Research on Preference Polyhedron Model Based Evolutionary Multiobjective Optimization Method for Multilink Transmission Mechanism Conceptual Design

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Parameter</td><td class="align_center" colspan="3">Value</td></tr><tr class="thead"><td class="align_center">Lower</td><td class="align_center">Base</td><td class="align_center">Upper</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left"><svg height="11.9316pt" id="M109" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 21.9298 11.9316" width="21.9298pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M387 665C175 665 46 498 46 318C46 123 194 -15 374 -15C558 -15 712 114 712 333C712 535 557 665 387 665ZM364 625C495 625 607 518 607 306C607 115 505 25 396 25C256 25 151 161 151 346C151 532 255 625 364 625Z" id="g58-77"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="757" vert-adv-y="757"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.854,3.132)"><path d="M682 0V33C615 38 603 49 571 134C507 305 441 494 378 665L343 655L136 136C101 48 86 41 22 33V0H246V33C170 41 161 50 183 112C196 152 209 192 224 232H441C461 176 478 126 493 87C504 49 499 41 433 33V0H682ZM425 279H242C273 363 303 448 335 533H337L425 279Z" id="g58-63"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="703" vert-adv-y="703"></glyph.data></g></svg> (mm)</td><td class="align_center">450</td><td class="align_center">490</td><td class="align_center">550</td></tr><tr><td class="align_left"><svg height="11.8174pt" id="M110" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 20.8063 11.8174" width="20.8063pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M682 0V33C615 38 603 49 571 134C507 305 441 494 378 665L343 655L136 136C101 48 86 41 22 33V0H246V33C170 41 161 50 183 112C196 152 209 192 224 232H441C461 176 478 126 493 87C504 49 499 41 433 33V0H682ZM425 279H242C273 363 303 448 335 533H337L425 279Z" id="g58-63"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="703" vert-adv-y="703"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.691,3.132)"><path d="M384 354C435 370 515 408 515 502C515 549 494 593 459 616C426 639 384 650 308 650H45V618C127 613 130 606 130 524V127C130 45 125 38 37 33V0H262C342 0 409 12 461 40C521 73 558 124 558 192C558 295 481 336 384 352V354ZM217 365V556C217 587 221 597 229 604C238 611 261 615 288 615C382 615 421 558 421 490C421 406 374 365 266 365H217ZM217 327H264C384 327 457 284 457 183C457 80 383 38 301 38C235 38 217 55 217 127V327Z" id="g58-64"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="598" vert-adv-y="598"></glyph.data></g></svg> (mm)</td><td class="align_center">350</td><td class="align_center">420</td><td class="align_center">450</td></tr><tr><td class="align_left"><svg height="11.9316pt" id="M111" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 20.715 11.9316" width="20.715pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M384 354C435 370 515 408 515 502C515 549 494 593 459 616C426 639 384 650 308 650H45V618C127 613 130 606 130 524V127C130 45 125 38 37 33V0H262C342 0 409 12 461 40C521 73 558 124 558 192C558 295 481 336 384 352V354ZM217 365V556C217 587 221 597 229 604C238 611 261 615 288 615C382 615 421 558 421 490C421 406 374 365 266 365H217ZM217 327H264C384 327 457 284 457 183C457 80 383 38 301 38C235 38 217 55 217 127V327Z" id="g58-64"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="598" vert-adv-y="598"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.918,3.132)"><path d="M618 181C565 77 513 26 413 26C264 26 151 150 151 336C151 486 240 625 407 625C516 625 573 582 600 475L634 483C627 540 622 581 613 638C585 643 518 665 435 665C211 665 46 526 46 315C46 158 157 -15 406 -15C480 -15 564 4 594 12C612 43 638 121 651 168L618 181Z" id="g58-65"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="673" vert-adv-y="673"></glyph.data></g></svg> (mm)</td><td class="align_center">330</td><td class="align_center">360</td><td class="align_center">390</td></tr><tr><td class="align_left"><svg height="11.9316pt" id="M112" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 22.1581 