Distribution network optimization: Finding the most economic solution by using genetic algorithms

lal Ib~ (c~ Fig. 6. Applying the 4-block heuristics for three-dimensional pallet loading. (a) Layer 1; (b) Layer 2; (c) Layer 3. In this paper the problem of calculating optimal packing patterns of small rectangles on a pallet is considered. We propose new heuristics which are based on the 4-block structure of packing patterns. Since, in general, for practical applications additional restrictions have to be regarded, we developed a recurrence formula for which it is relative easy to handle such conditions. This is shown by means of some concrete requirements of practical interest. Moreover, it should not be very difficult to take into account further restrictions in this way. Depending on the concrete circumstances when applying these heuristics further modifications may be required. The pictures in Fig. 6 illustrate such a situation. During the computation of the packing pattern for the second (third) layer in a three-dimensional packing process the height structure of the previous layer as well as remaining pieces of already used types have to be considered. A new heuristic approach is proposed in [ 14] for solving the (three-dimensional) multi-pallet loading problem which uses the heuristics described in this paper. "The three-dimensional pallet chart: An analysis of the factors affecting the set of feasible layouts for a class of two-dimensional packing problems",A comparative analysis of heuristics for the two-dimensional packing problem", in: Paper for Euro VI Conference. Abstract The problem of finding the optimal features in a distribution network is approached from an economic viewpoint. This problem is closely related to drops in pressure within the network, and is a complex mathematical problem with some empirically adjusted formulae that make the problem very difficult to solve analytically. Thus, a method is proposed for finding the optimal network features, based on a well known optimization procedure, genetic algorithms, which have proven to be useful in this type of problems. Furthermore, new problem-specific genetic operators are presented and shown to be intuitively and in practice better than the standard ones.