Modified genetic algorithm using Box Complex method: Application to optimal control problems

Abstract

Genetic algorithm (GA) is a popular stochastic optimization technique for past couple of decades and has been successfully applied to numerous applications of single and multi-objective optimization problems. Various modifications in GA are proposed in open literature to increase convergence rate and probability of obtaining global minimum by increasing population diversity. Box Complex is a gradient free optimization method having good convergence property. To enhance convergence property of GA, we in this work propose an extension of GA by combining the global search property of GA with a convergence property of Box Complex method. We add one or more population members created by Box Complex method using the current population and replace the equal number of worst population members every generation. A comparison study of the proposed GA with conventional GA and widely accepted jumping gene GA (JG GA) is presented in this work. We have considered two benchmark optimization functions, namely Rosenbrock's and Ackley's Path function. We also carry out the comparison of GAs for three optimal control problems. One of them is the maximization of product concentration with multiple reactions in a batch reactor. Minimization of the off-spec product during product grade transition in a polymerization reactor is considered as the second optimal control problem. The third test application is optimal control of a non-isothermal plug flow reactor.There are two user defined parameters in the proposed algorithm, namely number of Box Complex Members (BCM), and expansion/contraction factor α. Effect of both these parameters on the convergence profile have been presented in this work for the proposed GA. A statistical summary of ten simulation runs for the proposed GA, JG GA, and conventional GA has been discussed for each of the five applications.