Multi-directional search method with quadratic model
Date
1993
Authors
Ma, Haibo
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
In recent years, there has been a great deal of interest in the development of optimization algorithms which exploit the computational power of parallel computer architectures. V. Torczon has developed a new algorithm, called the Multi-Directional Search method, which is ideally suited for parallel computation.
The multi-directional search algorithm belongs to the class of direct search methods, a class of optimization algorithms wh.ich neither compute nor approximate any derivatives of the objective function . This method is inherently parallel because its basic idea is to perform concurrent searches in multiple directions which are free of any interdependencies. Another significant feature of Torczon 's algorithm is that a convergence theory was developed when the algorithm was proposed.
In this thesis, we incorporated the idea of approximating a general function by a quadratic function into Torczon's multi-directional search algorithm. proposing an algorithm called the Multi-Directional Search algorithm with Restart. Using our algorithm, when the objective function is a quadratic, the algorithm locates the minimizer in only two iterations. Even for a general objective function. by using the information obtained from the quadratic approximations, the overall searching process can be accelerated. In this sense our algorithm exhibits better performance than Torczon's origu1al method.
Another issue this thesis addressed is the implementation of the algorithm. We use a tree structure to replace the matrix Torczon used in her implementation. ·with the new data structure, we can considerably reduce the amount of storage used and the number of comparisons performed in the whole process.
Also presented here are the numerical results showing the comparisons of the performance of our algorithm with that of Torczon's original method, as well as the comparison of the performance of using a tree structure against Torczon's approach of using a matrix.
Description
Keywords
UN SDG 17: Partnerships