Hasofer-Lind可靠度指标问题的混合进化算法的极限行为
Limit-behavior of a hybrid evolutionary algorithm for the Hasofer-Lind reliability index problem
AI总结：
该研究针对Hasofer-Lind可靠度指标问题中的混合微遗传算法，通过马尔可夫链分析证明了其收敛性，并指出遗传修复机制为条件稳定，为等式约束优化提供了理论保障。
摘要：
在概率结构力学中，Hasofer-Lind可靠度指标问题是一个典型的等式约束问题，即寻找从一点到曲面的最小距离。在实际工程问题中，该曲面是隐式定义的，需要求解边值问题。近期，文献中提出了一种混合微遗传算法（HmGA），该算法采用实数-二进制混合基因型，并引入了新颖的确定性算子来处理等式约束，即遗传修复和区域缩放机制（G. das Neves Carneiro 和 C. Conceição António，“通过进化算法实现隐式复合材料层合结构全局最优可靠度指标”，《结构安全》，第79卷，第54-65页，2019年）。我们研究了HmGA的极限行为，并给出了该算法的收敛定理。证明了遗传修复是一种条件稳定的机制，并讨论了其收敛模式。基于马尔可夫链分析，给出并讨论了HmGA以概率1收敛的条件。
英文摘要：
In probabilistic structural mechanics, the Hasofer-Lind reliability index problem is a paradigmatic equality constrained problem of searching for the minimum distance from a point to a surface. In practical engineering problems, such surface is defined implicitly, requiring the solution of a boundary-value problem. Recently, it was proposed in the literature a hybrid micro-genetic algorithm (HmGA), with mixed real-binary genotype and novel deterministic operators for equality-constraint handling, namely the Genetic Repair and Region Zooming mechanisms (G. das Neves Carneiro and C. Conceição António, "Global optimal reliability index of implicit composite laminate structures by evolutionary algorithms", Struct Saf, vol. 79, pp. 54-65, 2019). We investigate the limit-behavior of the HmGA and present the convergence theorems for the algorithm. It is proven that Genetic Repair is a conditionally stable mechanism, and its modes of convergence are discussed. Based on a Markov chain analysis, the conditions for the convergence with probability 1 of the HmGA are given and discussed.
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