Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures

Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures

Abstract

A heuristic particle swarm ant colony optimization (HPSACO) is presented for optimum design of trusses. The algorithm is based on the particle swarm optimizer with passive congregation (PSOPC), ant colony optimization and harmony search scheme. HPSACO applies PSOPC for global optimization and the ant colony approach is used to update positions of particles to attain the feasible solution space. HPSACO handles the problem-specific constraints using a fly-back mechanism, and harmony search scheme deals with variable constraints. Results demonstrate the efficiency and robustness of HPSACO, which performs better than the other PSO-based algorithms having higher converges rate than PSO and PSOPC.

Introduction

In the last decade, many new natural evolutionary algorithms have been developed for optimization of pin-connected tructures, such as genetic algorithms (GAs) [1–5], particle swarm optimizer (PSO) [6,7], ant colony optimization (ACO) [8–10] and harmony
search (HS) [11–13]. These methods have attracted a great deal of attention, because of their high potential for modeling engineer- ing problems in environments which have been resistant to solu- tion by classic techniques. They do not require gradient information and possess better global search abilities than the con- ventional optimization algorithms [14]. Having in common pro- cesses of natural evolution, these algorithms share many similarities: each maintains a population of solutions which are evolved through random alterations and selection. The differences between these procedures lie in the representation technique uti- lized to encode the candidates, the type of alterations used to cre- ate new solutions, and the mechanism employed for selecting new patterns.

Compared to other evolutionary algorithms based on heuristics including evolutionary algorithms (EAs), evolutionary program-ming (EP) and evolution strategies (ES) [15], the advantages of PSO consist of easy implementation and smaller number of parameters to be adjusted. However, it is known that the original PSO (or SPSO) had difficulties in controlling the balance between exploration (global investigation of the search place) and exploita-tion (the fine search around a local optimum) [16]. In order to im-prove this character of PSO, it is hybridized with other approaches such as ACO or HS. PSACO (a hybrid particle swarm optimizer and ant colony approach) which was initially introduced by Shelokar et al. [17] for the solution of the continuous unconstrained prob-lems and recently utilized for truss structures [18], is applied to PSO as a global search technique and the idea of ant colony ap- proach is incorporated as a local search for updating the positions of the particles by applied pheromone-guided mechanism. HPSO (a hybrid particle swarm optimizer and harmony search scheme) was proposed by Li et al. [7] for truss design employed the har- mony memory (HM) operator for controlling the variable constraints.

The present paper hybridizes PSO, ACO and HS, and it is based on the principles of those two methods with some differences. We have applied PSOPC (a hybrid PSO with passive congregation [19]) instead of PSO to improve the performance of the new meth-od. The relation of standard deviation in ACO stage is different with that of Ref. [17], and the inertia weight is changed in PSOPC stage. New terminating criterion is employed to increase the probability of obtaining an optimum solution in a smaller number of itera- tions. In the proposed method, similar to HPSO, HS is utilized for controlling the variable constraint. The resulted method has a good control on the exploration and exploitation compared to PSO and PSOPC. It increases the exploitation, and guides the exploration, and as a result, the convergence rate of the proposed algorithm is higher than other heuristic approaches.

There are some problem-specific constraints in truss optimiza-tion problems that must be handled. The penalty function method has been the most popular constraint-handling technique due to its simple principle and ease of implementation. The main diffi-culty of the penalty function method lies in that the appropriate values of penalty factors are problem-dependent and a large amount of effort is needed for fine-tuning of the penalty factors. Therefore, several techniques have been incorporated to handle the constraints. Compared to other constraint-handling tech-niques, fly-back mechanism is relatively simple and easy to
implement into the PSO [7]. Therefore, this paper handles the problem-specific constraints by using this mechanism.

The present paper is organized as follows: In Section 2, we de-scribe the PSO, ACO and HS. Statement of the optimization design problemis formulated in Section 3. In Section 4, the fly-backmech-anism is described. In Section 5, the new method is presented. Var-ious examples are studied in Section 6. The efficiency of HPSACO is investigated in Section 7. Conclusions are derived in Section 8.

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