Elsevier

Computers & Structures

Volume 87, Issues 17–18, September 2009, Pages 1129-1140
Computers & Structures

Size optimization of space trusses using Big Bang–Big Crunch algorithm

https://doi.org/10.1016/j.compstruc.2009.04.011Get rights and content

Abstract

A Hybrid Big Bang–Big Crunch (HBB–BC) optimization algorithm is employed for optimal design of truss structures. HBB–BC is compared to Big Bang–Big Crunch (BB–BC) method and other optimization methods including Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization and Harmony Search. Numerical results demonstrate the efficiency and robustness of the HBB–BC method compared to other heuristic algorithms.

Introduction

Despite existing major preventive factors in performing optimum design of structures such as the large number of structural required analyses and large computational costs, designers and owners have always desired to have optimal structures. Truss optimization is one of the most active branches of the structural optimization. Size optimization of truss structures involves determining optimum values for member cross-sectional areas, Ai, that minimize the structural weight W. This minimum design should also satisfy the inequality constraints that limit design variable sizes and structural responses. The optimal design of a truss can be formulated as:minimizeW({x})=i=1nγi·Ai·Lisubject to:δminδiδmax,i=1,2,,mσminσiσmax,i=1,2,,nσibσi0,i=1,2,,nsAminAiAmax,i=1,2,,ngwhere W({x}) = weight of the structure; n = number of members making up the structure; m = number of nodes; ns = number of compression elements; ng = number of groups (number of design variables); γi = material density of member i; Li = length of member i; Ai = cross-sectional area of member i chosen between Amin and Amax; min = lower bound and max = upper bound; σi and δi = the stress and nodal deflection, respectively; σib=allowable buckling stress in memberiwhen it is in compression.

In the last decades, different natural evolutionary algorithms have been employed for structural optimization including Genetic Algorithms [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], Simulated Annealing algorithm [16], [17], [18], [19], [20], [21], Ant Colony Optimization [22], [23], [24], [25], [26], [27], [28], [29], Particle Swarm Optimizer [30], [31], [32] and Harmony Search [33], [34], [35]. These are heuristic procedures that incorporate random variation and selection [36], [37], [38], [39], [40], [41], [42]. The random selection and the information obtained in each cycle are used to choose the new points in the subsequent cycles. These algorithms do not require for a given function to be derivable and an explicit relationship between the objective function and constraints is not needed.

A new optimization method relied on one of the theories of the evolution of the universe namely, the Big Bang and Big Crunch theory is introduced by Erol and Eksin [43] which has a low computational time and high convergence speed. According to this theory, in the Big Bang phase energy dissipation produces disorder and randomness is the main feature of this phase; whereas, in the Big Crunch phase, randomly distributed particles are drawn into an order. The Big Bang–Big Crunch (BB–BC) Optimization method similarly generates random points in the Big Bang phase and shrinks these points to a single representative point via a center of mass in the Big Crunch phase. After a number of sequential Big Bangs and Big Crunches where the distribution of randomness within the search space during the Big Bang becomes smaller and smaller about the average point computed during the Big Crunch, the algorithm converges to a solution. The BB–BC method has been shown to outperform the enhanced classical Genetic Algorithm for many benchmark test functions [43].

In this study, a Hybrid Big Bang–Big Crunch optimization (HBB–BC) is implemented to solve the truss optimization problems. The HBB–BC method consists of two phases: a Big Bang phase where candidate solutions are randomly distributed over the search space, and a Big Crunch phase working as a convergence operator where the center of mass is generated. Then new solutions are created by using the center of mass to be used as the next Big Bang. These successive phases are carried repeatedly until a stopping criterion has been met. This algorithm not only considers the center of mass as the average point in the beginning of each Big Bang, but also similar to Particle Swarm Optimization-based approaches [42], utilizes the best position of each particle and the best visited position of all particles. As a result because of increasing the exploration of the algorithm, the performance of the BB–BC approach is improved. Another reformation is to use Sub-Optimization Mechanism (SOM), introduced by Kaveh et al. [28], [29] for ant colony approaches. SOM is based on the principles of finite element method working as a search-space updating technique. Some changes are made to prepare SOM for the HBB–BC algorithm. Numerical simulation based on the HBB–BC method including medium- and large-scaled trusses and comparisons with results obtained by other heuristic approaches demonstrate the effectiveness of the present algorithm. The remainder of this paper is organized as follows. Section 2 presents a brief review of BB–BC, the constraint handing approach, and then the HBB–BC is described. Design examples and comparisons are presented in Section 3. Finally, Section 4 contains the concluding remarks and future works.

