Nonlinear computer program for Mugele's method

This paper presents an analysis of the “Directed Step” or “PROBE and EDGE” program for optimal control of nonlinear processes, as described by its author, R.A. Mugele (1)(2). Fortran IV code of the algorithm was developed and tested with a multicell wide beam subjected to flexural bending. Prior to the main program, a subroutine randomly samples the space between the predetermined bounds and generates a feasible starting point. The main program is based on a univariant alteration of a hypervector, in the positive and negative direction, that seeks improvement of the merit function and is subject to constraints. The considered structural element exhibits a merit function and constraints that are nonlinear, with the multiple intersection of the hypersurfaces that generate various local optimum conditions. The program was compared with the Montecarlo (3) search scheme and proved to be three and one half times faster in converging to the optimums for the different initial conditions. Typical running times for PROBE and EDGE were in the order of 0. 43 minutes while Montecarlo averaged 1. 61 minutes; nevertheless there was no reliability in the results because many local optimums were found, while Montecarlo always converged to the global optimum. The PROBE and EDGE program may be feasible in nonlinear space with few local optimums and well conditioned functions.