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In a slight variation of the enumeration algorithm the cost test and the pressure test can be somewhat relaxed to yield a set of good solutions instead of one solution only. A solution can belong to this set if it has the property of being Pareto Optimal (non-inferior). This means that there must not be another combination which can produce greater pressure at less cost.

Using this concept, a functional combination is allowed to pass the cost test even if the cost is higher than the cost of the previous best solution, but remains within a certain tolerance (expressed as a percentage) from the cost of this best solution. The idea is to look for size combinations for which no solution offering a higher minimum pressure is less costly. Such a combination is said to be Pareto Optimal. If the combination is indeed Pareto Optimal, it is compared with a queue of previously found Pareto Optimal combinations. If appropriate, the combination is entered into the queue, and if the combination makes other entries in the queue inferior, they are eliminated from the queue.

A functional combination may also be allowed to pass the pressure test even if the minimum pressure is less than the required pressure, but within a certain pressure tolerance from the pressure requirements. This enables solutions which barely fail the pressure test to be included in the Pareto Optimal set even though they will not be the globally optimal solution.

The fact that a solution is slightly more expensive may not automatically exclude it from consideration. It is possible that minor additional expenditures may result in significantly better system performance. Considering the fact that the pipe network is designed for a projected (estimated) water output, a pressure slightly below the specified requirement does not necessarily imply that the combination of pipe sizes is unacceptable. The queue of Pareto Optimal solutions is therefore helpful information because of the uncertainties associated with the planning goals.

It is important to understand that the larger the allowable cost and pressure margins, the more combinations will meet the pressure test. This in turn increases computer time requirements.