A new heuristic for workload balancing on identical parallel machines and a statistical perspective on the workload balancing criteria

Minimizing workload balancing criteria on identical parallel machines

“…Although the criteria Á(S) and x 0 have been devised for number partitioning, it should be emphasized that they both might be equally used in the workload balancing problem for multiprocessor scheduling. Furthermore, a remarkable, perhaps unexpected mathematical relationship between NSSWD and x 0 arises, which gives further insight into these criteria (see Cossari et al [4] for details). In particular, for a given problem instance, W(S) and x 0 turn out to be proportional to each other, thus they may be used interchangeably for both multiprocessor scheduling and number partitioning, together with their associated algorithms.…”

“…Currently, a number of ad hoc criteria are available in both multiprocessor scheduling and number partitioning contexts. These criteria have been recently investigated by Cossari et al [4], who demonstrated that they all are essentially well-known statistical measures of data dispersion, and that two of them are closely related to each other. We now briefly present these existing criteria, then in Section 2.2 the choice of a performance criterion will be put into the broader perspective of choosing an appropriate dispersion measure from those available in statistical methodology.…”

“…This NSSWD criterion stems from the well-established practice of measuring data dispersion in terms of the squared deviations from the mean, and has the additional feature of being suited for the relative assessment of multiple problem instances. Later Cossari et al [4] showed that W…”

“…Cossari et al [4] showed that x 0 ¼ m 2 r 2 , where r 2 (square of the standard deviation) is the very popular variance, and hence, apart from a factor m 2 , x 0 is essentially equivalent to the variance and to the standard deviation itself. When solving a single instance m is fixed, thus the use of x 0 is unnecessary and r may again be equally employed.…”

An imperialist competitive algorithm for a bi-objective parallel machine scheduling problem with load balancing consideration

“…In other words, setup times between two jobs of j and k on machine i is different with setup time between two jobs of k and j on the same machine, i. In addition, setup times between two jobs of j and k on machine i is different with setup times of two jobs of j and k on i' (Allahverdiet al, 2008;Vallada, & Ruiz, 2011;Cossari et al, 2012). Lei (2009) provided an extensive review of the literature on the scheduling problems with multiple objectives.…”