Optimal design with the aid of randomization methods

Many design problems can be formulated in terms of a number of nonlinear equations and inequalities. A solution of such equations is called a design. In the present paper a method is given for the random generation of a large number of designs, which can be ordered according to some criterion. Using highspeed computer calculation, a large number of random designs is generated from which the designer can make a choice. A trend in selecting certain designs can be imposed: A requirement can be optimized or an optimal compromise between two or more conflicting requirements can be determined. An arbitrary number of variables can be specified. An interactive program has been written and implemented on a number of interactive computer graphics systems. Using the graphic functions, search areas in which the optimum is expected to lie can be modified interactively, thus increasing the speed of convergence. Information about the equations can be given either interactively or in a file, therefore equations can be given either interactively or in a file, therefore relieving the user from the task of programming. The program has been applied to the design of gear pairs, steam condensors, and bearings.