Table 6 Optimization results of CEC 2020 test suite.
BOA | CMA-ES | EBOwithCMAR | SPS_L_SHADE_EIG | LSHADE_cnEpSi | LSHADE | WSO | AVOA | RSA | MPA | TSA | WOA | GWO | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C20-F1 | Mean | 100 | 4654.416 | 269.3601 | 269.3601 | 269.3601 | 529,106.2 | 540.86 | 414.33 | 1379.043 | 5126.764 | 330.9591 | 947.9631 | 541.3533 |
Best | 100 | 218.7791 | 100 | 100 | 100 | 100 | 517.6785 | 227.5587 | 100 | 100 | 171.9595 | 333.0219 | 171.9595 | |
Worst | 100 | 12,862.76 | 586.7017 | 586.7017 | 586.7017 | 2,111,279 | 586.7017 | 586.7017 | 3775.674 | 19,599.7 | 704.3544 | 2487.268 | 846.2411 | |
Std | 1.11E–06 | 6388.102 | 241.4972 | 241.4972 | 241.4972 | 1,173,165 | 35.27051 | 220.4615 | 1823.838 | 10,733.99 | 278.5073 | 1147.849 | 311.3273 | |
Median | 100 | 2768.062 | 195.3693 | 195.3693 | 195.3693 | 2522.622 | 529.5298 | 421.5297 | 820.2491 | 403.6797 | 223.7613 | 485.7811 | 573.6063 | |
Rank | 1 | 10 | 2 | 2 | 3 | 12 | 6 | 5 | 9 | 11 | 4 | 8 | 7 | |
C20-F2 | Mean | 1109.997 | 2385.246 | 1861.024 | 1789.1 | 1933.271 | 2005.351 | 2670.564 | 2556.306 | 6156.211 | 96,100.19 | 3227.281 | 2268.84 | 2523.301 |
Best | 1100 | 1533.602 | 1248.242 | 1119.942 | 1247.209 | 1508.382 | 1876.703 | 1780.75 | 1119.942 | 1897.054 | 1119.942 | 1447.958 | 2063.44 | |
Worst | 1120.638 | 3247.528 | 2300.844 | 2300.844 | 2300.844 | 2615.147 | 3575.328 | 3423.353 | 10,169.03 | 170,027.9 | 4436.652 | 3009.309 | 2933.155 | |
Std | 9.411746 | 920.5457 | 495.7543 | 546.2998 | 521.8125 | 517.5414 | 1012.515 | 965.4905 | 4169.781 | 85,099.8 | 1662.701 | 710.8755 | 455.5074 | |
Median | 1109.674 | 2379.928 | 1947.504 | 1867.808 | 2092.516 | 1948.937 | 2615.113 | 2510.56 | 6667.939 | 106,237.9 | 3676.265 | 2309.047 | 2548.304 | |
Rank | 1 | 7 | 3 | 2 | 4 | 5 | 10 | 9 | 12 | 13 | 11 | 6 | 8 | |
C20-F3 | Mean | 710.7399 | 946.5239 | 1030.93 | 921.6721 | 928.7036 | 2140.083 | 1280.415 | 855.566 | 1098.417 | 842.7941 | 899.4639 | 1622.219 | 911.7972 |
Best | 700.0001 | 701.0209 | 703.0943 | 833.6536 | 700 | 833.6536 | 700 | 700.0174 | 700 | 700 | 759.5655 | 736.4907 | 825.1043 | |
Worst | 714.3198 | 1179.969 | 1526.272 | 1030.329 | 1040.175 | 3012.079 | 1909.583 | 1021.259 | 1497.344 | 1034.631 | 1196.107 | 2948.858 | 1063.042 | |
Std | 7.963452 | 293.0101 | 404.4373 | 92.58541 | 176.4788 | 1047.268 | 565.5208 | 178.9907 | 472.6718 | 156.6231 | 222.3403 | 1164.253 | 119.5282 | |
Median | 714.3198 | 952.5529 | 947.1777 | 911.3529 | 987.3195 | 2357.299 | 1256.038 | 850.4937 | 1098.163 | 818.2726 | 821.0917 | 1401.764 | 879.5213 | |
Rank | 1 | 8 | 9 | 6 | 7 | 13 | 11 | 3 | 10 | 2 | 4 | 12 | 5 | |
C20-F4 | Mean | 1941.536 | 2488.139 | 6176.896 | 2587.731 | 2744.026 | 2529.797 | 3257.763 | 2304.616 | 3135.115 | 2259.914 | 2570.478 | 3140.962 | 2394.711 |
Best | 1900 | 2126.172 | 2126.172 | 2126.172 | 1900 | 2070.681 | 2126.172 | 2078.726 | 1900 | 2005.014 | 1900 | 2049.193 | 1900 | |
