Abstract Memetic algorithms integrate local search into an evolutionary algorithm to combine the advantages of rapid exploitation and global optimisation. We provide a rigorous runtime analysis of memetic algorithms on the Hurdle problem, a landscape class of tunable difficulty with a “big valley structure”, a characteristic feature of many hard combinatorial optimisation problems. A parameter called hurdle width describes the length of fitness valleys that need to be overcome. We show that the expected runtime of plain evolutionary algorithms like the (1+1) EA increases steeply with the hurdle width, yielding superpolynomial times to find the optimum, whereas a simple memetic algorithm, (1+1) MA, only needs polynomial expected time. Surprisingly, while increasing the hurdle width makes the problem harder for evolutionary algorithms, it becomes easier for memetic algorithms. We further give the first rigorous proof that crossover can decrease the expected runtime in memetic algorithms. A (2+1) MA using mutation, crossover and local search outperforms any other combination of these operators. Our results demonstrate the power of memetic algorithms for problems with big valley structures and the benefits of hybridising multiple search operators.

中文翻译：

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模因算法在多模态优化中优于进化算法

摘要 Memetic 算法将局部搜索集成到进化算法中，结合了快速开发和全局优化的优点。我们对障碍问题的模因算法进行了严格的运行时分析，障碍问题是一种具有“大山谷结构”的可调难度景观类，这是许多硬组合优化问题的特征。一个称为障碍宽度的参数描述了需要克服的适应度谷的长度。我们表明，像 (1+1) EA 这样的简单进化算法的预期运行时间随着障碍宽度急剧增加，产生超多项式时间来找到最优值，而一个简单的模因算法，(1+1) MA，只需要多项式预期时间。令人惊讶的是，虽然增加障碍宽度使进化算法的问题变得更加困难，模因算法变得更容易。我们进一步给出了第一个严格证明，交叉可以减少模因算法中的预期运行时间。使用变异、交叉和局部搜索的 (2+1) MA 优于这些运算符的任何其他组合。我们的结果证明了模因算法对大山谷结构问题的强大作用，以及混合多个搜索运算符的好处。