The exhaustive enumeration procedure employed by the optimization module of Wadiso is described in detail in the Optimization section. A broad summary of the procedure is given here to show where and how the critical period algorithm for tank sizing fits in.
When using Wadiso for pipe network optimization, the user specifies all the pipe links, which are to be sized in the system. For each of these pipes a range of candidate diameters is supplied. A cost per unit length needs to be specified for each of the candidate diameters. The program then generates all the possible combinations of pipe diameters. Each of these combinations is tested to see whether the user-specified pressure constraints are violated. The total cost for each feasible combination is calculated based on pipe costs and energy costs. No storage costs are considered. After all the combinations have been enumerated the most economical feasible combination of pipes is selected as the solution. By its very nature such enumeration requires large amounts of computer time. To alleviate this problem, a number of special features and tests have been introduced into the program:
i) To minimize the number of possible combinations, pipes can be arranged into groups, with all the pipes in one group having the same diameter. This also assists in ensuring a clear conveyance concept in the final solution.
(ii) Each combination generated is tested against the previous best solution. If the pipe cost plus minimum energy cost is larger than the total cost of the previously best solution, the combination is not tested further.
(iii) Each combination is also tested against a queue of pipe combinations previously found to be non-functional solutions. If all the pipes in the generated combination are smaller than or equal to the pipes of a previous non-functional solution, the combination is not tested further.
(iv) If a combination has passed both the "cost-test" and the "size-test", the pressure distribution needs to be calculated in order to check for the violation of pressure constraints. To this end the very efficient network solver is used.
To include the pipe cost/storage cost trade-off into the optimization procedure, an efficient tank sizing algorithm such as the critical period technique is required to calculate the storage costs associated with each pipe combination which has passed all the "tests". The flow chart below shows where the critical period technique fits into the procedure. This extended version of the optimization routine can be invoked as an optional feature. It can be regarded as an optimization model which includes the pipe cost/storage cost trade-off, whereas Wadiso normally optimizes without taking storage into account.
Enumeration with Tank Sizing
