Stochastic Schemata Exploiter (SSE) is one of the evolutionary optimization algorithms for solving the combinatorial optimization problems. We present the Extended SSE (ESSE) algorithm which is composed of the original SSE and new ESSE operations. The ESSE is compared with the original SSE, simple genetic algorithm (SGA), and GA with Minimal Generation Gap (MGG) in some test problems in order to discuss its features.
*Keywords:* Genetic Algorithm (GA), Stochastic Schemata Exploiter (SSE), Extended SSE (ESSE), Minimal Generation Gap (MGG).

J.A. Kołodziej, T. Klekiel. Optimal parameters of method of fundamental solutions for Poisson problems in heat transfer by means of genetic algorithms. CAMES 2008 (15)

This paper describes the application of the method of fundamental solutions to the solution of the boundary value problems of the two-dimensional steady heat transfer with heat sources. For interpolation of an inhomogeneous term in Poisson equation the radial basis functions are used. Three cases of boundary value problems are solved and five cases of radial basis functions are used. For comparison purposes the boundary value problems for which exact solution exists were chosen. Application of method of fundamental solutions with boundary collocation and radial basis function for solution of inhomogeneous boundary value problems introduces some number of parameters related with these tools. For optimal choosing of these parameters the genetic algorithm is used. The results of numerical experiences related to optimal parameters are presented.
*Keywords:* method of fundamental solutions, meshless method, radial basis functions, steady heat transfer, Poisson's equation, genetic algorithm, particular solution.

C. Tran. Determination of the shear speed of soil triaxial testing based on fuzzy logic. CAMES 2008 (15)

To design foundations, embankments and other soil structures, geotechnical engineers require methods of assessing engineering properties of soils. Some of the more complex phenomena that occur in soils have often been difficult to recreate in a laboratory: seismic activity, vibration, unsaturated condition, control of principal stresses etc. are areas which have proven difficult to replicate, despite their importance of being understood. This was partly due to the lack of test systems capable of reproducing these effects and the complexity of test systems that were developed to carry out such work. A number of advanced computer/software controlled systems allow the geotechnical engineer to perform the most complex test regimes via a user-friendly software interface. However, it is difficult to determine firstly parameters needed, e.g. shear speed in soil triaxial testing. In this paper we represent a new approach to determine this shear speed by solving the inverse problem using testing results obtained by the forward procedure. Direct search method, i.e. Adaptive Neuro-Fuzzy Inference System (ANFIS), is developed and applied to soil triaxial shear tests. It allows us to use the advanced sensor and actuator technologies in order to change the traditional triaxial shear apparatus from a mechanical system to a mechatronics system in next work.
*Keywords:* soil triaxial testing, shear speed, fuzzy logic, neuro-fuzzy inference system.

S. Skatulla, C. Sansour. Essential boundary conditions in meshfree methods via a modified variational principle. Applications to shell computations. CAMES 2008 (15)

It has been recognized by many authors that the enforcement of the essential boundary conditions is not an easy task, when it comes to moving least square (MLS)-based meshfree methods. In particular, the modelling of non-linear problems requires high approximation accuracy in order to obtain a solution. This paper addresses the boundary approximation accuracy of MLS-based meshfree methods and shows more specifically its significance with respect to the imposition of essential boundary conditions by the penalty, the Lagrange multiplier method and their combination which results in a modified variational principle. The later is augmented by a stabilization term which uses individual stabilization parameters determined for each numerical integration point by an iteration procedure.
This methodology is demonstrated on shell deformations in non-linear structural mechanics involving the Green strain tensor and two different hyper-elastic material laws.
*Keywords:* Meshfree methods, moving least square method, essential boundary conditions, shell analysis.

M. Kamiński. Symbolic computations in modern education of applied sciences and engineering. CAMES 2008 (15)

A presentation of the modern issues related to the symbolic computing is contained here together with the detailed discussion of its application to the education of various scientific and engineering academic disciplines. The future expansion of the symbolic environment is described here on the basis of their historical and modern developments presentation. As it is shown on the example of the MAPLE system, symbolic computational environments play the very important role in supporting the lectures and the classes in the computer labs. Those environments may be also very useful in teaching basic natural sciences in all those cases, when some algebraic or differential equations appear, must be solved and their results should be precisely discussed. The application of the MAPLE and similar computer systems in the engineering education seems to be unquestionable now and some examples are contained here to show how to improve the lectures and make them very interesting and exciting. The key feature offered by the symbolic computing is the opportunity to discover the knowledge that the students may do by themselves, when they are specifically leaded by the instructors.
*Keywords:* symbolic computations, computer science, computers in education.