Multiscale multiresolution genetic algorithm with a golden sectioned population composition

A new genetic algorithm (GA) strategy called the multiscale multiresolution GA is proposed for expediting solution convergence by orders of magnitude. The motivation for this development was to apply GAs to a certain class of large optimization problems, which are otherwise nearly impossible to solve. For the algorithm, standard binary design variables are binary wavelet transformed to multiscale design variables. By working with the multiscale variables, evolution can proceed in multiresolution; converged solutions at a low resolution are reused as a part of individuals of the initial population for the next resolution evolution. It is shown that the best solution convergence can be achieved if three initial population groups having different fitness levels are mixed at the golden section ratio. An analogy between cell division and the proposed multiscale multiresolution strategy is made. The specific applications of the developed method are made in topology optimization problems.