The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.

[1]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[2]  Robert D. Logcher,et al.  Automated Optimum Design from Discrete Components , 1970 .

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

[4]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[5]  L. Schmit,et al.  Approximation concepts for efficient structural synthesis , 1976 .

[6]  W. A. Thornton,et al.  A New Optimality Criterion Method for Large Scale Structures. , 1979 .

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

[8]  J. Felix,et al.  Shape optimization of trusses subject to strength, displacement, and frequency constraints. , 1981 .

[9]  Judith S. Liebman,et al.  Discrete Structural Optimization , 1981 .

[10]  A. W. Westerberg,et al.  Application of a Reduced Quadratic Programming Technique to Optimal Structural Design , 1981 .

[11]  D. F. Yates,et al.  A Linear Programming Approach to the Discrete Optimum Design of Trusses , 1982 .

[12]  Hsichun M. Hua.  Optimization for structures of discrete-size elements , 1983 .

[13]  Hojjat Adeli,et al.  Efficient optimization of space trusses , 1986 .

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

[15]  K. G. Sharma,et al.  Minimum weight design of trusses using improved move limit method of sequential linear programming , 1987 .

[16]  Andrew B. Templeman,et al.  Discrete optimum structural design , 1988 .

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

[18]  Garret N. Vanderplaats,et al.  An approximation method for configuration optimization of trusses , 1988 .

[19]  Ulf Ringertz,et al.  ON METHODS FOR DISCRETE STRUCTURAL OPTIMIZATION , 1988 .

[20]  P. Hajela,et al.  GENETIC ALGORITHMS IN OPTIMIZATION PROBLEMS WITH DISCRETE AND INTEGER DESIGN VARIABLES , 1992 .

[21]  S. Rajeev,et al.  Discrete Optimization of Structures Using Genetic Algorithms , 1992 .

[22]  Wang Xi-cheng,et al.  A parallel iterative algorithm for structural optimization , 1992 .

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

[24]  Shyue-Jian Wu,et al.  Integrated discrete and configuration optimization of trusses using genetic algorithms , 1995 .

[25]  M. Galante,et al.  GENETIC ALGORITHMS AS AN APPROACH TO OPTIMIZE REAL‐WORLD TRUSSES , 1996 .

[26]  Hojjat Adeli,et al.  Hybrid CPN–Neural Dynamics Model for Discrete Optimization of Steel Structures , 1996 .

[27]  S Rajeev,et al.  GENETIC ALGORITHMS - BASED METHODOLOGY FOR DESIGN OPTIMIZATION OF TRUSSES , 1997 .

[28]  Shahram Pezeshk,et al.  Optimized Design of Two-Dimensional Structures Using a Genetic Algorithm , 1998 .

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

[30]  Shahram Pezeshk,et al.  Design of Nonlinear Framed Structures Using Genetic Optimization , 2000 .

[31]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[32]  Hyo Seon Park,et al.  Optimization of steel structures using distributed simulated annealing algorithm on a cluster of personal computers , 2002 .

[33]  Zong Woo Geem,et al.  New Methodology, Harmony Search, its Robustness , 2002, GECCO Late Breaking Papers.

[34]  Zong Woo Geem,et al.  Harmony Search Optimization: Application to Pipe Network Design , 2002 .

[35]  Ali Kaveh,et al.  Genetic algorithm for discrete‐sizing optimal design of trusses using the force method , 2002 .

[36]  K. Lee,et al.  A new structural optimization method based on the harmony search algorithm , 2004 .

[37]  Z. Geem.  Optimal cost design of water distribution networks using harmony search , 2006 .