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

Table 10

Comparison of accuracy for the upper level (UL) and lower level (LL) by the proposed algorithm and the algorithm in [28] for the test problems of the second set. A dash denotes that a feasible solution could not be obtained for the test problem. NA means the result is not available.

Problem	Dimension	Median value by the proposed algorithm		Median value in [28]
		UL accuracy	LL accuracy	UL accuracy	LL accuracy
SMD1	5	3.98𝑒−5	1.19𝑒−5	1.14𝑒−4	8.70𝑒−5
	10	6.61𝑒−5	3.66𝑒−5	3.32𝑒−4	1.80𝑒−5
	20	7.54𝑒−5	3.79𝑒−5	NA	NA
SMD2	5	5.61𝑒−5	2.19𝑒−5	7.30𝑒−5	1.60𝑒−5
	10	7.26𝑒−5	3.86𝑒−5	6.60𝑒−5	1.10𝑒−5
	20	8.47𝑒−5	3.24𝑒−5	NA	NA
SMD3	5	4.54𝑒−5	1.44𝑒−5	5.40𝑒−5	5.50𝑒−5
	10	6.35𝑒−5	3.09𝑒−5	3.59𝑒−4	3.30𝑒−5
	20	6.97𝑒−5	2.81𝑒−5	NA	NA
SMD4	5	3.98𝑒−5	1.02𝑒−5	2.30𝑒−5	5.70𝑒−5
	10	6.55𝑒−5	2.68𝑒−5	2.86𝑒−4	2.70𝑒−5
	20	7.62𝑒−5	4.70𝑒−5	NA	NA
SMD5	5	2.92𝑒−5	9.39𝑒−5	2.00𝑒−6	9.00𝑒−6
	10	6.23𝑒−5	9.72𝑒−5	5.20𝑒−5	9.00𝑒−6
	20	7.54𝑒−5	3.79𝑒−5	NA	NA
SMD6	5	3.98𝑒−5	1.19𝑒−5	1.08𝑒−4	6.10𝑒−5
	10	6.61𝑒−5	3.66𝑒−5	1.44𝑒−3	8.20𝑒−5
	20	6.73𝑒−5	2.33𝑒−5	NA	NA
SMD7	5	4.55𝑒−5	1.17𝑒−9	1.60𝑒−5	1.77𝑒−4
	10	6.55𝑒−5	3.15𝑒−8	6.26𝑒−3	1.27𝑒−4
	20	7.62𝑒−5	4.62𝑒−7	NA	NA
SMD8	5	6.16𝑒−5	4.38𝑒−2	1.74𝑒−4	2.70𝑒−5
	10	7.96𝑒−5	4.55𝑒−5	3.12𝑒−3	1.57𝑒−4
	20	8.61𝑒−5	6.77𝑒−5	NA	NA
SMD9	5	4.23𝑒−5	1.72𝑒−5	1.70𝑒−5	5.40𝑒−5
	10	5.90𝑒−5	3.17𝑒−5	—	—
	20	8.80𝑒−5	4.53𝑒−5	NA	NA
SMD10	5	1.58𝑒−5	9.49𝑒−6	3.48𝑒−2	1.85𝑒−2
	10	3.36𝑒−5	1.67𝑒−4	—	—
	20	—	—	NA	NA
SMD11	5	5.70𝑒−5	1.32𝑒−5	1.32𝑒−2	1.30𝑒−2
	10	9.66𝑒−5	1.40𝑒−5	—	—
	20	—	—	NA	NA
SMD12	5	5.98𝑒−5	2.02𝑒−5	3.24𝑒−2	2.06𝑒−4
	10	1.33𝑒−4	5.58𝑒−5	—	—
	20	—	—	NA	NA