A Comprehensive Review on Scatter Search: Techniques, Applications, and Challenges

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Subset type</td><td class="align_center">Description</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">Type-I</td><td class="align_center">SG contains two-element subsets</td></tr><tr><td class="align_left">Type-II</td><td class="align_center">Three-element subsets constituted from two-element subsets</td></tr><tr><td class="align_left">Type-III</td><td class="align_center">Four-element subsets constituted from three-element subsets</td></tr><tr><td class="align_left">Type-IV</td><td class="align_center">Subsets constituted from <i>k</i>-best elements (i.e., <i>k</i> lies in the range of [5, <svg height="12.5807pt" id="M33" style="vertical-align:-3.272799pt" version="1.1" viewbox="-0.0498162 -9.3079 28.2415 12.5807" width="28.2415pt" 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="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.112,0)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.637,0)"><path d="M54 437L27 408L31 397H101V103C101 37 94 32 30 26V0H266V25C187 33 180 36 180 110V397H288C299 404 304 428 298 437H180V477C179 562 190 610 203 630C214 647 230 659 256 659C289 659 318 641 337 622C346 612 355 612 364 619C374 627 380 635 383 643C388 655 387 667 378 678C362 697 333 710 299 712C260 707 225 689 189 659C135 613 119 563 112 541S101 490 101 458V437H54Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.551,3.132)"><path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.963,3.132)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,24.831,3.132)"><path d="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z"></path></g></svg>])</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Subset types in the SG method.</div>

Mathematical Problems in Engineering

tab4

Table 4

Table 4: A Comprehensive Review on Scatter Search: Techniques, Applications, and Challenges 