Entropy-Based Weighting for Multiobjective Optimization: An Application on Vertical Turning

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">GPE</td><td align="center">Entropy</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left"><span style="width: 35.2513ptpx;"><svg height="10.335pt" id="M86" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -10.1025 35.2513 10.335" width="35.2513pt" 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="M252 635C85 635 28 460 28 311C28 167 82 -12 250 -12C419 -12 472 166 472 312C472 457 419 635 252 635ZM248 594C314 594 335 455 335 314C335 174 318 29 252 29S165 180 165 315S181 594 248 594Z" id="g13-46"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.5,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g190-47"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.475,0)"><path d="M252 635C85 635 28 460 28 311C28 167 82 -12 250 -12C419 -12 472 166 472 312C472 457 419 635 252 635ZM248 594C314 594 335 455 335 314C335 174 318 29 252 29S165 180 165 315S181 594 248 594Z" id="g13-46"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,15.975,0)"><path d="M253 635C100 635 24 509 24 420C24 314 97 231 217 231C234 231 251 236 275 248L324 274C298 154 195 47 47 21L53 -15C98 -14 184 2 223 18C365 74 471 201 471 382C471 519 398 635 253 635ZM232 595C310 595 335 485 335 387C335 365 334 340 330 313C316 307 300 300 275 300C202 300 156 374 156 460C156 525 178 595 232 595Z" id="g13-55"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.475,0)"><path d="M252 635C85 635 28 460 28 311C28 167 82 -12 250 -12C419 -12 472 166 472 312C472 457 419 635 252 635ZM248 594C314 594 335 455 335 314C335 174 318 29 252 29S165 180 165 315S181 594 248 594Z" id="g13-46"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,29.073,-5.741)"><path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g></svg></span></td><td align="center">0.643</td></tr><tr><td align="left">0.213</td><td align="center"><span style="width: 35.2513ptpx;"><svg height="10.2828pt" id="M87" style="vertical-align:-0.1802998pt" version="1.1" viewbox="-0.0498162 -10.1025 35.2513 10.2828" width="35.2513pt" 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="M409 0V34C329 39 322 56 322 125V635C234 611 160 593 94 583V554L145 551C186 547 190 541 190 488V125C190 54 181 39 102 34V0H409Z" id="g13-47"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.5,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g190-47"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.475,0)"><path d="M409 0V34C329 39 322 56 322 125V635C234 611 160 593 94 583V554L145 551C186 547 190 541 190 488V125C190 54 181 39 102 34V0H409Z" id="g13-47"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,15.975,0)"><path d="M409 0V34C329 39 322 56 322 125V635C234 611 160 593 94 583V554L145 551C186 547 190 541 190 488V125C190 54 181 39 102 34V0H409Z" id="g13-47"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.475,0)"><path d="M440 175C403 110 395 108 335 108H173L293 222C391 316 432 379 432 457C432 568 349 635 250 635C187 635 137 610 100 573L36 479L65 456C97 502 138 544 199 544C268 544 303 495 303 425C303 349 264 274 194 191C145 133 86 78 33 26V0H434C445 42 457 105 473 164L440 175Z" id="g13-48"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,29.073,-5.741)"><path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g></svg></span></td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr><tr class="table-fn"><td><svg height="10.1524pt" id="M88" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -10.1025 6.17869 10.1524" width="6.17869pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,0,-5.741)"><path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g></svg>Optimum individual.<br/></td></tr></table>

Payoff matrix for the functions GPE and Entropy.

Mathematical Problems in Engineering

tab6

Table 6

Table 6: Entropy-Based Weighting for Multiobjective Optimization: An Application on Vertical Turning 