Composite Differential Evolution with Modified Oracle Penalty Method for Constrained Optimization Problems

<table class="table-group" id="tab13"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td align="left">Method</td><td align="center">Best</td><td align="center">Mean</td><td align="center">Worst</td><td align="center">Std</td><td align="center"><span style="width: 4.73688ptpx;"><svg height="8.35422pt" id="M343" style="vertical-align:-0.2130003pt" version="1.1" viewbox="-0.0498162 -8.14122 4.73688 8.35422" width="4.73688pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td align="left">CPSO [<a href="/journals/mpe/2014/617905/#B43">12</a>]</td><td align="center">6061.0777</td><td align="center">6147.1332</td><td align="center">6363.8041</td><td align="center">86.4545</td><td align="center">−10.1116</td></tr><tr><td align="left">CDE [<a href="/journals/mpe/2014/617905/#B19">13</a>]</td><td align="center">6059.7340</td><td align="center">6085.2303</td><td align="center">6371.0455</td><td align="center">43.0130</td><td align="center">−5.93216</td></tr><tr><td align="left">DUVDE + APM [<a href="/journals/mpe/2014/617905/#B27">9</a>]</td><td align="center">6059.71826</td><td align="center">6059.71826</td><td align="center">6059.71826</td><td align="center">0</td><td align="center">−2036618</td></tr><tr><td align="left">ES-DE [<a href="/journals/mpe/2014/617905/#B40">8</a>]</td><td align="center">6059.71</td><td align="center">6059.71</td><td align="center">6059.71</td><td align="center"><span style="width: 64.7808ptpx;"><svg height="9.36053pt" id="M344" 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transform="matrix(.0135,0,0,-0.0135,57.965,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></span></td><td align="center">0</td></tr><tr><td align="left">MOCoDE</td><td align="center">6059.7143</td><td align="center">6059.7143</td><td align="center">6059.7143</td><td align="center"><span style="width: 75.0888ptpx;"><svg height="9.06134pt" id="M345" style="vertical-align:-0.3625803pt" version="1.1" viewbox="-0.0498162 -8.69876 75.0888 9.06134" width="75.0888pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,6.503,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,9.592,0)"><path d="M244 635C114 635 38 519 38 422C38 317 111 240 217 240C236 240 255 244 277 256L345 292C311 140 203 39 59 15L64 -15C89 -15 150 -5 204 17C339 72 440 202 440 386C440 521 368 635 244 635ZM228 602C326 602 352 479 352 390C352 370 351 347 348 324C327 308 293 296 258 296C174 296 124 369 124 458C124 517 152 602 228 602Z" id="g113-58"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,16.096,0)"><path d="M456 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horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,61.728,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,68.231,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z" id="g113-57"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg></span></td><td align="center">—</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Statistical results of different methods for pressure vessel design problem.

Mathematical Problems in Engineering

tab13

Table 13

Table 13: Composite Differential Evolution with Modified Oracle Penalty Method for Constrained Optimization Problems 