A Multi-swarm Multi-objective Optimization Method for Structural Design

Abstract

In this chapter a multi-objective optimization algorithm is presented and applied to optimal design of large-scale skeletal structures [1]. Optimization is a process in which one seeks to minimize or maximize a function by systematically choosing the values of variables from/within a permissible set. In recent decades, a vast amount of research has been conducted in this field in order to design effective and efficient optimization algorithms. Besides, the application of the existing algorithms to engineering design problems has also been the focus of many studies (Gou et al. [2]; Lee and Geem [3]; Gero et al. [4]). In a vast majority of structural design applications, including previous studies (Kaveh and Talatahari [5]; Kaveh and Talatahari [6]; Kaveh and Talatahari [7]; Kaveh and Rahami [8]), the fitness function was based on a single evaluation criterion. For example, the total weight or total construction cost of a steel structural system has been frequently employed as the evaluation criterion in structural engineering applications. But in the practical optimization problems, usually more than one objective are required to be optimized, such as, minimum mass or cost, maximum stiffness, minimum displacement at specific structural points, maximum natural frequency of free vibration, maximum structural strain energy. This makes it necessary to formulate a multi-objective optimization problem, and look for the set of compromise solutions in the objective space. This set of solutions provides valuable information about all possible designs for the considered engineering problem and guides the designer to make the best decision. The application of multi-objective optimization algorithms to structural problems has attracted the interest of many researchers. For example, in (Mathakari et al. [9]) Genetic algorithm is employed for optimal design of truss structures, or in (Liu et al. [10]) Genetic algorithm is utilized for multi-objective optimization for performance-based seismic design of steel moment frame structures, and in (Paya et al. [11]) the problem of design of RC building frames is formulated as a multi-objective optimization problem and solved by simulated annealing. In all these studies, some well-known multi-objective algorithms have been applied to structural design problems. However, the approach which has attracted the attention of many researchers in recent years is to utilize a high-performance multi-objective optimization algorithm for structural design problems. For example, in (Su et al. [12]) an adaptive multi-island search strategy is incorporated with NSGA-II for solving the truss layout optimization problem, or in (Ohsaki et al. [13]) a hybrid algorithm of simulated annealing and tabu search is used for seismic design of steel frames with standard sections, and in (Omkar et al. [14]) the specific version of particle swarm optimization is utilized to solve design optimization problem of composite structures which is a highly multi-modal optimization problem. These are only three examples of such studies.