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最新推荐文章于 2024-11-20 13:50:10 发布

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最新推荐文章于 2024-11-20 13:50:10 发布

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原文链接：http://www.cnblogs.com/Marigolci/p/11244207.html

本文深入探讨了分支限界法的基本原理，这是一种通过限制搜索范围来寻找最优解的有效算法。文章详细解释了如何在每次分支后，排除那些界限超出已知可行解值的子集，从而大幅度减少了不必要的计算，确保了算法的高效性。

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1.分支限界法

在每次分支后，对凡是界限超出已知可行解值那些子集不再做进一步分支。这样，解的许多子集（即搜索树上的许多结点）就可以不予考虑了，从而缩小了搜索范围。这一过程一直进行到找出可行解为止，该可行解的值不大于任何子集的界限。因此这种算法一般可以求得最优解。

将问题分枝为子问题并对这些子问题定界的步骤称为分枝定界法。

Branch and bound method

After each branch, no further branches are made for those subsets whose boundaries exceed the known feasible solution values. In this way, many subsets of the solution (ie many nodes on the search tree) can be ignored, thus narrowing the search. This process continues until a feasible solution is found, the value of the feasible solution being no more than the bounds of any subset. Therefore, this algorithm can generally find the optimal solution.
The step of branching the problem into sub-problems and delimiting these sub-problems is called the branch and bound method.

转载于:https://www.cnblogs.com/Marigolci/p/11244207.html