Worst | 1983.073 | 2831.743 | 9355.236 | 2992.157 | 3531.494 | 3070.15 | 4541.494 | 2526.219 | 5411.428 | 2504.562 | 3376.309 | 5136.934 | 3195.114 | |
Std | 46.35488 | 320.7347 | 3341.428 | 417.9987 | 895.1909 | 563.3419 | 1300.7 | 271.2238 | 1742.225 | 258.0201 | 675.9606 | 1544.024 | 622.431 | |
Median | 1941.536 | 2497.32 | 6613.087 | 2616.297 | 2772.304 | 2489.178 | 3181.692 | 2306.759 | 2614.516 | 2265.041 | 2502.802 | 2688.861 | 2241.866 | |
Rank | 1 | 5 | 13 | 8 | 9 | 6 | 12 | 3 | 10 | 2 | 7 | 11 | 4 | |
C20-F5 | Mean | 1702.285 | 2239.525 | 1858.166 | 2164.36 | 1788.468 | 3207.768 | 2005.77 | 1907.013 | 2085.434 | 1892.865 | 1781.148 | 1790.773 | 2070.973 |
Best | 1700 | 1835.073 | 1776.535 | 1781.423 | 1700 | 1700 | 1705.567 | 1705.567 | 1700 | 1700 | 1730.202 | 1708.17 | 1705.567 | |
Worst | 1704.57 | 2849.541 | 1976.775 | 2627.538 | 1900.977 | 6222.57 | 2181.269 | 2292.72 | 2652.44 | 2036.165 | 1862.216 | 1842.893 | 2340.974 | |
Std | 2.680999 | 504.0245 | 94.06495 | 387.6702 | 109.7219 | 2368.197 | 243.0359 | 292.2743 | 505.8121 | 179.68 | 64.50852 | 69.43882 | 299.7735 | |
Median | 1702.285 | 2136.742 | 1839.677 | 2124.24 | 1776.448 | 2454.251 | 2068.123 | 1814.883 | 1994.648 | 1917.647 | 1766.086 | 1806.014 | 2118.676 | |
Rank | 1 | 12 | 5 | 11 | 3 | 13 | 8 | 7 | 10 | 6 | 2 | 4 | 9 | |
C20-F6 | Mean | 1603.727 | 2483.368 | 1941.492 | 1838.004 | 1832.404 | 2686.847 | 1939.455 | 3468.956 | 2894.062 | 2096.874 | 5826.813 | 3369.879 | 2283.484 |
Best | 1600 | 1755.053 | 1755.053 | 1674.294 | 1600 | 1755.053 | 1775.014 | 1909.611 | 1600 | 1755.053 | 1909.611 | 1755.053 | 1755.053 | |
Worst | 1609.322 | 2891.929 | 2177.142 | 1914.703 | 1989.928 | 3212.981 | 2074.295 | 4800.85 | 3855.79 | 2295.9 | 8875.029 | 5397.799 | 2723.037 | |
Std | 5.070415 | 564.6686 | 201.7032 | 125.9336 | 210.9064 | 732.4838 | 166.7318 | 1369.214 | 1078.798 | 264.6256 | 3305.629 | 1738.474 | 458.3604 | |
Median | 1602.793 | 2643.244 | 1916.887 | 1881.51 | 1869.845 | 2889.678 | 1954.255 | 3582.682 | 3060.23 | 2168.271 | 6261.306 | 3163.332 | 2327.923 | |
Rank | 1 | 8 | 5 | 3 | 2 | 9 | 4 | 12 | 10 | 6 | 13 | 11 | 7 | |
C20-F7 | Mean | 2206.269 | 3902.404 | 2958.347 | 2580.351 | 3965.246 | 3002.99 | 3379.417 | 3131.289 | 3038.459 | 3429.377 | 2835.707 | 3567.499 | 3383.971 |
Best | 2100 | 2380.15 | 2172.035 | 2172.035 | 2172.035 | 2834.606 | 2820.134 | 2491.375 | 2380.15 | 2343.686 | 2632.634 | 2343.686 | 2181.634 | |
Worst | 2327.209 | 5400.796 | 4233.579 | 3063.596 | 6111.454 | 3155.574 | 4696.493 | 4705.774 | 4283.549 | 4348.672 | 3092.797 | 4354.73 | 4373.827 | |
Std | 106.0625 | 1404.331 | 1038.734 | 407.8927 | 1835.668 | 149.6089 | 992.6682 | 1181.171 | 947.2925 | 1068.908 | 213.1073 | 1016.463 | 1167.87 | |
