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SUMMARYA parameter-less adaptive penalty scheme for genetic algorithms applied to constrained optimization problems is proposed. Using feedback from the evolutionary process the procedure automatically defines a penalty parameter for each constraint. The user is thus relieved from the burden of having to determine sensitive parameter(s) when dealing with every new constrained optimization problem. The procedure is shown to be effective and robust when applied to test problems from the evolutionary computation literature as well as several optimization problems from the structural engineering literature.

Summary.A finite element procedure for circumventing the Babu~ka-Brezzi condition in mixed formulations with Lagrange multipliers defined on the boundary is presented. Residual terms constructed from the Euler-Lagrange equations are added to the classical Galerkin formulation in order to attain coercivity in a mesh-dependent norm. Convergence is proven for the primal variable and the multiplier in the natural mesh-independent norm of the problem, generalizing results of a previous paper.

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Differential Evolution is a simple and efficient stochastic population-based heuristics for global optimization over continuous spaces. As with other nature inspired techniques, there is no provision for constraint handling in its original formulation, and a few possibilities have been proposed in the literature. In this paper an adaptive penalty technique (APM), which has been shown to be quite effective within genetic algorithms, is adopted for constraint handling within differential evolution. The technique, which requires no extra parameters, is based on feedback obtained from the current status of the population of candidate solutions, and automatically defines, for each constraint, its corresponding penalty coefficient. Equality as well as inequality constraints can be dealt with. In this paper we additionally introduce a mechanism for dynamically selecting the mutation operator, according to its performance, among several variants commonly used in the literature. In order to assess the applicability and performance of the proposed procedure, several test-problems from the structural and mechanical engineering optimization literature are considered.

In this work we present an implementation of symbolic regression which is based on genetic programming (GP). Unfortunately, standard implementations of GP in compiled languages are not usually the most eficient ones. The present approach employs a simple representation for treelike structures by making use of Read's linear code, leading to more simplicity and better per$ormance when compared with traditional GP implementations. Creation, crossover and mutation of individuals are formalized. An extension allowing for the creation of random coeficients is presented. The eficiency of the proposed implementation was conjirmed in computational experiments which are summarized in this papel: