A Modified Hybrid Genetic Algorithm for Solving Nonlinear Optimal Control Problems

<table class="table-group" id="tab8"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Method</td><td align="center">Mean rank</td><td align="center">Sum of ranks</td><td align="center">Test statistics</td><td align="center">Value</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">LI</td><td align="center">20.25</td><td align="center">405.0</td><td align="center">Mann-Whitney <svg height="9.21094pt" id="M753" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 9.98608 9.21094" width="9.98608pt" 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="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z" id="g113-86"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="727" vert-adv-y="727"></glyph.data></g></svg></td><td align="center">195</td></tr><tr><td align="left">SI</td><td align="center">20.75</td><td align="center">415.0</td><td align="center">Wilcoxon <svg height="9.21094pt" id="M754" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 13.3451 9.21094" width="13.3451pt" 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="M962 650H739L732 622L760 619C812 613 819 604 798 552C760 457 671 267 606 131H604L511 638H480L237 131H233L183 554C177 607 183 614 226 619L248 622L257 650H24L17 622C88 615 92 611 103 524L173 -11H203L450 491H453L543 -11H575L839 529C882 609 886 613 953 622L962 650Z" id="g113-88"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="974" vert-adv-y="974"></glyph.data></g></svg></td><td align="center">405</td></tr><tr><td align="left">—</td><td align="center">—</td><td align="center">—</td><td align="center"><span style="width: 9.51013ptpx;"><svg height="9.38774pt" id="M755" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -9.33792 9.51013 9.38774" width="9.51013pt" 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="M669 636L663 650H260C230 650 221 652 208 675H186C177 621 162 548 144 481L173 479C195 534 211 560 226 578C248 604 266 615 373 615H544C460 511 114 112 23 16L31 0H561C577 34 611 135 622 170L594 182C566 125 544 88 515 65C481 38 416 35 319 35C249 35 197 37 152 41C270 184 542 501 669 636Z" id="g113-91"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="692" vert-adv-y="692"></glyph.data></g></svg></span></td><td align="center"><span style="width: 37.2928ptpx;"><svg height="9.06134pt" 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Results of Mann-Whitney test on relative errors of the pair (LI, SI) for Time.

Mathematical Problems in Engineering

tab8

Table 8

Table 8: A Modified Hybrid Genetic Algorithm for Solving Nonlinear Optimal Control Problems 