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.