11.9316" width="22.1581pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M387 665C175 665 46 498 46 318C46 123 194 -15 374 -15C558 -15 712 114 712 333C712 535 557 665 387 665ZM364 625C495 625 607 518 607 306C607 115 505 25 396 25C256 25 151 161 151 346C151 532 255 625 364 625Z" id="g58-77"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="757" vert-adv-y="757"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,15.356,3.132)"><path d="M618 181C565 77 513 26 413 26C264 26 151 150 151 336C151 486 240 625 407 625C516 625 573 582 600 475L634 483C627 540 622 581 613 638C585 643 518 665 435 665C211 665 46 526 46 315C46 158 157 -15 406 -15C480 -15 564 4 594 12C612 43 638 121 651 168L618 181Z" id="g58-65"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="673" vert-adv-y="673"></glyph.data></g></svg> (mm)</td><td class="align_center">100</td><td class="align_center">115</td><td class="align_center">130</td></tr><tr><td class="align_left"><svg height="11.9316pt" id="M113" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 21.8659 11.9316" width="21.8659pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M618 181C565 77 513 26 413 26C264 26 151 150 151 336C151 486 240 625 407 625C516 625 573 582 600 475L634 483C627 540 622 581 613 638C585 643 518 665 435 665C211 665 46 526 46 315C46 158 157 -15 406 -15C480 -15 564 4 594 12C612 43 638 121 651 168L618 181Z" id="g58-65"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="673" vert-adv-y="673"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.418,3.132)"><path d="M43 650V617C122 612 130 606 130 522V128C130 44 122 37 34 32V0H275C400 0 497 25 573 82C652 142 698 229 698 350C698 445 662 518 613 565C549 625 456 650 327 650H43ZM217 544C217 580 220 591 229 599C240 607 264 613 311 613C380 613 437 599 482 570C561 523 598 436 598 336C598 177 511 40 324 40C248 40 217 61 217 135V544Z" id="g58-66"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="744" vert-adv-y="744"></glyph.data></g></svg> (mm)</td><td class="align_center">175</td><td class="align_center">190</td><td class="align_center">250</td></tr><tr><td class="align_left"><svg height="11.8174pt" id="M114" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 20.9525 11.8174" width="20.9525pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.294,3.132)"><path d="M43 650V617C122 612 130 606 130 522V128C130 44 122 37 34 32V0H275C400 0 497 25 573 82C652 142 698 229 698 350C698 445 662 518 613 565C549 625 456 650 327 650H43ZM217 544C217 580 220 591 229 599C240 607 264 613 311 613C380 613 437 599 482 570C561 523 598 436 598 336C598 177 511 40 324 40C248 40 217 61 217 135V544Z" id="g58-66"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="744" vert-adv-y="744"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,15,3.132)"><path d="M522 166C507 123 488 90 472 71C449 44 419 38 347 38C296 38 261 38 242 51C223 63 217 85 217 132V315H311C398 315 406 310 419 239H453V433H419C406 365 401 358 311 358H217V580C217 609 219 612 251 612H331C400 612 427 604 440 584C453 561 463 541 472 498L506 502C501 558 497 627 497 650H43V618C122 610 130 609 130 520V128C130 46 121 40 30 32V0H521C529 30 552 128 557 162L522 166Z" id="g58-67"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="580" vert-adv-y="580"></glyph.data></g></svg> (mm)</td><td class="align_center">1000</td><td class="align_center">1160</td><td class="align_center">1500</td></tr><tr><td class="align_left"><svg height="6.1673pt" id="M115" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt" 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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="568" vert-adv-y="568"></glyph.data></g></svg> (°)</td><td class="align_center">40</td><td class="align_center">45</td><td class="align_center">50</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab4

Table 4

Table 4: Research on Preference Polyhedron Model Based Evolutionary Multiobjective Optimization Method for Multilink Transmission Mechanism Conceptual Design 

Table 4 | Research on Preference Polyhedron Model Based Evolutionary Multiobjective Optimization Method for Multilink Transmission Mechanism Conceptual Design 