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Pipe network optimization is a relatively new field. Nevertheless, a fair number of algorithms have been suggested to perform optimization. But, there is no procedure yet which is generally accepted as “the best technique”. Optimization of networks is difficult for a number of reasons:

•Pipe sizes are selected from a list of available sizes, and thus size is not a continuous variable;

•Cost functions are rather arbitrary and cannot easily be put into a mathematical form;

•When cost for pumping energy is to be included, the pressure distribution in the system must be known;

•The cost function of a looped system, as a function of pipe sizes to be selected, may have several local minima, yet only the global minimum is of interest; and

•Optimization should be carried out for several design loads, so that pressure requirements, which may differ from load to load, can be met simultaneously.

 

In Wadiso, a relatively straightforward algorithm is employed, based on exhaustive enumeration. The user specifies the sizes to be considered for each pipe, and the program simply tests all possible combinations of pipe sizes, to check whether the specified pressure constraints are met. In the process of testing, the technique takes advantage of two considerations: after a functional combination of pipe sizes has been found, there is no need to test any other pipe size combination which is more expensive, and after a non-functional size combination has been encountered, any other size combination, with all sizes equal or less than in the non-functional solution, is non-functional as well. (There are some exceptions to this rule, which Wadiso takes into account.) As a result of considering those two aspects, Wadiso does not need to calculate flow and pressure distribution for all combinations. Indeed, the larger the total number of combinations, the smaller the percentage of combinations for which the pressure distribution needs to be calculated. It is not unusual for Wadiso to test less than one percent of all possible combinations for pressure.

 

The program also takes advantage of the convergence characteristics of the node method. If pressure needs to be calculated, the algorithm may quickly (in two or three iterations) determine that a combination will or will not work. Only in very few combinations will it be necessary to calculate pressure distribution to a high degree of accuracy.

 

Exhaustive enumeration has one more important advantage: it allows for the establishment of a queue of Pareto Optimal solutions; that is solutions which may cost a little bit more than the optimum solution, yet provide for better pressure, or solutions which may slightly violate the pressure requirement, but do offer some cost savings. In other words, the user gets immediate feedback on the sensitivity of the optimum to the specified pressure requirements. It is this queue of Pareto Optimal solutions which many users of Wadiso find to be of particular value.