Mixed Integer Linear Programming Based Speed Profile Optimization for Heavy-Haul Trains

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Segment</td><td class="align_center"><span style="width: 7.34167ptpx;"><svg height="9.39034pt" id="M323" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.34167 9.39034" width="7.34167pt" 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="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z"></path></g></svg></span></td><td class="align_center"><span style="width: 6.59789ptpx;"><svg height="9.49473pt" id="M324" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.59789 9.49473" width="6.59789pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g></svg></span></td><td class="align_center"><svg height="6.04987pt" id="M325" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -5.81737 5.98461 6.04987" width="5.98461pt" 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="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z"></path></g></svg> (m/s)</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center">3.8443</td><td class="align_center">95.2559</td><td class="align_center">9.72−11.25</td></tr><tr><td class="align_left">2</td><td class="align_center">7.6993</td><td class="align_center">51.9998</td><td class="align_center">11.25−20.83</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Coefficients of the piecewise linear function of basic resistance.</div>

Journal of Advanced Transportation

tab5

Table 5

Table 5: Mixed Integer Linear Programming Based Speed Profile Optimization for Heavy-Haul Trains 