Keywords: truss structures, weight minimization, big bang-big crunch, infrequent explosions, line search.

In sizing optimization of truss structures, structural weight is minimized under constraints on nodal displacements, member stresses, critical buckling loads, natural frequencies, etc. A variety of metaheuristic optimization methods inspired by biology, evolution theory, social sciences, music, physics and astronomy have been developed in purpose of rationalizing the search process [1,2]. Metaheuristic algorithms generate new trial designs by following a random search strategy (i.e. global search) which is however "guided" by the inspiring criterion.

Among the most recently developed metaheuristic optimization methods, Big Bang-Big Crunch (BB-BC) [3] seems to be the best formulated algorithm also in view of the relatively small amount of heuristics entailed by the optimization process. The BB-BC algorithm reproduces the process of evolution of the universe. In the optimization, a set of designs is randomly generated and their centre of mass is determined as a weighted average where each weighing coefficient depends on the value of cost function evaluated at a trial design. A new population is hence randomly generated by perturbing optimization variables in the neighbourhood of the centre of mass. This sequence is repeated until convergence to an optimum is achieved.

The inherent simplicity of BB-BC soon attracted structural optimization experts. However, classical BB-BC formulations [4,5,6] require a huge number of structural analyses to complete the optimization process. In order to overcome this limitation, an improved BB-BC algorithm is presented in this paper. Each new trial design is generated so to lie on a descent direction and a new explosion is performed only if the current generation is rated unsuccessful.

The new BB-BC algorithm described in this paper is tested in four classical sizing optimization problems of truss structures with up to 200 elements and 29 design variables. Optimization results fully demonstrate the efficiency of the proposed BB-BC algorithm with respect to classical BB-BC implementations and other state-of-the-art metaheuristic optimization algorithms.

1

M.P. Saka, "Optimum Design of Steel Frames using Stochastic Search Techniques Based on Natural Phenomena: A Review", in B.H.V. Topping, (Editor), "Civil Engineering Computations: Tools and Techniques", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 6, 105-147, 2007. doi:10.4203/csets.16.6

2

O. Hasancebi, S. Carbas, E. Dogan, F. Erdal, M.P. Saka, "Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures", Computers and Structures, 87, 284-302, 2009. doi:10.1016/j.compstruc.2009.01.002

3

O.K. Erol, I. Eksin, "New optimization method: Big Bang-Big Crunch", Advances in Engineering Software, 37, 106-111, 2006. doi:10.1016/j.advengsoft.2005.04.005

4

C.V. Camp, "Design of space trusses using Big Bang-Big Crunch optimization", ASCE Journal of Structural Engineering, 133, 999-1008, 2007. doi:10.1061/(ASCE)0733-9445(2007)133:7(999)

5

A. Kaveh, S. Talatahari, "Size optimization of space trusses using Big Bang-Big Crunch algorithm", Computers and Structures 87, 1129-1140, 2009. doi:10.1016/j.compstruc.2009.04.011

6

A. Kaveh, S. Talatahari, "Optimal design of Schwedler and ribbed domes via hybrid Big Bang-Big Crunch algorithm", Journal of Constructional Steel Research, 66, 412-419, 2010. doi:10.1016/j.jcsr.2009.10.013

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