Understanding Population Dynamics in Multi- and Many-Objective Evolutionary Algorithms for High-Resolution Approximations

<div>Accumulated number of Pareto optimal solutions and hypervolume of the accumulated joint nondominated sets. Algorithm <span class="nowrap"><svg height="9.01194pt" id="M132" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -8.7664 36.3621 9.01194" width="36.3621pt" 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="M673 0V28C608 34 594 43 563 129C499 303 432 494 370 665L339 656L132 132C98 43 84 37 20 28V0H238V28C162 35 154 45 175 108C188 150 203 192 219 237H432C454 176 474 122 487 83S491 36 428 28V0H673ZM418 280H234C265 362 296 450 328 535H330L418 280Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.983,0)"><path d="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.496,0)"><path d="M409 504C401 567 396 607 392 642C354 654 312 665 266 665C137 665 60 583 60 487C60 374 161 325 225 290C300 250 355 215 355 141C355 68 311 21 235 21C131 21 86 122 71 183L41 176C48 128 61 42 68 21C78 16 93 8 118 0C142 -7 175 -15 216 -15C349 -15 438 69 438 174C438 287 344 333 265 374C186 414 138 449 138 522C138 576 172 631 249 631C336 631 363 562 380 499L409 504Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.658,0)"><path d="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.171,0)"><path d="M729 650H468V622C546 615 554 610 554 527V365H213V527C213 610 221 616 297 622V650H38V622C120 616 128 611 128 527V123C128 39 120 34 40 28V0H303V28C221 34 213 40 213 123V322H554V123C554 39 546 34 460 28V0H728V28C647 34 639 39 639 123V527C639 610 647 615 729 622V650Z"></path></g></svg>,</span> <i>M</i> = 3 objectives, population size 200, and number of generations 100. (a) Accumulated PO solutions and (b) hypervolume.</div>

Advances in Operations Research

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Figure 3

Figure 3: Understanding Population Dynamics in Multi- and Many-Objective Evolutionary Algorithms for High-Resolution Approximations 