Modelling of Regional Networks for Minimum Cost

Abstract

<p>A computer model is developed for the solution of regional network systems on a minimum cost basis. Different network problem types are identified to define the scope of the model. Generally, the problem involves the determination of the optimum conveyance schedule required to supply a set of consumer nodes with a commodity or public service provided by one or more processing centres (i.e. water supply, solid waste or wastewater collection networks). The system costs include costs incurred due to conveyance of material and the processing of that material; both of these cost components exhibit economies of scale and generally lead to the centralization of processing.</p> <p>A mathematical statement of the problem is developed which is applicable to all network types, can be utilized easily and efficiently in a digital computer and facilitates the use of a variety of optimization routines. A number of algorithms, ranging from linear approximation to nonlinear gradient search routines, are investigated for possible inclusion in the model with the advantages and disadvantages of each being identified.</p> <p>A modular package, NETSOL, is developed which facilitates the use of alternate optimization routines and allows for the inclusion of complex design functions in the computation of system costs. An interactive command structure permits the user to modify the network system parameters thereby combining intuitive design with the capacity to select an optimal solution from a large number of alternatives. Thus a model is obtained which is flexible enough to answer many of the questions that arise in network problems and also determine the optimum.</p> <p>In view of the disadvantages found in the existing optimization techniques (e.g. convergence to local minima), the properties of the network problems are investigated in detail to isolate any special characteristics. For a system involving separable concave cost functions, the minimum cost solution to a network problem lies at one of the vertices formed by the problem constraints. A new solution algorithm, HYVRST, is developed which takes advantages of this important property utilizing a direct search technique. This results in an efficient and stable algorithm with good convergence properties. A number of example are presented to test the optimization algorithms and demonstrate the usefulness of the NETSOL package in solving regional network problems.</p>