Free Search in Multidimensional Space III

Abstract

Various scientific and technological fields, such as design, engineering, physics, chemistry, economics, business, and finance often face multidimensional optimisation problems. Although substantial research efforts have been directed in this area, key questions are still waiting for answers, such as: What limits computer aided design systems on optimisation tasks with high variables number? How to improve capabilities of modern search methods applied to multidimensional problems? What are software and hardware constraints? Approaching multidimensional optimisation problems raises in addition new research questions, which cannot be seen or identified on low dimensional tasks, such as: What time is required to resolve multidimensional task with acceptable level of precision? How dimensionality reflects on the search space complexity? How to establish search process orientation, within multidimensional space? How task specific landscapes embarrass orientation? This article presents an investigation on 300 dimensional heterogeneous real-value numerical tests. The study aims to evaluate relation between tasks’ dimensions’ number and required for achieving acceptable solution with non-zero probability number of objective function evaluations. Experimental results are presented, analysed and compared to other publications.