12th International Symposium on District Heating and Cooling

The <strong>12th</strong> <strong>International</strong> <strong>Symposium</strong> on District Heating and Cooling,September 5 th to September 7 th , 2010, Tallinn, EstoniaThis shape leads to the fact that as a solution under therequirements mentioned above a graph free ofmeshes, thus a tree, arises.This complex course of the objective function requiresespecially suitable methods.Development of mathematical proceduresDifferent mathematical methods are used:a) The classical non-linear optimization which isapplied for the diameter optimization for fixeddevelopment ways.b) Topological optimizations to the determination ofthe shortest ways (shortest path problem) and theshortest networks (spanning tree problem) whichare combined under use of the procedure from a)to a special iteration process.c) Stochastic methods for the improvement of theoptimization results of the algorithm of b): A specialimplementing of the Monte Carlo Method and aspecial implementing of the Evolutionary Algorithm.Project processingThe help file and the user's manual of this programcontain detailed instructions to its operation and for theproject processing which occurs typically in six steps inthe change of STEFaN (steps 2, 3, 5 and 6 a) and of aGIS (steps 1, 4 and 6 b).These necessary steps 1 to 6 are demonstrated at afictive example. As a GIS system the recommendedand provided program ShapeUp (www.nilione.com) isused. It is freeware too.ExampleStep 1: Gathering of Geographical informationWith the GIS layers (themes) with geo-referencedinformation (vertices for the source and for thecustomer as well as edges for consisting and possibleroutes) invested and in a special standardized format(MIF – MapInfo Interchange format) exports:a) The geo-referenced background image is imported(© OpenStreetMap, pale colors in Fig. 7). Thefigures of the buildings (darkly) and the courses ofthe streets (white) allow a good orientation.Fig. 7 step 1323