Chaos Enhanced Differential Evolution in the Task of Evolutionary Control of Selected Set of Discrete Chaotic Systems

<table class="table-group" id="tab9"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2">Parameter</td><td align="center">Case study 5 <br/>CF<sub>simple</sub></td><td align="center">Case study 6 <br/>CF<sub>UNI</sub></td></tr><tr class="thead"><td align="center">Value</td><td align="center">Value</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left"><span style="width: 10.3669ptpx;"><svg height="9.04777pt" id="M91" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3669 9.04777" width="10.3669pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z" id="g113-76"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="755" vert-adv-y="755"></glyph.data></g></svg></span></td><td align="center">−1.11259</td><td align="center">−0.859989</td></tr><tr><td align="left"><span style="width: 24.4693ptpx;"><svg height="12.4305pt" id="M92" style="vertical-align:-3.43255pt" version="1.1" viewbox="-0.0498162 -8.99795 24.4693 12.4305" width="24.4693pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z" id="g113-71"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="607" vert-adv-y="607"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,7.072,3.264)"><path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z" id="g58-107"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="834" vert-adv-y="834"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,14.953,3.264)"><path d="M442 39L431 68C420 63 406 57 394 57C377 57 359 71 359 118V301C359 353 349 393 314 424C291 443 261 451 230 451C171 438 107 401 79 381C59 366 46 355 46 340C46 316 72 295 91 295C106 295 117 303 122 319C131 350 139 371 152 384C163 397 178 404 197 404C246 404 281 365 281 293V278C260 262 186 232 124 213C69 194 41 161 41 112C41 47 92 -12 163 -12C195 -12 243 25 283 51C288 35 293 22 308 7C319 -4 339 -12 354 -12L442 39ZM281 87C262 68 226 51 199 51C169 51 129 74 129 126C129 162 151 181 190 198C211 208 259 229 281 240V87Z" id="g58-95"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="449" vert-adv-y="449"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,19.211,3.264)"><path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 409V439H18V409C74 401 87 395 117 349L204 213C173 168 147 130 119 95C78 46 67 38 5 30V0H195V30C144 38 143 47 162 79C181 112 202 149 225 181L297 70C314 43 307 35 264 30V0H482Z" id="g58-118"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="481" vert-adv-y="481"></glyph.data></g></svg></span></td><td align="center">0.9</td><td align="center">0.643099</td></tr><tr><td align="left"><span style="width: 8.62618ptpx;"><svg height="9.21094pt" id="M93" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 8.62618 9.21094" width="8.62618pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627"></glyph.data></g></svg></span></td><td align="center">0.289232</td><td align="center">0.065669</td></tr><tr><td align="left">CF value</td><td align="center">0.520639</td><td align="center">3.5331 · 10<sup>−15</sup></td></tr><tr><td align="left">Istab. Value</td><td align="center">21</td><td align="center">9</td></tr><tr><td align="left">Average error per iteration</td><td align="center">7.21 · 10<sup>−15</sup></td><td align="center">0</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Characteristics of the best solution: joined case studies 5 and 6, Lozi map as CPRNG/controlled system.

The Scientific World Journal

tab9

Table 9

Table 9: Chaos Enhanced Differential Evolution in the Task of Evolutionary Control of Selected Set of Discrete Chaotic Systems 