OPTIMUS: Self-Adaptive Differential Evolution with Ensemble of Mutation Strategies for Grasshopper Algorithmic Modeling

Abstract

Most of the architectural design problems are basically real-parameter optimization problems. So any type of evolutionary and swarm algorithms can be used in this field. However there is a little attention on using optimization methods within the computer aided design (CAD) programs. In this paper we present Optimus which is a new optimization tool for grasshopper algorithmic modeling in Rhinoceros CAD software. Optimus implements self-adaptive differential evolution algorithm with ensemble of mutation strategies (jEDE). We made an experiment using standard test problems in the literature and some of the test problems proposed in IEEE CEC 2005. We reported minimum maximum average standard deviations and number of function evaluations of five replications for each function. Experimental results on the benchmark suite showed that Optimus (jEDE) outperforms other optimization tools namely Galapagos (genetic algorithm) SilverEye (particle swarm optimization) and Opossum (RbfOpt) by finding better results for 19 out of 20 problems. For only one function Galapagos presented slightly better result than Optimus. Ultimately we presented an architectural design problem and compared the tools for testing Optimus in the design domain. We reported minimum maximum average and number of function evaluations of one replication for each tool. Galapagos and Silvereye presented infeasible results whereas Optimus and Opossum found feasible solutions. However Optimus discovered a much better fitness result than Opossum. As a conclusion we discuss advantages and limitations of Optimus in comparison to other tools. The target audience of this paper is frequent users of parametric design modelling e.g. architects engineers designers. The main contribution of this paper is summarized as follows. Optimus showed that near-optimal solutions of architectural design problems can be improved by testing different types of algorithms with respect to no-free lunch theorem. Moreover Optimus facilitates implementing different type of algorithms due to its modular system.