Abstract In this paper, we develop a new approach for solving a large class of global optimization problems for objective functions which are only continuous on a rectangle of R n . This method is based on the reducing transformation technique by running in the feasible domain a single parametrized Lissajous curve, which becomes increasingly denser and progressively fills the feasible domain. By means of the one-dimensional Evtushenko algorithm, we realize a mixed method which explores the feasible domain. To speed up the mixed exploration algorithm, we have incorporated a DIRECT local search type algorithm to explore promising regions. This method converges in a finite number of iterations to the global minimum within a prescribed accuracy e > 0 . Simulations on some typical test problems with diverse properties and different dimensions indicate that the algorithm is promising and competitive.

中文翻译：

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使用稠密曲线进行连续全局优化的确定性方法

摘要 在本文中，我们开发了一种新方法，用于求解仅在 R n 的矩形上连续的目标函数的一大类全局优化问题。该方法基于减少变换技术，通过在可行域中运行单个参数化 Lissajous 曲线，该曲线变得越来越密集并逐渐填充可行域。通过一维Evtushenko算法，我们实现了一种探索可行域的混合方法。为了加速混合探索算法，我们采用了直接局部搜索类型算法来探索有希望的区域。该方法在有限次数的迭代中收敛到规定精度 e > 0 内的全局最小值。