LAGRANGEAN RELAXATION AND SUBGRADIENT OPTIMIZATION APPLIED TO OPTIMAL DESIGN WITH DISCRETE SIZING

Abstract

The discrete sizing problem in optimal design is adressed. Lagrangean dual approaches earlier published are briefly reviewed and it is noted that quite sophisticated procedures have been used to solve the dual problems. The simple concept of Lagrangean relaxation combined with subgradient optimization and Lagrangean heuristics has, however, not been applied to the discrete sizing problem. In this paper a scheme based on this concept is described and tested on some small problems. The results indicate that subgradient optimization is completely capable of solving the dual problem. Moreover it is possible to devise heuristics that construct feasible solutions to the original problem, using the Lagrangean subproblem solution.

KEY WORDS:

• Lagrangean duality
• subgradient optimization
• optimal design
• discrete variables
• structural optimization