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.