Tabu Search Algorithm Based on Lower Bound and Exact Algorithm Solutions for Minimizing the Makespan in Non-Identical Parallel Machines Scheduling

<table class="algorithm-group"><tr><td><table class="algorithm" id="alg1"><tr><td> </td><td>Put LB<sub>3</sub> ← (smallest overall processing time of the jobs/total machines).</td></tr><tr><td> </td><td>LB<sub>2</sub> ← LB<sub>3</sub></td></tr><tr><td> </td><td><b>While</b> LB<sub>2</sub> ≤ LB<sub>3</sub><b>do</b></td></tr><tr><td> </td><td>Remove jobs that have the lowest <svg height="12.7178pt" id="M20" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 19.9989 12.7178" width="19.9989pt" 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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.331,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.829,0)"><path d="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.329,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> percentage with preemption from machines that have makespan greater than LB<sub>2</sub> to their second-fastest machines.</td></tr><tr><td> </td><td>LB<sub>3</sub> ← (new minimum overall processing time of the jobs/total machines).</td></tr><tr><td> </td><td>LB<sub>2</sub> = LB<sub>2</sub> + 1</td></tr><tr><td> </td><td><b>end while</b></td></tr><tr><td> </td><td>LB<sub>2</sub> = LB<sub>2</sub> − 1</td></tr></table></td></tr></table>

<div> The algorithm to calculate LB<sub>2</sub>.</div>

Mathematical Problems in Engineering

alg1

Algorithm 1

Algorithm 1: Tabu Search Algorithm Based on Lower Bound and Exact Algorithm Solutions for Minimizing the Makespan in Non-Identical Parallel Machines Scheduling 

Algorithm 1 | Tabu Search Algorithm Based on Lower Bound and Exact Algorithm Solutions for Minimizing the Makespan in Non-Identical Parallel Machines Scheduling 