Enhancing Hyperheuristics for the Knapsack Problem through Fuzzy Logic

Table 4

Percentage of times when the hyperheuristics get better or equal results than the Oracle applied to the sets of hard instances.

Metrics		Set of instances	Methods
			HH4	HH6	HH8	FuzzyHH
Average	Equal	20	43.67%	51.75%	56.14%	59.94%
		50	41.31%	50.55%	55.10%	59.13%
		100	43.01%	51.38%	55.00%	59.08%
		200	38.64%	36.95%	35.26%	33.90%
	Better	20	3.10%	3.30%	2.76%	7.13%
		50	2.47%	2.60%	1.97%	5.18%
		100	1.74%	1.69%	1.27%	3.22%
		200	0.82%	0.96%	0.66%	1.73%
Standard deviation	Equal	20	12.19%	12.19%	13.12%	8.05%
		50	19.67%	18.40%	20.39%	10.63%
		100	25.03%	22.80%	25.76%	14.38%
		200	29.45%	26.67%	30.12%	17.16%
	Better	20	3.96%	3.72%	3.44%	2.76%
		50	3.11%	3.05%	2.46%	2.72%
		100	2.06%	1.86%	1.63%	1.86%
		200	0.92%	0.87%	0.73%	1.37%
Best	Equal	20	59.83%	74.83%	83.83%	93.16%
		50	59.33%	74.16%	83.16%	92.83%
		100	59.66%	74.83%	83.83%	93.16%
		200	55.16%	66.16%	74.33%	82.33%
	Better	20	12.50%	12.16%	12.50%	13.66%
		50	9.16%	9.00%	8.00%	12.00%
		100	7.16%	6.16%	6.33%	6.16%
		200	3.16%	2.50%	2.66%	5.16%
Worst	Equal	20	21.00%	14.16%	20.00%	28.50%
		50	16.83%	12.66%	13.83%	23.50%
		100	15.33%	12.16%	9.50%	17.66%
		200	13.83%	11.66%	7.00%	14.33%
	Better	20	0	0	0	2.00%
		50	0	0	0	0.66%
		100	0	0	0	0.50%
		200	0	0	0	0.16%

Results in bold are the best.