Section snippets

Introduction to BB–BC method

The BB–BC method developed by Erol and Eksin [43] consists of two phases: a Big Bang phase, and a Big Crunch phase. In the Big Bang phase, candidate solutions are randomly distributed over the search space. Similar to other evolutionary algorithms, initial solutions are spread all over the search space in a uniform manner in the first Big Bang. Erol and Eksin [43] associated the random nature of the Big Bang to energy dissipation or the transformation from an ordered state (a convergent

Design examples

In this section, five truss structures are optimized utilizing the present method. Then the final results are compared to the solutions of other advanced heuristic methods to demonstrate the efficiency of this work. These optimization examples include:

  • A 25-bar spatial truss structure;

  • A 72-bar spatial truss structure;

  • A 120-bar dome shaped truss;

  • A square on diagonal double-layer grid; and

  • A 26-story-tower spatial truss.

For the proposed algorithm, a population of 50 individuals is used for the

Concluding remarks

In this paper a new heuristic population-based search relied on the Big Bang and Big Crunch theory (BB–BC) of the evolution of the universe is implemented to solve the truss optimization problem. The proposed hybrid BB–BC algorithm considers the combinational of the center of mass, the best position of each candidate and the best visited position of all candidates as an average point in the beginning of each Big Bang. Additional improvement is due to use Sub-Optimization Mechanism (SOM), based

References (49)

  • A. Kaveh et al.

    Structural topology optimization using ant colony methodology

    Eng Struct

    (2008)
  • L.J. Li et al.

    A heuristic particle swarm optimizer for optimization of pin connected structures

    Comput Struct

    (2007)
  • R.E. Perez et al.

    Particle swarm approach for structural design optimization

    Comput Struct

    (2007)
  • K.S. Lee et al.

    A new structural optimization method based on the harmony search algorithm

    Comput Struct

    (2004)
  • M.P. Saka

    Optimum design of steel sway frames to BS5950 using harmony search algorithm

    J Construct Steel Res

    (2009)
  • O.K. Erol et al.

    New optimization method: Big Bang–Big Crunch

    Adv Eng Software

    (2006)
  • A. Kaveh et al.

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

    Comput Struct

    (2009)
  • S. He et al.

    A particle swarm optimizer with passive congregation

    Biosystem

    (2004)
  • S. Rajeev et al.

    Discrete optimization of structures using genetic algorithms

    J Struct Eng, ASCE

    (1992)
  • V.K. Koumousis et al.

    Genetic algorithms in discrete optimization of steel truss roofs

    J Comput Civil Eng, ASCE

    (1994)
  • C.V. Camp et al.

    Optimized design of two dimensional structures using a genetic algorithm

    J Struct Eng, ASCE

    (1998)
  • S.M. Shrestha et al.

    Evolution of optimization structural shapes using genetic algorithm

    J Struct Eng, ASCE

    (1998)
  • A. Kaveh et al.

    Genetic algorithm for discrete sizing optimal design of trusses using the force method

    Int J Numer Methods Eng

    (2002)
  • A. Kaveh et al.

    Topology optimization of trusses using genetic algorithm, force method, and graph theory

    Int J Numer Methods Eng

    (2003)
  • Cited by (332)

    • Termite life cycle optimizer

      2023, Expert Systems with Applications
    View all citing articles on Scopus
    1

    On leave from Iran University of Science and Technology, Narmak, Tehran 16, Iran.

    View full text