10 th World Congress on Structural and Multidisciplinary Optimization May 19 -24, 2013, Orlando, Florida, USA 1 Topological optimization of microstructure by means of bio-inspired methods Tadeusz Burczyński 1,2 , Waclaw Kuś 1 , Arkadiusz Poteralski 1 1 Silesian University of Technology, Gliwice, Poland, tb@polsl.pl 2 Cracow University of Technology, Cracow, Poland, tburczyn@pk.edu.pl 1. Abstract Optimization of structures in the macro scale is widely used nowadays. The goal of the paper is to apply optimization techniques to obtain better performance on the micro level. The presented approach opens new possibilities. The structures build with the use of materials with optimal microstructure can obtain the best performance. The microstructure can be optimized taking into account loads of the macro structure. Optimization of the microstructure is not easy currently, but in the future, the presented approach may be used with success when performance of the structure is very important. A bio-inspired method based on the artificial immune system (AIS) is used to solve the optimization problem. Immune computing provides a great probability of finding the global optimum. It is developed on the basis of a mechanism discovered in biological immune systems. An immune system is a complex system which contains distributed groups of specialized cells and organs. The main purpose of the immune system is to recognize and destroy pathogens - funguses, viruses, bacteria and improper functioning cells. The artificial immune system takes only a few elements from the biological immune systems. Mutation of the B cells, proliferation, memory cells, and recognition by using the B and T cells are used the most frequently. The unknown global optimum is represented by the searched pathogen. The memory cells contain design variables and proliferate during the optimization process. The B cells created from memory cells undergo the mutation. The B cells evaluate and better ones exchange memory cells. The optimal topology is generated by the level set approach. The crowding mechanism is used - the diverse between memory cells is forced. A new memory cell is randomly created and substitutes the old one, if two memory cells have similar design variables. The crowding mechanism allows finding not only the global optimum but also other local ones. Additional the Gaussian mutation is used in this approach. The paper presents methodology, algorithm of optimization and numerical examples. 2. Keywords: topology optimization, artificial immune system, multiscale modeling 3. Introduction Shape and topology optimization have been an active research area for some time. Recently, several innovative approaches for topology optimization have been developed. Perhaps one of the simplest optimization method is the method based on removing inefficient material from a structure. This method is named Evolutionary Structural Optimization [26]. However, this method is not based on the application of the evolutionary algorithm but on different rejection criteria for removing material which depends on the types of design constraints. One of the most famous structural optimization approaches is the approach based on material homogenization method [4][5] and it has been applied to various optimization problems. The homogenization design method assumes the introduction of the periodic microstructures of a particular shape into the finite elements of the discretized domain. The size and the orientation of the microstructures in the elements determine the density and the structural characteristics of the material in the elements. An optimization process consisting in application of the mathematical programming techniques leads to the minimization of the structure compliance by changing the orientation and size of the microstructures. As a result the optimization process composite structures emerge. Another approach to the structural optimization is based on generating inside a domain a new void (so-called bubble) on the basis of special criteria and next on performing simultaneous shape and topology optimization. This approach was originated by Eschenauer and Schumacher [17]. Coupling of this approach, the boundary elements and the genetic algorithms was considered by Burczyński and Kokot [6]. From the mathematical point of view this approach is based on replacing a one-connected domain with a multi-connected domain. Another interesting approach assumes the discretization of the domain into binary material/void elements introduced by Anagnostou at al [1]. This approach was developed by Kirkpatrick at al [18], who proposed finding the optimal material configuration within the design domain by using simulated annealing. Jensen and Sandgren [22], proposed the application of the genetic algorithm in order to solve similar optimization problems. This approach has been developed by Chapman [16]. One of the most interesting recent approaches to the structural optimization problem is method named Multi-GA System introduced by Woon at al [25] which assumes the application of two simultaneously and parallel running genetic algorithms. The first external genetic algorithm is used to define the optimum shape of the structure