Hybrid Genetic Algorithm and Particle Swarm Optimization for the Force Method-Based Simultaneous Analysis and Design

Hybrid genetic algorithm and particle swarm optimization for

the force method-based simultaneous analysis and design

A. Kaveh*

Institute for Mechanics of Materials and Structures, Vienna University of Technology,

Karlsplatz 13, A-1040 Wien, Austria

S. Malakouti Rad

Department of Civil Engineering, Iran University of Science and Technology, Tehran-16,

Iran

Abstract

The computational drawbacks of existing numerical methods have forced researchers to

rely on heuristic algorithms. Heuristic methods are powerful in obtaining the solution of

optimization problems. Although they are approximate methods (i.e. their solution are

good, but not probably optimal), they do not require the derivatives of the objective

function and constraints. Also, they use probabilistic transition rules instead of

deterministic rules. Here, an evolutionary algorithm based on the hybrid genetic

algorithm (GA) and particle swarm optimization (PSO), denoted by HGAPSO, is

developed in order to solve force method based simultaneous analysis and design

problems for frame structures. Suitability of the developed hybrid algorithm HGAPSO is

compared to both GA and PSO for all the design examples, demonstrating its efficiency

and superiority especially for frames with larger number of redundant forces.

Keywords Simultaneous analysis and design, force method, frames, hybrid, genetic

algorithm, particle swarm optimization.

1. Introduction

In the structural optimization literature, the simultaneous analysis and design (SAND)

formulation is a major class of alternative formulations that has been discussed since the

1960s. In this approach, the state and design variables are treated simultaneously as

optimization variables. The analysis equations become an equality constraint in terms of

the variables. SAND basically formulates the optimization problem in a mixed space of

design and state variables to imbed the analysis equations in one single optimization

problem. Therefore no...