组合问题的黑盒复杂性
Black-Box Complexities of Combinatorial Problems
摘要：
黑盒复杂度是一种复杂性理论的度量，用于衡量一个问题通过通用优化算法进行优化的难度。因此，它是试图了解哪些问题对于遗传算法和其他随机搜索启发式算法来说是可处理的少数方法之一。以前大多数关于黑盒复杂性的工作都是关于人工测试函数的。本文对最小生成树和单源最短路这两个组合问题进行了深入的研究和分析。除了给他们的黑盒复杂性有趣的界限，我们的工作表明，如何建模的优化问题的选择是不平凡的。这在搜索空间不包括位串的情况下以及在无偏性的合理定义必须达成一致的情况下尤其适用。
英文摘要：
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic algorithms and other randomized search heuristics. Most previous work on black-box complexity is on artificial test functions. In this paper, we move a step forward and give a detailed analysis for the two combinatorial problems minimum spanning tree and single-source shortest paths. Besides giving interesting bounds for their black-box complexities, our work reveals that the choice of how to model the optimization problem is non-trivial here. This in particular comes true where the search space does not consist of bit strings and where a reasonable definition of unbiasedness has to be agreed on.
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