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Combinatorial APS?

For some problems that are at least partly discrete, the basic APS applies a \emph{quantisation} operator. If the quantum is qd for the dimension d, the operator is defined by

xi,dqd(0.5+xi,d/qd)

where is the floor operator.

Now, for combinatorial, it is certainly better to define specific operators for Expansion, Contraction, and Local search, as it has been done, for example, for PSO.