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In this work, a partial enumeration procedure is presented which is based on the merging reduction.
To overcome this limitation, in this work, the eigenstructure assignment is formulated firstly as an inverse eigenvalue problem within the frame of constrained nonlinear integer programming, and then is solved by means of a partial enumeration technique with a reduced number of iterations.
The suboptimal methods only execute a partial enumeration of cost function for a subset of all possible combinations of phase vectors.
We call this sampling a " Partial Enumeration of Traces" and, in this work, we propose three new algorithms for doing this sampling.
With the objective of calculating alternative evolutionary scenarios for big permutations, we developed three different algorithms that perform a partial enumeration of the complete set of solution traces of a given permutation.
A partial enumeration of traces is a sampling of the complete set of traces and can be an alternative for the study of distinct evolutionary scenarios of big permutations.
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This function is extremized using a directed partial enumeration strategy guided by physical considerations related to transport processes.
A very simple solution for the partial enumeration of traces is to construct random traces.
Notice however that, as we shall see later, since the number of traces with high height or high average reversal length are rare in general, this will not affect much the observed distributions of such parameters for the partial enumeration of traces relatively to a full enumeration.
Before introducing the algorithms for partial enumeration of traces, in this section we make a quick presentation of the algorithms which were designed for the enumeration of the complete set of solution traces.
They can be used as stand-alone procedures or can be integrated into (partial) enumeration procedures, like branch and bound or dynamic programming, and heuristic solution methods.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com