Safe-fail line method: An algorithm to reduce the calculation of complex constraints in design optimization

A rather simple but quite effective algorithm is proposed for reducing the number of calculations of complex constraint functions in optimization problems. A type of monotonicity is used to set up a direct relationship between the design variables and the critical constraints. It can frequently be predicted whether or not the constraints are satisfied at a design point just by checking the variation in the design variables. It can be established in advance that a given constraint function varies with respect to a design variable in one of four ways, and rules can be defined, based on the previous history of function values, whether or not a constraint function needed be evaluated. Trial calculations of a sample of problems suggest typical savings of 40-50%. The procedure is illustrated by stress constraints; but the same method can be used in other types.