Table 5 Search space of different encodings for systems
From: An effective encoding scheme of obtaining radial topology structures in distribution networks
Reference | 33-bus system | 69-bus system | m-bus system | ||||||
|---|---|---|---|---|---|---|---|---|---|
Size of solution space | Feasible solution (%) | Rt1 (s) | Rt2 (s) | Size of solution space | Feasible solution (%) | Rt1 | Rt2 (s) | Size of solution space | |
Sivanagaraju et al. (2008) | 237 = 1.3744 × 1011 | 0.00004 | – | 197.04 | 273 = 5.9030 × 1020 | 3.4714 × 10−15 | – | 1018.34 | 2 m |
Fontan (2008) | \({\text{C}}_{ 3 6}^{ 5}\) = 376,992 | 13.46 | 465.94 | 2.5131 | \({\text{C}}_{ 7 1}^{ 5}\) = 4,187,106 | 7.83 | – | 2.6507 | \(C_{m }^{n}\) |
Zhu (2002) | 375 = 69,343,957 | 0.0732 | – | 125.9735 | 735 = 2.0731 × 109 | 0.0158 | – | 541.0476 | m n |
Sawa (2009) | 10 × 15 × 7 × 21 × 11 = 242,550 | 20.92 | 294.76 | 0.0154 | 17 × 8 × 24 × 32 × 17 = 1,775,616 | 18.47 | 8.1 h | 0.0482 | \(\prod\nolimits_{i}^{n} {m_{i} }\) |
Asrari et al. (2015) | 242,550 | 20.92 | 253.72 | 0.0143 | 1,775,616 | 18.47 | 7.6 h | 0.0445 | – |
Jikeng et al. (2013) | 50,751 | 100 | 79.35 | 0.0049 | 327,868 | 100 | 292.02 s | 0.0088 | – |
de Macedo Braz and de Souza (2011) | – | – | – | 0.0032 | – | – | – | 0.0059 | – |
Proposed scheme | 50,751 | 100 | 0.1092 | 0.0024 | 327,868 | 100 | 0.2068 s | 0.0034 | \(\sum\nolimits_{j = 1}^{j} {\prod\nolimits_{n = 1}^{n} {m_{jn} } }\) |