Optimization by signal flow graph method
Five related objectives were realized in this research; 1. A modified linear programming technique was developed. The procedure follows the simplex algorithm, but signal flow graph (SFG) methods rather than matrix manipulations are used. 2. It is shown that all the ordinary post-optimum analysis, including sensitivity analysis, may be performed by the SFG method using the final graph instead of the simplex final tableau. 3. The SFG methods to solve linear equations were used to obtain the gradient vectors of objective functions with equality constraints. 4. The techniques developed in 1 and 2 were incorporated into the method of "feasible direction" (MFD), one of the most powerful methods of constrained optimization. 5. Two large, nonlinear, heat exchanger networks were studied, and the total heat exchanger area was minimized using the MFD in conjunction with the LP system developed. This research points to the possibility that signal flow graph methods can be a useful tool for solving linear and nonlinear constrained optimization problems.