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A realization of constraint feasibility in a moving least squares response surface based approximate optimization

机译：基于移动最小二乘响应面的近似优化约束可行性的实现

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摘要

In the context of approximate optimization, the most extensively used tools are the response surface method (RSM) and the moving least squares method (MLSM). Since traditional RSMs and MLSMs are generally described by second-order polynomials, approximate optimal solutions can, at times, be infeasible in cases where highly nonlinear and/or nonconvex constraint functions are to be approximated. This paper explores the development of a new MLSM-based meta-model that ensures the constraint feasibility of an approximate optimal solution. A constraint-feasible MLSM, referred to as CF-MLSM, makes approximate optimization possible for all of the convergence processes, regardless of the multimodalityonlinearity in the constraint function. The usefulness of the proposed approach is verified by examining various nonlinear function optimization problems.
机译：在近似优化的情况下，使用最广泛的工具是响应面法（RSM）和移动最小二乘法（MLSM）。由于通常用二阶多项式描述传统的RSM和MLSM，因此有时在逼近高度非线性和/或非凸约束函数的情况下，近似最优解可能不可行。本文探索了一种新的基于MLSM的元模型的开发，该模型可确保近似最优解的约束可行性。约束可行的MLSM（称为CF-MLSM）使所有收敛过程的近似优化成为可能，而与约束函数中的多峰/非线性无关。通过研究各种非线性函数优化问题，验证了该方法的有效性。

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