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

<table class="table-group" id="tab7"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_center" colspan="2">Cost</td><td class="align_center" colspan="2"><span style="width: 20.3144ptpx;"><svg height="15.2114pt" id="M1051" style="vertical-align:-5.91002pt" version="1.1" viewbox="-0.0498162 -9.30138 20.3144 15.2114" width="20.3144pt" 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></svg></span></td><td class="align_center" colspan="2"><span style="width: 20.3144ptpx;"><svg height="15.2114pt" id="M1052" style="vertical-align:-5.91002pt" version="1.1" viewbox="-0.0498162 -9.30138 20.3144 15.2114" width="20.3144pt" 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></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">240770</td><td class="align_center">249870</td><td class="align_center">866389</td><td class="align_center">872789</td><td class="align_center">224375</td><td class="align_center">231115</td><td class="align_center">33</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Closest solution to the ideal one in the objective space (<svg height="9.49473pt" id="M1050" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.84582 9.49473" width="6.84582pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z"></path></g></svg> =0.75).</div>

Mathematical Problems in Engineering

tab7

Table 7

Table 7: An Interval-Based Evolutionary Approach to Portfolio Optimization of New Product Development Projects 