Research Article
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 |
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Results in bold are the best.
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