Given a submatrix A′ i, j) of an m × n haplotype matrix A and a diversity upper limit D, for all constrained intervals [ i, j*], i ≤ j* ≤ j, find a segmentation consisting of k feasible blocks such that the total length can be maximized in O(| j − i | k) time after the preprocessed leftmost markers (tag SNP selection), L[ i]'s are prepared.
Lemma 5 Given a submatrix A ′ i, j ) of an m × n haplotype matrix A and a diversity upper limit D, for all constrained intervals [ i, j *], i ≤ j * ≤ j, find a segmentation consisting of k feasible blocks such that the total length can be maximized in O (| j − i | k ) time after the preprocessed leftmost markers (tag SNP selection), L [ i ]'s are prepared.
To overcome these shortcomings, a novel optimization algorithm is proposed for directly solving the nonlinear constrained interval optimization models based on a novel concept of the degree of interval constraint violation (DICV) and the DICV-based preferential guidelines.
The constrained interval robust optimization model in Eq. (12) is utilized as a benchmark example, which is firstly solved by the proposed algorithm with the GA parameters listed in Table 1.
A robust optimization algorithm integrating Kriging models and nested GA is proposed to directly solve the constrained interval robust optimization model of the uncertain structure.
Then the robustness based preferential guidelines were proposed for directly ranking various design vectors and an algorithm integrating Kriging technique and nested GA was put forward to realize the direct solution of the constrained interval robust optimization problem.
The constrained interval robust optimization model in Eq. (13) is also solved by our previous algorithm [27] with the GA parameters and convergent threshold settled the same as those in the proposed algorithm.
The inner layer GAs integrated with Kriging models calculate in parallel the intervals of the mechanical performance indices under the influence of uncertain parameters while the outer layer GA realizes the direct sorting of various design vectors according to the robustness-based preferential guidelines and locates the optimal solution to the constrained interval robust optimization model.
Digital imaging analysis was performed and images were captured at 0.25 µm intervals, and stacks were deconvoluted with a constrained iterative algorithm, using a cooled charge-coupled device camera Retiga-2000RR: Q-Imaging).
