NEURAL NETWORK BASED APPROACH FOR OPTIMIZATION

Abstract

Optimization concerns the minimization or maximization of functions. These objective functions may be formulated from technical and/or economic viewpoint. In the optimization problem many a times independent variables should satisfy various equality and/or inequality constraints. In chemical engineering, processes are highly non-linear with constraints arising from safety considerations, process limitations etc., which leads to non-linear constrained optimization problem. There are number of methods for solving non-linear constrained optimization problems. These methods can be divided into two broad categories: Classical methods like gradient search and direct search; and Non classical methods like genetic algorithms and ANN etc. Although ANN is being used for optimization in other engineering fields like Electronics/Electrical etc. and to be more specific in analog VLSI technologies and electrooptics. Relatively a few studies available in optimization, which is specifically concerned with ANN based approach for optimization in Chemical engineering field. Neural networks have now becomes focus of attention, largely because it can easily handle complex and non-linear problems which contains imprecise or noisy data. For model development, it does not require the prior knowledge of process and physics associated with it thus poorly understood systems can also be modeled with ease. The only requirement is considerable number of input/output data sets. To study the applicability of ANN based approach for non-linear constrained optimization a number of mathematical as well as Chemical engineering problems has been selected through literature survey. In all six problems, two mathematical and four chemical engineering were chosen. MATLAB environment with its Neural network and Optimization toolbox, is used for ANN modeling and then optimization of selected problems respectively. To compare the efficiency of ANN based approach, the same problems were solved by conventional approach. Function "constr", which is nonlinear constrained optimizer of MATLAB optimization toolbox is used for optimization in conventional mathematical model based approach. For ANN based approach, first the mathematical objective function is replaced by its equivalent ANN model then this ANN model is used in a modified nonlinear constrained optimizer of MATLAB optimization toolbox named function "opti" to optimize the problem. This study successfully demonstrated the use of ANN based approach for optimizing mathematical is well as Chemical engineering problems. ANN based approach has shown edge over conventional approach both in terms of time required and number of function evaluation needed for optimization of Chemical engineering problems. It has been noted in this present work that number of function evaluation needed to converge at optimum depends upon choice of initial guess of decision variables. Further it is also observed that ANN model takes less time in computing objective functions than that required in conventional approach. The limitation of this present work is that MATLAB optimizer may some time give local solutions, which obviously can be overcome by running the optimizer with several initial guesses of decision variables. ii