Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

<table class="table-group" id="tab11"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">VS</td><td class="align_center"><i>R</i>+</td><td class="align_center"><i>R</i>−</td><td class="align_left"><svg height="8.68572pt" id="M464" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 8.15071 8.68572" width="8.15071pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path></g></svg> value</td><td class="align_center"><span style="width: 44.1999ptpx;"><svg height="8.55521pt" id="M465" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 44.1999 8.55521" width="44.1999pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path></g><g transform="matrix(.013,0,0,-0.013,11.017,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,22.28,0)"><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></g><g transform="matrix(.013,0,0,-0.013,28.52,0)"><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></g><g transform="matrix(.013,0,0,-0.013,31.484,0)"><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></g><g transform="matrix(.013,0,0,-0.013,37.724,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path></g></svg></span></td><td class="align_center"><span style="width: 37.9365ptpx;"><svg height="8.55521pt" id="M466" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 37.9365 8.55521" width="37.9365pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path></g><g transform="matrix(.013,0,0,-0.013,11.017,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,22.28,0)"><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></g><g transform="matrix(.013,0,0,-0.013,28.52,0)"><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></g><g transform="matrix(.013,0,0,-0.013,31.484,0)"><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></g></svg></span></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">CMA-ES</td><td class="align_center">274</td><td class="align_center">26</td><td class="align_center">0.000375</td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M467" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path></g></svg></span></td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M468" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path></g></svg></span></td></tr><tr><td class="align_left">LBBO</td><td class="align_center">238.5</td><td class="align_center">86.5</td><td class="align_center">0.039554</td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M469" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path></g></svg></span></td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M470" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path></g></svg></span></td></tr><tr><td class="align_left">GL-25</td><td class="align_center">261</td><td class="align_center">64</td><td class="align_center">0.007727</td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M471" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path></g></svg></span></td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M472" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path></g></svg></span></td></tr><tr><td class="align_left">SaDE</td><td class="align_center">183</td><td class="align_center">117</td><td class="align_center">0.338495</td><td class="align_center">=</td><td class="align_center">=</td></tr><tr><td class="align_left">MPEDE</td><td class="align_center">216</td><td class="align_center">84</td><td class="align_center">0.057433</td><td class="align_center">=</td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M473" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path></g></svg></span></td></tr><tr><td class="align_left">SHADE</td><td class="align_center">183</td><td class="align_center">117</td><td class="align_center">0.338495</td><td class="align_center">=</td><td class="align_center">=</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Results obtained by the multiple-problem Wilcoxon test for DEMR and other six algorithms on CEC2005.</div>

International Journal of Aerospace Engineering

tab11

Table 11

Table 11: Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization 