Table 6 Average number of nondominated solutions in the approximated Pareto front (Mean) with the corresponding standard deviation (Std) for each algorithm
From: Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures
Problem | Dataset | NSGA-IIb | NSGA-IIa | SPEA 2b | SPEA 2a | ||||
|---|---|---|---|---|---|---|---|---|---|
| Â | Â | Mean | std | Mean | Std | Mean | Std | Mean | Std |
Mean-SV | DowJones | 52.10 | 5.75 | 248.06 | 4.93 | 55.65 | 6.12 | 250 | 0 |
| Â | FF49Industries | 16.65 | 4.61 | 250 | 0 | 15.20 | 3.68 | 250 | 0 |
| Â | NASDAQ100 | 14.25 | 2.90 | 250 | 0 | 13.40 | 2.89 | 250 | 0 |
| Â | SP500 | 11.55 | 3.22 | 250 | 0 | 11.50 | 3.32 | 250 | 0 |
| Â | NASDAQComp | 13.60 | 2.93 | 202.50 | 20.97 | 13.60 | 2.93 | 245.20 | 9.29 |
Mean-CVaR | DowJones | 49.70 | 6.24 | 247.33 | 4.86 | 51.15 | 6.66 | 250 | 0 |
| Â | FF49Industries | 16.10 | 3.80 | 249.95 | 0.22 | 17.25 | 3.19 | 250 | 0 |
| Â | NASDAQ100 | 16.45 | 3.27 | 250 | 0 | 16.80 | 3.86 | 250 | 0 |
| Â | SP500 | 12.60 | 2.84 | 250 | 0 | 12.45 | 2.68 | 250 | 0 |
| Â | NASDAQComp | 15.80 | 3.43 | 238.60 | 13.18 | 16.10 | 3.91 | 249.05 | 2.21 |
Mean-CVaR-SV | DowJones | 92.90 | 14.62 | 246.33 | 7.57 | 91.75 | 11.96 | 250 | 0 |
| Â | FF49Industries | 22.25 | 7.04 | 250 | 0 | 21.25 | 6.70 | 250 | 0 |
| Â | NASDAQ100 | 22.45 | 5.82 | 250 | 0 | 22.50 | 3.90 | 250 | 0 |
| Â | SP500 | 18.20 | 6.18 | 250 | 0 | 18.85 | 7.51 | 250 | 0 |
| Â | NASDAQComp | 25.65 | 6.03 | 250 | 0 | 25.65 | 5.59 | 250 | 0 |