Optimization technique based on learning automata

Optimization techniques are finding increasingly numerous applications in process design, in parallel to the increase of computer sophistication. The process synthesis problem can be stated as a largescale constrained optimization problem involving numerous local optima and presenting a nonlinear and nonconvex character. To solve this kind of problem, the classical optimization methods can lead to analytical and numerical difficulties. This paper describes the feasibility of an optimization technique based on learning systems which can take into consideration all the prior information concerning the process to be optimized and improve their behavior with time. This information generally occurs in a very complex analytical, empirical, or know-how form. Computer simulations related to chemical engineering problems (benzene chlorination, distillation sequence) and numerical examples are presented. The results illustrate both the performance and the implementation simplicity of this method.Nomenclature c _i penalty probability - cp precision parameter on constraints - D variation domain of the variablex - f(·) objective function - g(·) constraints - i,j indexes - k iteration number - N number of actions - P probability distribution vector - p _i ith component of the vectorP as iterationk - r number of reactors in the flowsheet - u(k) discrete value or action chosen by the algorithm at iterationk - u _i discrete value of the optimization variable in u _min,u _max] - u _min lowest value of the optimization variable - u _max largest value of the optimization variable - Z random number - x variable for the criterion function - xp precision parameter on criterion function - W(k) performance index unit output at iterationk - ₀, ₁ reinforcement scheme parameters - _p sum of the probability distribution vector components