Median | 2198.933 | 3914.336 | 2713.887 | 2542.885 | 3788.747 | 3010.89 | 3000.519 | 2664.004 | 2745.068 | 3512.575 | 2808.699 | 3785.79 | 3490.211 | |
Rank | 1 | 12 | 4 | 2 | 13 | 5 | 8 | 7 | 6 | 10 | 3 | 11 | 9 | |
C20-F8 | Mean | 2218.874 | 2568.297 | 2497.947 | 2377.194 | 2551.459 | 2541.787 | 2362.74 | 2500.844 | 2519.123 | 2375.379 | 2351.969 | 2365.86 | 2405.083 |
Best | 2200 | 2284.306 | 2267.622 | 2284.306 | 2233.587 | 2267.622 | 2284.306 | 2233.587 | 2284.306 | 2284.306 | 2267.622 | 2267.622 | 2267.622 | |
Worst | 2237.305 | 2691.31 | 2675.148 | 2471.186 | 2826.468 | 2882.077 | 2397.15 | 2742.492 | 2685.164 | 2552.073 | 2436.719 | 2505.304 | 2563.966 | |
Std | 21.86637 | 212.4807 | 195.617 | 85.71142 | 352.9057 | 295.8129 | 58.56492 | 252.1761 | 208.096 | 134.8033 | 104.6396 | 113.6305 | 136.6297 | |
Median | 2219.095 | 2648.786 | 2524.509 | 2376.642 | 2572.891 | 2508.724 | 2384.751 | 2513.649 | 2553.512 | 2332.569 | 2351.768 | 2345.257 | 2394.372 | |
Rank | 1 | 13 | 8 | 6 | 12 | 11 | 3 | 9 | 10 | 5 | 2 | 4 | 7 | |
C20-F9 | Mean | 2404.914 | 2505.427 | 2928.06 | 2930.358 | 2493.553 | 2643.167 | 2696.627 | 2462.19 | 2498.552 | 2519.963 | 2443.155 | 2588.241 | 2495.838 |
Best | 2400 | 2413.197 | 2426.192 | 2434.644 | 2416.702 | 2416.702 | 2416.702 | 2416.702 | 2413.197 | 2426.192 | 2418.582 | 2416.702 | 2426.192 | |
Worst | 2411.095 | 2602.213 | 3278.573 | 3337.795 | 2586.208 | 2936.937 | 3079.996 | 2493.618 | 2621.356 | 2612.492 | 2480.385 | 2701.826 | 2545.829 | |
Std | 5.296123 | 95.25177 | 401.2837 | 429.2936 | 78.36549 | 257.5471 | 348.6891 | 39.39015 | 106.2098 | 110.0469 | 29.28298 | 139.1959 | 65.39078 | |
Median | 2404.28 | 2503.149 | 3003.739 | 2974.495 | 2485.651 | 2609.514 | 2644.905 | 2469.221 | 2479.828 | 2520.583 | 2436.827 | 2617.218 | 2505.665 | |
Rank | 1 | 7 | 12 | 13 | 4 | 10 | 11 | 3 | 6 | 8 | 2 | 9 | 5 | |
C20-F10 | Mean | 2500.005 | 5501.834 | 2506.285 | 2508.548 | 2500.793 | 2505.697 | 2514.842 | 2502.45 | 2505.446 | 2503.433 | 29,528.4 | 2503.527 | 2501.114 |
Best | 2500 | 2500.002 | 2501.462 | 2500.629 | 2500.018 | 2500.002 | 2500.826 | 2500.629 | 2500.002 | 2500.629 | 2501.462 | 2500.024 | 2500.629 | |
Worst | 2500.017 | 6539.912 | 2518.054 | 2514.524 | 2501.462 | 2516.926 | 2546.822 | 2503.583 | 2511.038 | 2509.539 | 38,553.66 | 2511.966 | 2501.879 | |
Std | 0.008848 | 2226.021 | 8.761668 | 6.46181 | 0.659229 | 8.498574 | 23.89477 | 1.412787 | 5.072157 | 4.572588 | 20,040.18 | 6.293057 | 0.594907 | |
Median | 2500.001 | 6483.71 | 2502.813 | 2509.519 | 2500.847 | 2502.93 | 2505.86 | 2502.794 | 2505.372 | 2501.782 | 38,529.23 | 2501.059 | 2500.975 | |
Rank | 1 | 12 | 9 | 10 | 2 | 8 | 11 | 4 | 7 | 5 | 13 | 6 | 3 | |
Sum rank | 10 | 94 | 70 | 63 | 59 | 92 | 84 | 62 | 90 | 68 | 61 | 82 | 64 | |
Mean rank | 1 | 9.4 | 7 | 6.3 | 5.9 | 9.2 | 8.4 | 6.2 | 9 | 6.8 | 6.1 | 8.2 | 6.4 | |
Total rank | 1 | 13 | 8 | 5 | 2 | 12 | 10 | 4 | 11 | 7 | 3 | 9 | 6 | |
