An optimization algorithm for structured design systems

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Abstract
Structured design systems are systems which may be represented by generally nonlinear equality and inequality constraints, each of which contains few of the variables in the system. Assuming the existence of an automatic capabity to derive and modify as needed effective solution procedures for sets of structured equality constraints, a two‐step strategy for optimizing design systems is presented in the form of two algorithms. An earlier paper presented an algorithm for locating a first feasible point, and this paper presents a companion algorithm based on the strategy known as restriction to optimize the system once feasible.This companion algorithm divides the set of inequality constraints into three sets: the set of those currently being held as equality constraints, the set currently released but being used as search coordinates, and the set of all remaining constraints which are not currently part of the problem. Solution procedures are modified as inequality constraints and are moved from one set to another. Added constraints in the set being held tend to aid the optimization process by reducing the dimension of search space for what is usually a marginal added burden in solving an enlarged set of (structured) equations.The strategy has proved remarkably effective on three relatively simple examples, including a nonlinear 31 constraint, 10 variable alkylation problem.