# WaterModels Examples

The `examples`

directory contains two water network optimization instances that have been developed or modified from two literature instances.

The first is the famous "two-loop" water network design instance. (It is sometimes titled after one of its authors as `shamir`

.) This design instance dates back to 1977, first appearing in [1]. The globally optimal design cost is known to be $419,000. Solutions of this instance using various formulation types and assumptions appeared in the Quick Start Guide. As an example, it can be solved using a linear relaxation-based formulation (`LRDWaterModel`

) via the following:

```
using WaterModels
import HiGHS
data = parse_file("examples/data/json/shamir.json")
set_flow_partitions_si!(data, 0.5, 1.0e-4)
result = solve_des(data, LRDWaterModel, HiGHS.Optimizer)
```

The second is a modified version of the popular `van_zyl`

optimal water flow instance, which first appeared in [2] and is also named after one of that article's authors. Unlike the design problem, this problem has temporal aspects. It can be constructed and solved (e.g., using the `LRDWaterModel`

formulation) using the following:

```
using WaterModels
import HiGHS
import JuMP
data = parse_file("examples/data/epanet/van_zyl.inp")
data_mn = WaterModels.make_multinetwork(data)
set_flow_partitions_si!(data_mn, 1.0, 1.0e-4)
highs = JuMP.optimizer_with_attributes(HiGHS.Optimizer, "time_limit" => 60.0)
result = solve_mn_owf(data_mn, LRDWaterModel, highs)
```

The instance is challenging, and only a feasible solution is returned within the time limit for the script above. Also note that results are presented in an automatically-applied per-unit system. To convert the solution to SI units, the following can be executed:

`make_si_units!(result["solution"])`

## References

[1] Alperovits, E., & Shamir, U. (1977). Design of optimal water distribution systems. *Water Resources Research*, *13*(6), 885-900.

[2] Van Zyl, J. E., Savic, D. A., & Walters, G. A. (2004). Operational optimization of water distribution systems using a hybrid genetic algorithm. *Journal of Water Resources Planning and Management*, *130*(2), 160-170.