Keywords: Extremely Modular System, Truss-Z, discrete optimization, image processing, rasterization, GPU, CUDA, Mathematica, Wolfram Lightweight Grid.

Truss-Z (TZ) is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic unit subjected to affine transformations (mirror reflection, rotation and combination of both). This paper presents a new approach to the optimization of the layout of a singlebranch Truss-Z (STZ) in constrained environment (E). The problem is formulated as follows: create an STZ from a start (sP) to end point (eP) without self-intersections and collisions with two obstacles. This is a multi-criterial optimization problem where three independent objectives are subjected to minimization: the total number of modules (n), the “reaching error” to eP and the “overlapping error”. All three criteria are weighted and aggregated to a single cost function (CF). The calculation of CF is based on image processing of rendered geometry of individual STZs in E. The optimization is performed by population-based classic heuristic method - Evolution Strategy (ES). The computation of CF is the most time consuming, however, its parallelization is rather straightforward. Two parallelization methods are presented: distribution over Wolfram Lightweight Grid and application of general purpose graphical processing units (GPGPUs) with the use of CUDA platform.

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