LOCAL MONOTONICITY IN OPTIMAL DESIGN.

摘要

In design optimization, there usually exists a large number of inequality constraints, many of them satisfied as equalities at the optimum (active). The method of monotonicity was developed to identify these active constraints analytically and globally. The analytical approach may be inhibited by the need for extensive algebraic manipulations and a computational implementation of the method is desirable.; A monotonicity-based strategy for selecting active constraints in a constrained nonlinear design optimization problem is implemented computationally. The concept of local monotonicity is introduced as the basis for iterating on the active set. A prototype algorithm is developed utilizing a local monotonicity strategy, constrained derivatives, and descent-type techniques such as gradient and Golden-Section. The algorithm (called ACCME, for Automated Constraint Criticality by Monotonicity Evaluations) is applied to several demonstration examples as well as five engineering design problems, namely, helical compression spring, ride-ring for rotary kilns, passive vehicle suspension, gear reducer, and flywheel for a punch-press. For these problems the results are compared with those obtained from global monotonicity analysis. The algorithm is also tested on a set of 40 test problems with different mathematical forms from the collection of Hock and Schittkowski {lcub}25{rcub}. Although the algorithm in its current form needs numerical refinements, the test results are judged to be fairly competitive with the other techniques tested, i.e., generalized reduced gradient and sequential quadratic programming.; A strategy for constraint activity identification that couples the local algorithm with global information possibly available for a given problem, is also implemented. This information may be provided by global monotonicity analysis or a design expert. The strategy is a first attempt towards development of iteration procedures for optimal design which may use knowledge or information other than the one provided by traditional local calculations.