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Application of Evolutionary Algorithm for Optimization of the Sequence of Initial Conditions for the Cellular Automaton-Based Shading
Machi Zawidzki and Marcin Bator

This paper presents an application of evolutionary algorithm (EA) for multi-objective optimization of the sequence of initial conditions (SIC) for a cellular automaton (CA) used for a potential implementation in the field of architecture. In the proposed application, a modular shading system for building facade is driven by a two color, one dimensional, range 2 CA rule {3818817080,2,2}. The SIC optimization criteria are: visual attractiveness, gradual and intuitive transition from one density level to another and even distribution of the pattern over the entire array. The ideal solutions for 10 square arrays of 7×7, 8×8,…, 16×16 cells are found by an exhaustive search method – the backtracking. The encoding of SICs using the order-based representation is introduced. A cost function evaluating both monotonicity of the average density transition, and the distribution of shading pattern is introduced. For a 100×100 cell array EA is implemented with three setups: without crossover but with intensive mutation, with crossover and without mutation, and with both crossover and mutation. Two types of crossover operations are used: uniform (UX) and onepoint (OPX). A number of experiments with various combinations of parameters were performed. The results are compared and the recommended strategy is briefly discussed. The best result was produced by EA with OPX and mutation rate 0.4.

Keywords: Modular shading system; initial conditions; multi-objective optimization; discrete optimization; backtracking; order-based representation; evolutionary algorithm

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