Keywords: evolution strategy, modular truss system, Truss-Z, discrete optimization.

This paper presents an application of evolution strategy for optimization of a single branch of Truss-Z - the modular truss system which was introduced in Reference [1]. The Truss-Z is a concept of a construction system which composed of only two modular units allows the creation of complex three-dimensional structural networks in a given environment. The elements of the environment model real obstacles such as buildings, roads and watercourses which may constrain the runs of branches of the truss. The system also permits the creation of loops and multiple branches of the structure. Such free-form networks can connect almost any given number of points in space (terminals). The parts of the structure can be disassembled after a certain period and reconfigured into an alternative configuration. Since the system is modular, the optimization of the structure is discrete and therefore has a combinatorial characteristic. Implementation of an algorithm based on the evolution strategy [2], the classic heuristic method is demonstrated. The binary encoding and the hexadecimal notation of a single branch of the truss, operation of mutation and the fitness function (FF) are introduced. As a result of the specific properties of the encoding, the probability of mutation is not uniform and grows proportionally along the genotype. In order to maintain the constant length of genotypes, the units that "go away" from the closest proximity of the end terminal are ignored in the FF calculations, however mutation operates on the entire genotype. The FF has a bipartite form and is a product of two distinct parts: one that rewards the solutions where the units go in a proper direction and one that penalizes the units which violate the constraints. A minimization example where a single branch of Truss-Z is to link two given terminals without colliding with three obstacles at minimal number of units is demonstrated. After adjusting the parameters of the algorithm, an experiment with the population size of 100 and number of generations 20 with mutation density of 10 (out of 50 genes) and the maximal number of units arbitrarily set to 50 was carried out.

The best results (of fitness 393.31) and mean results are compared with manually created reference solution (of fitness 378.24) and solutions produced by a random search (RS) (of fitness 507.47). The mean values of FF of solutions generated by the method proposed tend to decrease, which indicates the improvement. There is no such tendency in RS. The proposed method produces quiet good solutions for this type of problems - better than RS; The method is universal and can be applied in much more complicated cases, where deterministic methods may be inapplicable or inefficient.

1

M. Zawidzki, "A Modular Truss System for Pedestrian Traffic and a Computer Implementation of an Algorithm for Creating the Truss Structure", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 363, 2010. doi:10.4203/ccp.93.363

2

I. Rechenberg, "Evolutionsstrategie. Optimierung technischer Systeme nach Prinzipien der biologischen Evolution", Frommann Holzboog, 1973.

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