| Random search techniques have been applied to the optimization of a number of chemical process problems. These procedures have been demonstrated to be highly successful in solving these large, heavily constrained problems. The efficiency of the algorithms, although better when compared with other techniques on these complicated problems, is low and is an impediment to industrial applications.This procedure searches for improvements in the objective function by sampling from a probability distribution of possible values of each independent variables. The shape of the distribution, and, hence, the step size, is controlled by the rate of progress in improving the objective function.A new algorithm, termed the Adaptive Randomly Directed Search, ARDS, has been developed to improve the efficiency of the ARS. This technique randomly searches for improvements in the objective function from the surface of an n-dimensional ellipsoid centered about the current best search point.The axes of the n-dimensional allipsoid are the ranges of the independent variables. The ranges, and thus the size of the ellipsoid, are decreased as the search progresses to maintain a satisfactory ratio of improved search points to function evaluations. The algorithm repeats steps in a successful direction. It also reverses an unsuccessful step, since the probability of this step improving the objective function is greater than another random move.The Adaptive Random Search, ARS, has been demonstrated to be effective in solving complicated process optimization problems.This paper describes the function of the ARDS, and the method is applied to the solution of several example process optimization problems from the literature. The efficiency is compared with established methods used to solve these same problems. The ARDS shows improvements of up to 80 percent fewer function evaluations in reaching 0.1 percent of the optimum for these problems.Finally, the ARDS and ARS are used to optimize the maleic anhydride process. The ARDS requires 63 percent fewer function evaluations to reach 1 percent of the optimum and converged to this limit for all starting points used. The ARS converges for only 67 percent of the starting points. The optimization shows an improvement from 19.6 percent to 27.1 percent in the process return on investment. |
