Abstract
Truss-Z (TZ) is an Extremely Modular System for creating skeletal free-form ramps and ramp networks. The TZ structures are comprised of four variations of two types of basic unit subjected to rotation. The two types of units are: R and L being a mirror reflection of each other. This paper presents a novel method based on image processing, evolutionary algorithm and intensive parallelization of multi-objective optimization of TZ layouts.The algorithm returns a sequence of modules. The result guarantees a TZ connection between two given points (regions) and minimizes the fitness function representing certain costs associated with setting up the TZ structure.The fitness function depends on the cost of TZ structure as well as the variety of costs related to the environment where the it is to be placed. E.g.: the earthworks, vegetation removal, obstacles avoidance, etc. There are no restrictions on the fitness function definition. It can depend on any variable which can be represented by a two-dimensional map of any property of the environment.The formulation of the presented method is suited for application of well-established image processing methods which efficiently evaluate candidate solutions on a GPU. As a result, the employed genetic algorithm efficiently probes the search space. The practical applicability of this approach is demonstrated with three case-studies:1simultaneous paving of a path with congruent units in a hilly environment with trees & bushes and finding the best location for a pier over an existing river;2constructing of a TZ connector spanning over a mountain valley with lakes (where supports can not be placed);3retrofitting of an existing railway station with a large wheelchair TZ ramp of over 10 m elevation while preserving trees and minimizing the earthworks.
Highlights
The idea of Extremely Modular System (EMS) has been introduced in [1]
Any two Pipe-Z modules can be connected at practically any relative twist angle, and any two Truss-Z modules (TZMs) in a single-branch structure can be connected in four distinct configurations
In the case of the supports placed under each TZM the TZ path runs between the lakes and after passing the valley runs along the second slope to minimize the total length of supports
Summary
The idea of Extremely Modular System (EMS) has been introduced in [1]. In a nutshell, the purpose of EMS is to create free-form modular objects in given environments without obstacle violations, and self-collisions. This work is a continuation of preliminary results presented in the conference paper [4], which introduced the problem of self-intersection to the optimization of a two-dimensional single-branch. The introduction of the formal cost matrix C It allows for optimization of a TZP in environment E where obstacles can have any shape and the associated cost depending on location in E is expressed by a real number. The introduction of the cost flow matrix F It substantially improves the efficiency of the algorithm, so the good solutions can be found consistently and relatively quickly in highly constrained environments. The environment setups made possible to ignore the self-intersection prohibition In all those cases it was intuitive to assume that the best TZs, that is comprised of the smallest number of modules would not self-intersect.
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