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

Table 11

Comparison of function evaluations (FE) for the upper level (UL) and lower level (LL) by the proposed differential evolution algorithm (DE) and the nested bilevel evolutionary algorithm (NBEA) in [28] for 5-dimensional test problems of the second set.

Problem	Algorithm	Best FE		Median FE		Worst FE
		UL	LL	UL	LL	UL	LL
SMD1	DE	440	19,257	760	30,510	960	35,661
	NBEA	438	256,858	668	375,488	1,008	582,770
SMD2	DE	360	16,583	680	28,759	880	35,672
	NBEA	380	196,744	628	332,197	1,102	613,221
SMD3	DE	440	18,070	760	28,386	960	33,556
	NBEA	488	262,703	604	315,598	844	439,316
SMD4	DE	400	12,284	600	17,694	800	21,990
	NBEA	420	259,486	608	366,294	796	480,675
SMD5	DE	520	14,673	720	21,356	920	27,649
	NBEA	444	222,078	930	457,265	1,232	610,108
SMD6	DE	440	4,789	760	8,157	960	10,210
	NBEA	540	334,763	696	427,114	936	585,358
SMD7	DE	400	10,572	740	17,428	920	21,213
	NBEA	468	246,375	652	333,629	1,342	685,029
SMD8	DE	560	36,486	1,200	87,965	1,800	134,656
	NBEA	812	443,430	1,008	582,583	2,076	1,218,196
SMD9	DE	120	7,430	840	41,365	1,080	52,429
	NBEA	330	183,231	514	284,648	696	395,735
SMD10	DE	1,840	69,110	2,380	89,266	4,040	165,797
	NBEA	480	179,986	758	277,696	1,316	501,639
SMD11	DE	280	11,769	800	37,108	960	44,865
	NBEA	4,348	11,489,609	5,086	13,408,524	7,764	20,540,610
SMD12	DE	2,120	117,423	2,740	149,102	4,040	297,407
	NBEA	354	6,211,173	738	12,950,512	1,196	20,983,708