Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods have been the most popular approach, because of their simplicity and ease of implementation. However, since the penalty function approach is generic and applicable to any type of constraint (linear or nonlinear), their performance is not always satisfactory. Thus, researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization. However, the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum. In this paper, GA's population-based approach and ability to make pair-wise comparison in tournament selection operator are explo...

An algorithm for solving large-scale nonlinear ' programs with linear constraints is presented. The method combines efficient sparse-matrix techniques as in the revised simplex method with stable quasi-Newton methods for handling the nonlinearities. A general-purpose production code (MINOS) is described, along with computational experience on a wide variety of problems.

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Direct analysis of normal incidence seismogram inversion with respect to a velocity profile is available now due to applying of a new global optimization algorithm. The latter is based upon regularized global approximation of an objective function which is not supposed to be differentiable. The new technique allows to see clearly a nonuniqueness of the inversion problem, no matter how high is a quality of the input data. It is induced by a few factors: a source wavelet is a function of a finite frequency band, an effective wave length of the sounding signal is increasing jointly with the velocity, and the power of a media response is decreasing with respect to the depth. The nonuniqueness means that there is no inversion/processing enable to solve the problem if it does not take into account a priori information about the recovered velocity profile. It is shown how an a priori assumption about a trend of the profile can essentially reduce the nonuniqueness of the problem. The correspon...