EM323: A line search based algorithm for solving high-dimensional continuous non-linear optimization problems

This paper presents a performance study of a one-dimensional search algorithm for solving general high-dimensional optimization problems. The proposed approach is a hybrid between a line search algorithm of Glover (The 3-2-3, stratified split and nested interval line search algorithms. Research report, OptTek Systems, Boulder, CO, 2010) and an improved variant of a global method of Gardeux et al. (Unidimensional search for solving continuous high-dimensional optimization problems. In: ISDA '09: Proceedings of the 2009 ninth international conference on intelligent systems design and applications, IEEE Computer Society, Washington, DC, USA, pp 1096-1101, 2009) that uses line search algorithms as subroutines. The resulting algorithm, called EM323, was tested on 19 scalable benchmark functions, with a view to observing how optimization techniques for continuous optimization problems respond with increasing dimension. To this end, we report the algorithm's performance on the 50, 100, 200, 500 and 1,000-dimension versions of each function. Computational results are given comparing our method with three leading evolutionary algorithms. Statistical analysis discloses that our method outperforms the other methods by a significant margin.