Design and Maintenance Optimisation of Substation Automation Systems: A Multiobjectivisation Approach Exploration

Table 5

Statistical analysis (3-objective problem) of hypervolume indicator.

ID	Method	Encoding	Mutation	Average	Median	Maximum	Minimum	Standard deviation	Average rank (Friedman test)
1	NSGA-II	Real	0.5	4.0442	4.0420	4.0862	3.9998	0.0229	6.2857
2	NSGA-II	Real	0.1	4.0422	4.0394	4.0856	4.0144	0.0167	6.4761
3	NSGA-II	Real	1.5	4.0377	4.0372	4.0613	4.0066	0.0158	7.6190
4	NSGA-II	Binary	0.5	4.0473	4.0445	4.0716	4.0184	0.0151	5.4285
5	NSGA-II	Binary	1.0	4.0453	4.0413	4.0948	4.0053	0.0228	5.9523
6	NSGA-II	Binary	1.5	4.0436	4.0430	4.1269	4.0002	0.0265	6.4761
7	SMS-EMOA	Real	0.5	4.0527	4.0480	4.1046	4.0160	0.0259	5.3809
8	SMS-EMOA	Real	1.0	4.0531	4.0512	4.1035	4.0255	0.0191	4.9523
9	SMS-EMOA	Real	1.5	4.0487	4.0472	4.0892	4.0177	0.0192	5.8095
10	SMS-EMOA	Binary	0.5	4.0382	4.0383	4.1104	4.0056	0.0261	7.5714
11	SMS-EMOA	Binary	1.0	4.0373	4.0352	4.0704	4.0168	0.0147	7.3809
12	SMS-EMOA	Binary	1.5	4.0301	4.0308	4.0603	4.0069	0.0148	8.6666
value									0.0260

Best values (column-wise), in bold type.