A Differential Evolution with Two Mutation Strategies and a Selection Based on an Improved Constraint-Handling Technique for Bilevel Programming Problems

Table 8

Statistical results obtained by the proposed algorithm for second set of nonlinear BLPPs.

Problem	5 dimensions			10 dimensions			20 dimensions
	SR (%)	MNFE	SD	SR (%)	MNFE	SD	SR (%)	MNFE	SD
SMD1	100	750	2.45𝑒−5	100	2,069	2.24𝑒−5	100	3,996	2.02𝑒−5
SMD2	100	673	2.90𝑒−5	100	1,635	2.72𝑒−5	100	3,756	1.49𝑒−5
SMD3	100	748	2.86𝑒−5	100	2,086	2.43𝑒−5	100	3,920	2.30𝑒−5
SMD4	100	606	2.93𝑒−5	100	1,554	2.48𝑒−5	100	3,436	1.32𝑒−5
SMD5	100	712	3.17𝑒−5	100	1,953	2.51𝑒−5	100	3,996	2.02𝑒−5
SMD6	100	750	2.46𝑒−5	100	2,069	2.24𝑒−5	100	4,091	2.17𝑒−5
SMD7	100	739	2.85𝑒−5	100	2,162	2.18𝑒−5	82	5,175	3.50𝑒−2
SMD8	100	1,181	2.81𝑒−5	100	3,447	2.07𝑒−5	100	6,024	1.12𝑒−5
SMD9	100	838	2.96𝑒−5	100	2,432	2.50𝑒−5	100	6,604	1.96𝑒−5
SMD10	92	2,513	4.38𝑒+0	100	6,680	5.26𝑒−5	—	—	—
SMD11	100	771	2.40𝑒−5	100	10,429	2.88𝑒−4	—	—	—
SMD12	80	2,951	1.59𝑒+1	100	7,625	4.75𝑒−5	—	—	—