Enhancing Hyperheuristics for the Knapsack Problem through Fuzzy Logic

Table 3

Results from the hyperheuristics with the 2400 hard instances.

Methods		Hard Pisinger instances
		20	50	100	200
Default		3804271	9562959	18985439	37922860
MaxP		3724588	9269841	18382930	36723430
MinW		3867345	10055148	20287616	40898138
MaxPW		4039708	10353555	20791627	41776413
Oracle		4084003	10380851	20802281	41783753
HH4	Average	3949205.76	10048476.70	20107840.33	40333536.33
	Standard deviation	99734.35 (2.52%)	380935.64 (3.79%)	874132.26 (4.34%)	1871087.96 (4.63%)
	Best	4045507	10355658	20791627	41776413
	Worst	3734571	9312890	18502165	36963737
HH6	Average	3950021.50	10079568.63	20193352.10	40525684.03
	Standard deviation	84499.05 (2.13%)	324209.91 (3.21%)	747259.32 (3.70%)	1601814.81 (3.95%)
	Best	4038167	10350020	20786768	41775010
	Worst	3741617	9314130	18502041	36957315
HH8	Average	3957540.76	10089769.23	20192245.86	40509777.40
	Standard deviation	92317.06 (2.33%)	333676.40 (3.30%)	777075.35 (3.84%)	1681688.34 (4.15%)
	Best	4042198	10353705	20791627	41776413
	Worst	3741978	9307530	18303016	36466476
Binary GA	Average	4073227.76	9755928.90	18475255.43	35069085.23
	Standard deviation	3096.26 (0.07%)	7888.44 (0.08%)	17760.93 (0.09%)	41037.09 (0.11%)
	Best	4078723	9767818	18503545	35167446
	Worst	4067968	9738018	18433895	34989419
FuzzyHH	Average	4008457.76	10175892.16	20342907.40	40794413.63
	Standard deviation	43384.17 (1.08%)	155492.79 (1.52%)	359855.26 (1.76%)	772999.81 (1.89%)
	Best	4050373	10355610	20777933	41757401
	Worst	3886225	9787082	19477163	39003392

Results in bold are the best.