Robust optimization of valve management to improve water quality in WDNs under demand uncertainty

Figures & data

Figure 1. Flow chart of the method.

Figure 2. Scheme of the cases of study: a) Sys473, b) Sys365, c) Sys47 and d) Sys40.

Figure 3. Pareto fronts obtained using Deterministic Optimization (DO) and Robust Optimization (RO), for different networks.

Table 1. Metadata of the distribution systems.

	Sys473		Sys365		Sys47		Sys40
	NoC1 = 122	NoC2 = 20	NoC1 = 116	NoC2 = 20	NoC1 = 6	NoC2 = 3	NoC1 = 15	NoC2 = 9
Unique solutions	1000	836	683	39	43	7	16	7
Reliable solutions	176	108	675	39	1	1	1	7
DOS reliability (%)	92.9	94.3	100	100	0	10.7	99.3	100
Sampling confidence(%)	96.11	96.11	96.11	96.11	96.11	96.11	95.09	95.09

Figure 4. Reliability and frequency of unique solutions.

Figure 5. Comparison among ROS1 (R1), ROS2 (R2), DOS (D), and the rest of the reliable solutions for all the cases.

Figure 6. Network Sys47, all pipes open (a), and optimum solutions closing six pipes (i.e. NoC1), deterministic (b) and robust (c).