In this work, we are interested in a class of problems of great importance in many areas of industry and engineering. It is the invese problem for the biharmonic equation. It consists to complete the missing data on the inaccessible part from the measured data on the accessible part of the boundary. To solve this ill-posed problem, we opted for the alternative iterative method developed by Kozlov, Mazya and Fomin which is a convergent method for the elliptical Cauchy problems in general. The numerical implementation of the iterative algorithm is based on the application of the boundary element method (BEM) for a sequence of mixed well-posed direct problems. Numerical results are performed for a square domain showing the effectiveness of the algorithm by BEM to produce accurate and stable numerical results.

The genetic algorithm includes some parameters that should be adjusted, so as to get reliable results. Choosing a representation of the problem addressed, an initial population, a method of selection, a crossover operator, mutation operator, the probabilities of crossover and mutation, and the insertion method creates a variant of genetic algorithms. Our work is part of the answer to this perspective to find a solution for this combinatorial problem. What are the best parameters to select for a genetic algorithm that creates a variety efficient to solve the Travelling Salesman Problem (TSP)? In this paper, we present a comparative analysis of different mutation operators, surrounded by a dilated discussion that justifying the relevance of genetic operators chosen to solving the TSP problem.

The aim of this paper is to evaluate the train/track induced loads on the substructure by modelling the wheel, at each instant, as a moving sinusoidal pulse applied in a very short period of time. This assumption has the advantage of being more realistic as it reduces the impact of time on the load definition. To that end, mass, stiffness, and dumping matrices of an elementary section of track will be determined. As a result, the equations of motion of a section of track subjected to a sinusoidal pulse and a rectangular pulse respectively is concluded. Two numerical methods of resolution of that equation, depending on the nature of the dumping matrix, will be presented. The computation results will be compared in order to conclude about the relevance of that load model. This approach is used in order to assess the nature and the value of the loads received by the substructure.

In this paper, we present a new mutation operator, Hybrid Mutation (HPRM), for a genetic algorithm that generates high quality solutions to the Traveling Salesman Problem (TSP). The Hybrid Mutation operator constructs an offspring from a pair of parents by hybridizing two mutation operators, PSM and RSM. The efficiency of the HPRM is compared as against some existing mutation operators; namely, Reverse Sequence Mutation (RSM) and Partial Shuffle Mutation (PSM) for BERLIN52 as instance of TSPLIB. Experimental results show that the new mutation operator is better than the RSM and PSM.