Augmented Lagrangian Genetic Algorithm for Structural Optimization

TLDR

Genetic algorithms avoid line searches and derivative calculations for objectives and constraints. This paper introduces a robust hybrid genetic algorithm that optimizes space structures using the augmented Lagrangian method. The hybrid algorithm retains the derivative‑free nature of genetic algorithms and removes trial‑and‑error tuning of penalty coefficients by avoiding arbitrary adjustments. Compared with penalty‑function genetic algorithms, the new method needs only a few extra evaluations, eliminates extensive tuning of penalty coefficients, and is broadly applicable to many optimization problems.

Abstract

This paper presents a robust hybrid genetic algorithm for optimization of space structures using the augmented Lagrangian method. An attractive characteristic of genetic algorithm is that there is no line search and the problem of computation of derivatives of the objective function and constraints is avoided. This feature of genetic algorithms is maintained in the hybrid genetic algorithm presented in this paper. Compared with the penalty function‐based genetic algorithm, only a few additional simple function evaluations are needed in the new algorithm. Furthermore, the trial and error approach for the starting penalty function coefficient and the process of arbitrary adjustments are avoided. There is no need to perform extensive numerical experiments to find a suitable value for the penalty function coefficient for each type or class of optimization problem. The algorithm is general and can be applied to a broad class of optimization problems.