient way of modeling variants of the line optimization problem as well as a general solution technique. The objectives for the line optimization problem discussed in this thesis present service- and cost evaluations of line plans. The service quality of a line plan is determined by the number of direct travelers. The model improvements, which lead to fast solution times even for large scale real world problem instances, are based on techniques of polyhedral optimization.Die vorliegende Arbeit beschäftigt sich mit dem Thema der optimalen Linienführung für getaktete spurgeführte Verkehrsysteme, wie der Eisenbahn. Der Linienfuuml;hrung zugrundeliegende Linienplan besteht aus einer Menge von Wegen im Schienennetz, denen Takte bzw. Frequenzen zugeordnet sind. Ziel der Linienoptimierung ist es, einen Linienplan zu finden, der unter Berücksichtigung des Verkehrsaufkommens eine Zielfunktion optimiert. Die Linienplanung läßt sich in vier hierarchisch angeordnete Aufgaben zerteilen, unter denen die Linienoptimierung den zentralen Aspekt darstellt. Die bisher vorgeschlagenen Verfahren zur Linienoptimierung beruhen ausschließlichen auf Heuristiken, die keine Gütegarantien für generierte Lösungen liefern können. Die in dieser Arbeit präsentierten Modelle zur Linienoptimierung basieren auf ganzzahligen linearen Programmen. Die grundlegenden theoretischen Konzepte zur Modellierung, Klassifizierung und Lösung dieser Programme werden für verschiedene Varianten des Linienoptimierungsproblems präsentiert. In den Modellen steht sowohl die kostenorientierten Bewertung als auch die Bewertung der Linienpläne aus Kundensicht mittels des Konzepts der Direktfahrer im Zentrum. Durch den Einsatz von Methoden der polyedrischen Optimierung werden die ganzzahligen linearen Modelle verbessert, so daß Instanzen von praktisch relevanten Größe mit ausreichender Genauigkeit in akzeptabler Zeit gelöst werden können

Short Note on Edge Connectivity Augmentation

Consider a network N = (V; Ec ; c) with an integer valued capacity function c: V \Theta V ! Z+ , and let k be a positive integer. What is the minimal total increase fl by which the individual capacities must be increased such that the edge connectivity number is at least k? Clearly the defect r(u) := max(k \Gamma ffi c (u); 0) summing over all vertices, called fl T is a lower bound for fl. Kajitani and Ueno [7] proved that if (V; Ec ) is a tree then fl = fl T . We extend this result to the larger class of acyclic digraphs. Frank [4] gives a min-max formula for fl which is proved using Maders [8] splitting theorem. In order to obtain an efficient implementation of the resulting strong polynomial time algorithm, one must carry out some reduction and splitting operations which, in turn, entail performing several maximal flow computations. We give an implementation which significantly decreases the time complexity of the reduction phase, and substantially reduces the running time of the e..