Particle Swarm Optimization in Structural Design

Optimization techniques play an important role as a useful decision making tool in the design of structures. By deriving the maximum benefits from the available resources, it enables the construction of lighter, more efficient structures while maintaining adequate levels of safety and reliability. A large number of optimization techniques have been suggested over the past decades to solve the inherently complex problem posed in structural design. Their scope varies widely depending on the type of stru ctural problem to be tackled. Gradient-based methods, for example, are highly effectively in finding local optima when the design space is convex and continuous and when the design problem involves large number of design variables and constraints. If the problem constraints and objective function are convex in nature, then it is possible to conclude that the local optimum will be a global optimum. In most structural problems, however, it is practically impossible to check the convexity of the design space, therefore assuring an obtained optimum is the best possible among multiple feasible solutions. Global non-gradient-based methods are able to traverse along highly non-linear, non-convex design spaces and find the best global solutions. In this category many unconstrained optimization algorithms have been developed by mimicking natural phenomena such as Simulated Annealing (Kirkpatrick et al., 1983), Genetic Algorithms (Goldberg, 1989), and Bacterial Foraging (Passino, 2002) among others. Recently, a new family of more efficient global optimization algorithms have been developed which are better posed to handle constraints. They are based on the simulation of social interactions among members of a specific species looking for food sources. From this family of optimizers, the two most promising algorithms, which are the subject of this book, are Ant Colony Optimization (Dorigo, 1986), and Particle Swarm Optimization or PSO. In this chapter, we present the analysis, implementation, and improvement strategies of a particle swarm optimization suitable for constraint optimization tasks. We illu strate the functionality and effectiveness of this algorithm, and explore the effect of the different PSO setting parameters in the scope of classical structural optimization problems.

[1]  S. Wu,et al.  Steady-state genetic algorithms for discrete optimization of trusses , 1995 .

[2]  M. El-Sayed,et al.  Structural optimization using unconstrained nonlinear goal programming algorithm , 1994 .

[3]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[4]  P. Fourie,et al.  The particle swarm optimization algorithm in size and shape optimization , 2002 .

[5]  V. Venkayya.  Design of optimum structures , 1971 .

[6]  M. A. Abido.  Optimal des'ign of Power System Stabilizers Using Particle Swarm Opt'imization , 2002, IEEE Power Engineering Review.

[7]  Carlos A. Coello Coello,et al.  Use of Particle Swarm Optimization to Design Combinational Logic Circuits , 2003, ICES.

[8]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[9]  Philip E. Gill,et al.  Practical optimization , 1981 .

[10]  O. Weck,et al.  A COMPARISON OF PARTICLE SWARM OPTIMIZATION AND THE GENETIC ALGORITHM , 2005 .

[11]  Paulo Rizzi,et al.  Optimization of multi-constrained structures based on optimality criteria , 1976 .

[12]  M. A. Abido,et al.  Optimal power flow using particle swarm optimization , 2002 .

[13]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[14]  L. Schmit,et al.  Some Approximation Concepts for Structural Synthesis , 1974 .

[15]  A Kaveh,et al.  ENGINEERING OPTIMIZATION WITH HYBRID PARTICLE SWARM AND ANT COLONY OPTIMIZATION , 2009 .

[16]  O. Hasançebi,et al.  Optimal design of planar and space structures with genetic algorithms , 2000 .

[17]  R. Eberhart,et al.  Comparing inertia weights and constriction factors in particle swarm optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[18]  M. W. Dobbs,et al.  Application of optimality criteria to automated structural design , 1976 .

[19]  Hojjat Adeli,et al.  Efficient optimization of plane trusses , 1991 .

[20]  L. A. Schmit,et al.  Discrete-continuous variable structural synthesis using dual methods , 1980 .

[21]  Lin Wang,et al.  Multidisciplinary optimization of a butterfly valve. , 2009, ISA transactions.

[22]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[23]  A. Belegundu,et al.  Trust region methods for structural optimization using exact second order sensitivity , 1991 .

[24]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[25]  M. Galante,et al.  Structures optimization by a simple genetic algorithm. , 1992 .

[26]  R. A. Gellatly,et al.  Optimal Structural Design. , 1971 .

[27]  Jaroslaw Sobieszczanski-Sobieski,et al.  Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization , 2002 .

[28]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[29]  L. A. Schmit,et al.  A new structural analysis/synthesis capability - ACCESS , 1975 .

[30]  Andries Petrus Engelbrecht,et al.  A study of particle swarm optimization particle trajectories , 2006, Inf. Sci..

[31]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[32]  Liyan Zhang,et al.  Robust PID controller design using particle swarm optimizer , 2003, Proceedings of the 2003 IEEE International Symposium on Intelligent Control.

[33]  Du Ming-zhu,et al.  An improved Templeman's algorithm for the optimum design of trusses with discrete member sizes , 1986 .

[34]  L. A. Schmit,et al.  Some approximation concepts for structural synthesis , 1973 .

[35]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[36]  E. Hinton,et al.  Optimization of trusses using genetic algorithms for discrete and continuous variables , 1999 .

[37]  Peter Eberhard,et al.  Constrained Particle Swarm Optimization of Mechanical Systems , 2005 .

[38]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[39]  George I. N. Rozvany,et al.  DCOC: An optimality criteria method for large systems Part I: theory , 1992 .

[40]  Kevin M. Passino,et al.  Biomimicry of bacterial foraging for distributed optimization and control , 2002 .

[41]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[42]  R. Eberhart,et al.  Empirical study of particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).