Application of Multilevel Optimization Algorithms

Abstract

In our industry researches we often face very difficult problems where ordinary algorithms fail to find the global optimum. Mostly they have difficult, high-dimensional count, very large design space where even the concept of direction and distance are non-existent and have to be defined, the neighbourship in the feasible space also needs definition. In these cases, these terms are often defined and calculated by heuristic functions. On these problems the applied optimization methods often fail, they stuck in local optima, working very slowly and find suboptimal solution. So we decided to try to link optimization methods and create multi-level optimization methods to cope these problems. As a base concept in the first stage we use some simple, fast, rapidly converging algorithm, then some finer grade algorithm like population based swarm optimization method. In this paper, we will show and evaluate some multi-level optimization methods tested on several test functions, comparing the convergence and computational needs.