Computerized Approach to a Multivariable, Constrained, Nonlinear OptimizationBlending Problem Using a Monte Carlo Simulation

摘要

This design project dealt with a blending problem in the format of amultivariable, constrained, nonlinear optimization problem, where a typical application of this problem may be an incinerator that burns waste. The incinerator accepts a blend of several sources, each of which has particular characteristics in terms of thermal output. Should the different sources be inappropriately blended, it could result in a safety hazard for the entire incinerator. The problem is to determine the appropriate proportions so that the maximum value of thermal output for the blend is minimized. The maximum value will be approximated by the mean of the blend plus a selected number standard deviations. The first phase of the project was a brief study of similar blending problems by searching relevant literature. It was found that very little has been done on this problem in terms of computer implementation for industry. Secondly, various possible methods for solving the blending problem were considered. Among these methods were classical calculus, gradient searches, exhaustive searches, and iterative direct searching. An extension of an iterative direct search is a Monte Carlo simulation, where a statistical approach is taken. The Monte Carlo search method is based on the theory that the optimization problem has a distribution of answers and that a random sample of those answers will yield an answer in the lower tail to within a certain degree of accuracy. Then, the feasible region of answers will be halved and another random sample of possible answers will be taken. The search proceeds in this manner, taking random samples from an ever-decreasing region of feasible answers. The method focuses on the optimal answer. The third aspect of the project was implementing the Monte Carlo method in computer code.