This work concerns the design of matrix adaptation evolution strategies for black-box optimization under nonlinear equality constraints. First, constraints in form of elliptical manifolds are considered. For those constraints, an algorithm is proposed that evolves itself on that manifold while optimizing the objective function. The specialty about the approach is that it is possible to ensure that the population evolves on the manifold with closed-form expressions. Second, an algorithm design for general nonlinear equality constraints is presented. For those constraints considered, an iterative repair approach is presented. This allows the evolution to happen on the nonlinear manifold defined by the equality constraints for this more general case as well. For both cases, the algorithms are interior point methods, i.e., the objective function is only evaluated at feasible points in the parameter space, which is often required in the area of simulation-based optimization. For the experimental evaluation, different test problems are introduced. The proposed algorithms are evaluated on those providing insights into the working principles of the different approaches. It is experimentally shown that correcting the mutation vectors after the repair step is important for an effective evolution strategy. Additional experiments are conducted for providing a comparison to other evolutionary black-box optimization methods, which show that the developed algorithms are competitive.

这项工作涉及在非线性等式约束下用于黑箱优化的矩阵适应进化策略的设计。首先，考虑椭圆流形形式的约束。针对这些约束，提出了一种在优化目标函数的同时在该流形上发展自己的算法。该方法的特色在于可以确保总体在具有封闭形式的表达式上发展。其次，给出了一般非线性等式约束的算法设计。针对这些约束条件，提出了一种迭代修复方法。对于这种更一般的情况，这也允许演化在由等式约束定义的非线性流形上进行。对于这两种情况，算法都是内点法，即 目标函数仅在参数空间中的可行点处评估，这在基于仿真的优化领域中经常需要。为了进行实验评估，引入了不同的测试问题。对提供的算法进行了评估，以提供对不同方法的工作原理的见解。实验表明，在修复步骤后校正突变载体对于有效的进化策略很重要。为了提供与其他进化黑盒优化方法的比较，还进行了其他实验，这些实验表明所开发的算法具有竞争力。对提供的算法进行了评估，以提供对不同方法的工作原理的见解。实验表明，在修复步骤后校正突变载体对于有效的进化策略很重要。为了提供与其他进化黑盒优化方法的比较，还进行了其他实验，这些实验表明所开发的算法具有竞争力。对提供的算法进行了评估，以提供对不同方法的工作原理的见解。实验表明，在修复步骤后校正突变载体对于有效的进化策略很重要。为了提供与其他进化黑盒优化方法的比较，还进行了其他实验，这些实验表明所开发的算法具有竞争力。