A Packing Problem , Solved by Genetic Algorithms Georg

An arbitrary number of points are arranged in a given twodimensional simply connected region such that their mutual distances and the distance from the region boundary becomes a maximum. Category: D.2.2, J.5 1 Genetic algorithms as optimization tool for packing problems We report the solution of twodimensional packing problems by the method of genetic algorithms. Thereby, we do not seek a con guration which minimizes the space necessary to arrange rigid objects, but rather we attempt to maximize the space available to any single object. Problems of this kind appear in as diverse research areas as physical potential theory as well as in architectural urban planning strategies. Genetic algorithms [1, 2, 3, 4, 5] represent an optimization method for computationally \hard" problems [6, 7, 8]. A \genetic pool" of solutions to a given problem is transformed by random \mutations" and \crossovers" of their respective codes. The new solutions are then evaluated by a \ tness function," such that only the best solutions \survive." This procedure can be applied until the \pool" of solution reaches a (statistical) xed point. Although there is no e ective guarantee to nd (one of) the optimal solution(s), for many applications the method converges quite fast and to a reasonable result. To be more speci c, consider an arbitrary number of n dimensionless objects. Assume further an arbitrary closed polygon with m edges de ning a simply connected twodimensional region. Every single possible solution s is encoded by the concatenation of the x; y-coordinate pair of each object; i.e., s = fx1; y1; x2; y2; :::; xn; yng: Journal of Universal Computer Science, vol. 5, no. 8 (1999), 464-470 submitted: 20/8/99, accepted: 25/8/99, appeared: 28/8/99  Springer Pub. Co.