Context-free grammars are useful tools for modeling the solution space of problems that can be solved by optimization algorithms. For a given solution space, there exists an infinite number of grammars defining that space, and there are clues that changing the grammar may impact the effectiveness of the optimization. In this article, we investigate theoretically and experimentally the possibility of specializing a grammar in a problem, that is, of systematically improving the quality of the grammar for the given problem. To this end, we define the quality of a grammar for a problem in terms of the average fitness of the candidate solutions generated using that grammar. Theoretically, we demonstrate the following findings: 1) that a simple mutation operator employed in a (1 + 1)-EA setting can be used to specialize a grammar in a problem without changing the solution space defined by the grammar and 2) that three grammars of equal quality for a grammar-based version of the ONEMAX problem greatly vary in how they can be specialized with that (1 + 1)-EA, as the expected time required to obtain the same improvement in quality can vary exponentially among grammars. Then, experimentally, we validate the theoretical findings and extend them to other problems, grammars, and a more general version of the mutation operator.

中文翻译：

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使用 (1+1)-EA 专门化上下文无关语法

上下文无关文法是对可以通过优化算法解决的问题的解空间进行建模的有用工具。对于给定的解决方案空间，存在无数定义该空间的语法，并且有线索表明改变语法可能会影响优化的有效性。在本文中，我们从理论上和实验上研究了将语法专门用于问题的可能性，即系统地提高给定问题的语法质量的可能性。为此，我们根据使用该语法生成​​的候选解决方案的平均适应度来定义问题的语法质量。从理论上讲，我们证明了以下发现：1) 在 (1 + 1)-EA 设置中使用的简单变异算子可用于专门化问题中的文法，而无需改变文法定义的解决方案空间 2) 文法的三个同等质量的文法-基于 ONEMAX 问题的版本在如何专门化 (1 + 1)-EA 方面有很大差异，因为获得相同质量改进所需的预期时间在语法之间可能呈指数变化。然后，通过实验，我们验证了理论发现并将它们扩展到其他问题、语法和变异算子的更一般版本。因为获得相同质量改进所需的预期时间在语法之间可能呈指数变化。然后，通过实验，我们验证了理论发现并将它们扩展到其他问题、语法和变异算子的更一般版本。因为获得相同质量改进所需的预期时间在语法之间可能呈指数变化。然后，通过实验，我们验证了理论发现并将它们扩展到其他问题、语法和变异算子的更一般版本。