We study the performance of two popular jump neighborhoods on the classical scheduling problem of minimizing the makespan on related parallel machines under the additional restriction that jobs are only allowed to be scheduled on a subset of machines. In particular, we analyze the performance guarantee of local optima with respect to the jump and the lexicographical jump neighborhood.
Rutten, C., Recalde, D., Schuurman, P., & Vredeveld, T. (2012). Performance guarantees of jump neighborhoods on restricted related parallel machines. Operations Research Letters, 40(4), 287-291. https://doi.org/10.1016/j.orl.2012.04.002