Keywords: topological optimization, estimation of distribution algorithm, empirical selection distribution, parallel computation.

The shape optimization problem has been largely studied, it is defined as finding the best shape for a mechanical structure given a set of service conditions. This paper proposes a new methodology for the shape optimization problem. We combined various interesting features for our proposal, such as:

1. An estimation of distribution algorithm as optimization method. That uses a special candidate solution generation, and a procedure to improve the candidate solution before it is integrated into the population.
2. The evaluation considers the Von Mises stresses, the nodal displacements (from the finite element method), the weight of the structure. Nevertheless there are three function values to evaluate, the algorithm just needs the order of the solutions, or to determine if a solution is better than other to perform the search.
3. We introduce a parallel asynchronous proposal that performs local optimization procedures, while sharing information concerning local distributions and the best solution found.

It is important to note that this a remarkable difference with other population based algorithms which must share candidate solutions, in this case the important information we want to share is codified in a probability distribution. This way of approaching the problem does not need explicit user given a priori information, that could bias the search to some specific solutions. Thus, the approximated optimum solution is totally inferred during the search process without any given user information. The inferred information could be useful and interesting from the designer's point of view, because the algorithm is capable of synthesizing the acquired knowledge in the probability distribution. We present case studies to show the performance of the proposed methodology. The results have an important weight reduction, and even the optimization process delivers feasible solutions when the initial mesh with all the elements present is unfeasible. Hence the results seem encouraging and will be further explored. Finally, this is one of the first papers in the literature that explores the use of a parallel asynchronous estimation of distribution algorithm applied to the shape optimization problem. The use of a probability distribution points out the direction of possible future work:

1. to use the knowledge in the distribution for enhancing the search in similar problems,
2. to use the distribution to inherit the knowledge in multi-grid approaches,
3. to obtain knowledge about the problem from the statistical learning.

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