Table 2 Performance comparison of different algorithms on ZDT functions, the indicators’ values are the means and the variance in brackets.
Functions | Indicator | MOPSO | NSGA-II | MOAOA |
|---|---|---|---|---|
ZDT1 | IGD | 0.0599/(0.0437) | \({\textbf {0.0395}}\)/(0.0087) | 0.0841/(\({\textbf {0.0018}}\)) |
SP | 0.007/(0.0048) | 0.1124/(0.0011) | \({\textbf {0.0033/(0.0003)}}\) | |
HV | 0.6714/(0.0307) | \({\textbf {0.6741}}\)/(0.0106) | 0.4251/(\({\textbf {0.0034}}\)) | |
\(\Delta\) | 0.8107/(0.1343) | \({\textbf {0.4239}}\)/(0.0593) | 0.9257/(\({\textbf {0.0199}}\)) | |
ZDT2 | IGD | \({\textbf {0.2363}}\)/(0.0302) | 0.0266/(0.0067) | 0.2696/(\({\textbf {0.0028}}\)) |
SP | \({\textbf {0.0022}}\)/(0.0021) | 0.0032/(\({\textbf {0.0003}}\)) | 0.1616/(0.0917) | |
HV | \({\textbf {0.5621}}\)/(0.0322) | 0.4039/(0.0100) | 0.4251/(\({\textbf {0.0034}}\)) | |
\(\Delta\) | 0.9543/(0.0341) | \({\textbf {0.4434/(0.0235}}\)) | 0.9257/(0.0593) | |
ZDT3 | IGD | 0.2411/(0.0207) | \({\textbf {0.0412}}\)/(0.0086) | 0.0728/(\({\textbf {0.0029}}\)) |
SP | 0.0041/(0.0021) | 0.0035/(0.0027) | \({\textbf {0.0170/(0.0019)}}\) | |
HV | 0.5091/(\({\textbf {0.0031}}\)) | \({\textbf {0.5880}}\)/(0.0186) | 0.4251/(0.0034) | |
\(\Delta\) | 0.7356/(0.0423) | 0.6845/(0.0223) | \({\textbf {0.6536/(0.0211)}}\) | |
ZDT4 | IGD | 0.0599/(0.0437) | 0.5452/(0.3919) | \({\textbf {0.0179/(0.0018)}}\) |
SP | 0.0632/(\({\textbf {0.0043}}\)) | \({\textbf {0.0042}}\)/(0.0057) | 0.0708/(0.0082) | |
HV | 0.5428/(0.0342) | 0.2631/(0.2701) | \({\textbf {0.8550/(0.0014)}}\) | |
\(\Delta\) | 0.7653/(0.1587) | \({\textbf {0.6521}}\)/(0.1284) | 0.9257/(\({\textbf {0.0593}}\)) |
