Multi-objective calibration of Tank model using multiple genetic algorithms and stopping criteria

Parameter	Description	Unit	Range
Parameter	Description	Unit	Minimum	Maximum
S1I^a a Parameter common to both the 3-tank and 4-tank structures of the Tank model;	Initial storage of tank 1	mm	5	50
S2I^a	Initial storage of tank 2	mm	10	50
S3I^a	Initial storage of tank 3	mm	20	100
S4I^b	Initial storage of tank 4	mm	30	500
H1^a	Height of side outlet 1 in tank 1	mm	10	70
H2^a	Height of side outlet 2 in tank 1	mm	10	45
H3^a	Height of side outlet of tank 2	mm	10	70
H4^b b Parameter presents only in the 4-tank structure.	Height of side outlet of tank 3	mm	10	70
A1^a	Runoff coefficient (tank 1)	min^-1	0.09	0.5
A2^a	Sub-surface flow coefficient (tank 1)	min^-1	0.09	0.5
A3^a	Intermediate flow coefficient (tank 2)	min^-1	0.09	0.5
A4^a	Sub-base flow coefficient (tank 3)	min^-1	0.01	0.1
A5^b	Base flow coefficient (tank 4)	min^-1	0.001	0.01
B1^a	Infiltration coefficient in tank 1	min^-1	0.01	0.1
B2^a	Infiltration coefficient in tank 2	min^-1	0.01	0.1
B3^b	Infiltration coefficient in tank 3	min^-1	0.001	0.1

Basin	MOEA	3-tank structure				4-tank structure
		CALIBRATION^a a Standard stopping criterion;		CALIBRATION^b b Ticona stopping criterion;		CALIBRATION^a		CALIBRATION^b
		NS	RMSE_inv^*	NS	RMSE_inv^* * Unit: (s/m3);	NS	RMSE_inv^*	NS	RMSE_inv^*
Ijuí	NSGA-II	0.6519	19963.5	0.6515	19887.1	0.7645	0.00626	0.7640	0.00628
	NSGA-III	0.6521	19887.1	0.6518	20190.7	0.7638	0.00623	0.7585	0.00620
	SPEA-II	0.6489	18947.0	0.6528	20039.5	0.7650	0.00626	0.7633	0.00632
Vila Canoas	NSGA-II	0.7002	23317.6	0.7004	23692.0	0.7914	0.03604	0.7913	0.03615
	NSGA-III	0.6934	20884.0	0.6921	20743.1	0.7925	0.03627	0.7900	0.03607
	SPEA-II	0.7001	23484.8	0.7004	23567.9	0.7885	0.03617	0.7902	0.03644

MOEA	Metrics^a a Standard stopping criterion;			Metrics^b b Ticona stopping criterion;
MOEA	SP	MS	GD	SP	MS	GD
NSGA-II	0.000055	0.009015	0.000248	0.000045	0.008048	0.000286
NSGA-III	0.000447	0.016029	0.000247	0.001193	0.031362	0.000331
SPEA-II	0.000633	0.032155	0.000441	0.000178	0.024078	0.000398

Basin	MOEA	CALIBRATION^a a Standard stopping criterion;		CALIBRATION^b b Ticona stopping criterion;		VALIDATION^a		VALIDATION^b
Basin	MOEA	NS	RMSE_inv^*	NS	RMSE_inv^* * Unit: (s/m3);	NS	RMSE_inv^*	NS	RMSE_inv^*
Ijuí	NSGA-II	0.7645	0.0063	0.7640	0.0063	0.6192	0.0056	0.6131	0.0057
	NSGA-III	0.7638	0.0062	0.7585	0.0062	0.6325	0.0056	0.6178	0.0057
	SPEA-II	0.7650	0.0063	0.7633	0.0063	0.6334	0.0056	0.6295	0.0055
Vila Canoas	NSGA-II	0.7914	0.0360	0.7913	0.0361	0.8107	0.0293	0.8110	0.0292
	NSGA-III	0.7925	0.0363	0.7900	0.0361	0.8118	0.0294	0.8094	0.0297
	SPEA-II	0.7885	0.0362	0.7902	0.0364	0.8072	0.0326	0.8093	0.0318

NS = 1 - [\frac{\sum_{t = 1}^{NT} {(Q_{Obs, t} - Q_{Calc, t})}^{2}}{\sum_{t = 1}^{NT} {(Q_{Obs, t} - {\underline{Q}}_{Obs})}^{2}}]

D_{i, w} = {[\frac{1}{{ND}_{i}} \sum_{j = 1}^{{ND}_{i}} {({OF}_{1 (i, j)} - {OF}_{1 rel})}^{2} + {({OF}_{2 (i, j)} - {OF}_{2 rel})}^{2}]}^{0.5}

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