An Interval-Based Evolutionary Approach to Portfolio Optimization of New Product Development Projects

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_center" colspan="2">Resource consumption</td><td class="align_center" colspan="2"><span style="width: 26.6583ptpx;"><svg height="16.207pt" id="M1033" style="vertical-align:-5.910001pt" version="1.1" viewbox="-0.0498162 -10.297 26.6583 16.207" width="26.6583pt" 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="M643 650C643 674 620 703 568 703C539 703 474 688 406 626C353 578 331 527 307 437H239L206 397L212 389H298L241 48C216 -100 205 -139 202 -146C195 -162 186 -169 167 -169C143 -169 100 -154 80 -134C74 -128 70 -127 61 -133C43 -145 21 -167 21 -192C21 -222 62 -246 96 -246C127 -246 164 -228 202 -201C280 -146 325 -81 368 90C390 180 410 289 427 389L544 397L564 437H436C471 644 487 650 508 650S552 624 578 593C586 584 593 585 604 589C619 594 643 621 643 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.664,3.668)"><path d="M415 0V41C335 46 327 62 327 127V635C236 611 161 593 93 583V547L150 544C187 541 192 535 192 483V127C192 59 182 46 102 41V0H415Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.295,3.668)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.452,3.668)"><path d="M438 606C438 643 416 671 376 671C316 671 292 618 292 593C292 548 318 525 359 525C405 525 438 566 438 606ZM398 325C417 418 409 457 373 457C331 457 247 411 178 351L194 318C210 330 254 356 265 356C272 356 272 343 266 311L182 -115C172 -161 161 -166 147 -166C127 -166 97 -150 75 -134C67 -128 64 -130 58 -136C43 -149 22 -174 22 -199C22 -225 47 -242 73 -242C101 -242 126 -235 193 -191C283 -132 322 -44 338 34L398 325Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.215,-6.009)"><path d="M499 152C501 180 492 209 480 228C432 233 403 235 357 256C403 278 432 279 480 284C492 303 504 328 499 359C477 375 447 382 424 380C396 342 380 317 338 288C342 339 356 364 376 408C366 429 350 451 320 463C295 451 274 429 265 408C284 364 297 339 301 288C259 317 244 341 216 380C193 382 166 379 141 359C139 332 148 303 160 284C208 279 237 277 283 256C237 234 208 233 160 228C148 209 136 184 141 152C163 137 193 130 216 132C244 170 260 195 302 224C298 173 284 148 265 104C274 83 290 61 320 49C345 61 366 83 376 104C356 148 343 173 339 224C381 195 396 171 424 132C447 130 474 133 499 152Z"></path></g></svg></span></td><td class="align_center" colspan="2"><span style="width: 26.6583ptpx;"><svg height="16.207pt" id="M1034" style="vertical-align:-5.910001pt" version="1.1" viewbox="-0.0498162 -10.297 26.6583 16.207" width="26.6583pt" 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="M643 650C643 674 620 703 568 703C539 703 474 688 406 626C353 578 331 527 307 437H239L206 397L212 389H298L241 48C216 -100 205 -139 202 -146C195 -162 186 -169 167 -169C143 -169 100 -154 80 -134C74 -128 70 -127 61 -133C43 -145 21 -167 21 -192C21 -222 62 -246 96 -246C127 -246 164 -228 202 -201C280 -146 325 -81 368 90C390 180 410 289 427 389L544 397L564 437H436C471 644 487 650 508 650S552 624 578 593C586 584 593 585 604 589C619 594 643 621 643 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.664,3.668)"><path d="M440 180C404 113 397 110 338 110H183L298 220C398 316 438 379 438 456C438 568 354 635 254 635C192 635 138 610 101 572L36 479L69 452C103 500 144 541 204 541C270 541 306 494 306 425C306 350 267 276 197 193C148 136 89 81 36 30V0H440C451 42 463 106 480 167L440 180Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.295,3.668)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.452,3.668)"><path d="M438 606C438 643 416 671 376 671C316 671 292 618 292 593C292 548 318 525 359 525C405 525 438 566 438 606ZM398 325C417 418 409 457 373 457C331 457 247 411 178 351L194 318C210 330 254 356 265 356C272 356 272 343 266 311L182 -115C172 -161 161 -166 147 -166C127 -166 97 -150 75 -134C67 -128 64 -130 58 -136C43 -149 22 -174 22 -199C22 -225 47 -242 73 -242C101 -242 126 -235 193 -191C283 -132 322 -44 338 34L398 325Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.215,-6.009)"><path d="M499 152C501 180 492 209 480 228C432 233 403 235 357 256C403 278 432 279 480 284C492 303 504 328 499 359C477 375 447 382 424 380C396 342 380 317 338 288C342 339 356 364 376 408C366 429 350 451 320 463C295 451 274 429 265 408C284 364 297 339 301 288C259 317 244 341 216 380C193 382 166 379 141 359C139 332 148 303 160 284C208 279 237 277 283 256C237 234 208 233 160 228C148 209 136 184 141 152C163 137 193 130 216 132C244 170 260 195 302 224C298 173 284 148 265 104C274 83 290 61 320 49C345 61 366 83 376 104C356 148 343 173 339 224C381 195 396 171 424 132C447 130 474 133 499 152Z"></path></g></svg></span></td><td class="align_center">Cardinality</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">240265</td><td class="align_center">250165</td><td class="align_center">1384860</td><td class="align_center">1393360</td><td class="align_center">298740</td><td class="align_center">308040</td><td class="align_center">37</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The closest solution <svg height="11.9936pt" id="M1032" style="vertical-align:-3.2272pt" version="1.1" viewbox="-0.0498162 -8.7664 29.2423 11.9936" width="29.2423pt" 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="M614 175C564 76 510 21 408 21C256 21 146 149 146 336C146 488 235 629 402 629C510 629 570 586 597 480L626 488C620 541 614 582 606 638C578 643 510 665 429 665C206 665 44 527 44 316C44 157 153 -15 402 -15C474 -15 558 5 586 11C604 45 629 119 643 165L614 175Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.645,3.132)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.804,3.132)"><path d="M698 650H468V617C551 609 555 599 536 543C506 457 432 264 379 129H377C311 297 238 488 212 560C196 604 198 609 271 617V650H21V617C80 612 98 603 127 532C183 396 268 173 335 -9H370C445 196 551 450 578 511C615 602 630 609 698 617V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.329,3.132)"><path d="M871 0V33C783 41 780 45 777 152L768 506C765 610 771 609 860 617V650H683L453 157L228 650H59V617C150 609 154 606 146 481L132 275C124 170 117 125 112 93C105 50 84 39 27 34V0H267V34C200 39 176 48 173 93C170 130 171 172 176 256L190 540H192L414 8H438L682 554H685L689 152C689 45 686 41 604 33V0H871Z"></path></g></svg> to the ideal one (in the portfolio space).</div>

Mathematical Problems in Engineering

tab3

Table 3

Table 3: An Interval-Based Evolutionary Approach to Portfolio Optimization of New Product Development Projects 