An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design

Abstract

An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one, and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher and Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer/discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.