Global Optimization Algorithms Based On Space-filling Curves And A Modified Tunnelling Algorithm

The global optimization problem is an important topic in the study of optimization theory and method. Global optimization algorithms can be divided into two categories: deterministic algorithm and random algorithm. This article focuses on two algorithms: a two-stage algorithm based on α-dense curve and a modified tunnelling algorithm.The full text is divided into three chapters:Chapter 1, we introduce the basic concept of global optimization problem, several local algorithms and several kinds of deterministic algorithms for global optimization problem, and in the last section, geometric approximate、one-dimensional information algorithm and multi-dimensional information algorithm are introduced. Geometric approximate provides guidance for studying a two-stage algorithm based on α-dense curve.Chapter 2, we introduce α-dense curve and its property and construct a new α-dense curve, thus multi-dimensional global optimization problem can be transformed into one-dimensional global optimization problem, coupled with geometric approximate, we provide a new algorithm-a two-stage algorithm based on α-dense curve, then the convergence of the algorithm is proved, finally the numerical experiments are gived, the experimental results show that the algorithm is effective and feasible.Chapter 3, we construct two modified tunnelling functions, based on these two functions, this paper proposes a modified tunnelling algorithm for solving global opti-mization problem, the algorithm overcomes the drawbacks of tunnelling algorithm, and numerical experiments also demonstrate the effectiveness of the proposed algorithm.