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The problem of off-line simultaneous estimation of temporal O-D matrices is tackled in this paper adopting a simulation approach, which avoids introducing assignment matrices [9].
Therefore, as n→∞, we expect the corresponding sequence of assignment matrices ({boldsymbol {X}^{(n)}}_{nin {mathbb N}}) (note that (tilde {boldsymbol {x}}^{(n)} =: text {vec}(mathbf {X}^{(n)}) )) to evolve towards network configurations with low energy consumption.
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We use X=[x i,j ]∈{0,1} M×N to denote the assignment matrix where x i,j =1 if TP j is assigned to cell i and x i,j =0 otherwise.
The assignment matrix A is subject to the following constraints: Each part must be assigned to exactly one worker, i.e., (sum _{k=1}^{m} A_{jk} = 1) for all j∈{1,…,n}.
The channel assignment matrix.
(i) Channel Assignment Matrix.
Also, the binary assignment variables form the subcarrier assignment matrix CN × M.
Below we describe how to choose an optimal assignment matrix (A in mathcal {K}).
This simple and efficient clustering algorithm significantly reduces the size of redundancy-rate assignment matrix, such that one can find the optimal channel-aware cluster-level redundancy-rate assignment matrix using a low-complexity full search approach.
The solution is encoded as a two-part representation including a permutation vector and a machine assignment matrix.
The assignment matrix A[ c i,j ] represents all the possible associations and the costs generated by these associations.
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