Hybrid Algorithm of Harmony Search, Particle Swarm and Ant Colony for Structural Design Optimization

Abstract

This chapter considers the implementation of the heuristic particle swarm ant colony optimization (HPSACO) methodology to find an optimum design of different types of structures. HPSACO is an efficient hybridized approach based on the harmony search scheme, particle swarm optimizer, and ant colony optimization. HPSACO utilizes a particle swarm optimization with a passive congregation algorithm as a global search, and the idea of ant colony approach worked as a local search. The harmony search-based mechanism is used to handle the variable constraints. In the discrete HPSACO, agents are allowed to select discrete values from the permissible list of cross sections. The efficiency of the HPSACO algorithm is investigated to find an optimum design of truss structures with continuous or discrete search domains and for frame structures with a discrete search domain. The results indicate that the HPSACO is a quite effective algorithm to find the optimum solution of structural optimization problems with continuous or discrete variables. 160A. Kaveh and S. Talatahari does not necessarily correspond to the global optimum or even the neighborhood of it, in some cases.The computational drawbacks of classical numerical methods have forced researchers to rely on heuristic algorithms such as genetic algorithms (GAs), particle swarm optimizer (PSO), ant colony optimization (ACO) and harmony search (HS). These methods have attracted a great deal of attention, because of their high potential for modeling engineering problems in environments which have been resistant to a solution by classic techniques. They do not require gradient information and possess better global search abilities than the conventional optimization algorithms. Although these are approximate methods (i.e. their solutions are good, but not provably optimal), they do not require the derivatives of the objective function and constraints [3]. Having in common the processes 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 utilized to encode the candidates, the type of alterations used to create new solutions, and the mechanism employed for selecting new patterns.The genetic algorithm is one of the heuristic algorithms initially suggested by Holland, and developed and extended by some of his students, Goldberg and De Jong. These algorithms simulate a natural genetics mechanism for synthetic systems based on operators that are duplicates of natural ones. In the last decade, GA has been used in the optimum structural design. One of the first applications was the weight minimization of a 10-bar truss by Goldberg and Samtani [4]. Also, many researchers have used genetic search in the design of various structures in which the search space was non-convex or discrete, Hajela [5], Rajeev and Krishnamoorthy [6,7], Koumousis and Georgious [8], Hajela and Lee [9], Wu and Chow [10], Soh and...

Imperialist Competitive Algorithm

“…The configuration and applied loads of a three-bay fifty-story frame structure [5] is shown in Fig. 11.5.…”

“…This can be expressed as where {x} is the set of design variables; ng is the number of member groups in structure (number of design variables); D i is the allowable set of values for the design variable x i ; W({x}) presents weight of the structure; nm is the number of members of the structure; ρ i denotes the material density of member i; L i and x i are the length and the cross-sectional of member i, respectively; g j ({x}) denotes design constraints; and n is the number of the constraints. D i can be considered either as a continuous set or as a discrete one [5]. In the continuous problems, the design variables can vary continuously in the optimization process…”

A new meta-heuristic algorithm: vibrating particles system

“…The proposed method yields the least weight for this example, which is 86,985 lb. The other design weights are 95,850 lb by HPSACO (a hybrid algorithm of harmony search, particle swarm, and ant colony) [33], 97,689 lb by HBB-BC (a hybrid big bang-big crunch optimization) [34], 93,846 lb by ICA (Imperialist Competitive Algorithm) [35], 92,723 lb by CSS [36], 86,986 lb by ECBO [37], 93,315 lb by ES-DE (Eagle Strategy with Di erential Evolution) [38], and 91,248 lb by DSOS (Discrete Symbiotic Organisms Search) [39]. The best design of VPS has been achieved in 19,600 analyses.…”

Accelerated Particle Swarm for Optimum Design of Frame Structures

“…The optimum designs for PSO [18], HBB-BC [33], and ICA [34] had the weights of 496.68 kN, 434.54 kN, and 417.46 kN, respectively. Table 2 summarizes the optimal results for these different algorithms.…”