The problem of determining the minimum-cost hypothetical ancestral sequences for a given cladogram is known to be NP-complete. This "tree alignment" problem has motivated the considerable effort placed in multiple sequence alignment procedures. Wheeler in 1996 proposed a heuristic method, direct optimization, to calculate cladogram costs without the intervention of multiple sequence alignment. This method, though more efficient in time and more effective in cladogram length than many alignment-based procedures, greedily optimizes nodes based on descendent information only. In their proposal of an exact multiple alignment solution, Sankoff et al. in 1976 described a heuristic procedure--the iterative improvement method--to create alignments at internal nodes by solving a series of median problems. The combination of a three-sequence direct optimization with iterative improvement and a branch-length-based cladogram cost procedure, provides an algorithm that frequently results in superior (i.e., lower) cladogram costs. This iterative pass optimization is both computation and memory intensive, but economies can be made to reduce this burden. An example in arthropod systematics is discussed.

中文翻译：

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序列数据的迭代遍历优化。

确定给定克拉德图的最小成本假设祖先序列的问题已知是NP完全的。该“树比对”问题激发了在多个序列比对程序中付出的巨大努力。惠勒（Wheeler）在1996年提出了一种启发式方法，即直接优化，可在无需多序列比对的情况下计算分支图成本。这种方法尽管比许多基于对齐的过程在时间上更有效，并且在克拉德图长度上更有效，但它仅基于后代信息贪婪地优化节点。在他们提出的精确多重比对解决方案的建议中，Sankoff等人。1976年，他描述了一种启发式程序-一种迭代改进方法-通过解决一系列中位数问题来在内部节点处创建对齐方式。具有迭代改进的三序列直接优化与基于分支长度的分支图成本过程的结合，提供了一种算法，该算法通常会导致更高（即更低）的分支图成本。这种迭代遍历优化既需要计算，也需要占用大量内存，但是可以通过经济性来减轻这种负担。讨论了节肢动物系统学中的一个例子。