Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems

In this article, a hybrid global–local optimization algorithm is proposed to solve continuous engineering optimization problems. In the proposed algorithm, the harmony search (HS) algorithm is used as a global-search method and hybridized with a spreadsheet ‘Solver’ to improve the results of the HS algorithm. With this purpose, the hybrid HS–Solver algorithm has been proposed. In order to test the performance of the proposed hybrid HS–Solver algorithm, several unconstrained, constrained, and structural-engineering optimization problems have been solved and their results are compared with other deterministic and stochastic solution methods. Also, an empirical study has been carried out to test the performance of the proposed hybrid HS–Solver algorithm for different sets of HS solution parameters. Identified results showed that the hybrid HS–Solver algorithm requires fewer iterations and gives more effective results than other deterministic and stochastic solution algorithms.

[1]  Lynne Stokes,et al.  Using spreadsheet solvers in sample design , 2004, Comput. Stat. Data Anal..

[2]  N. Stander,et al.  On the robustness and efficiency of the SAM algorithm for structural optimization , 1995 .

[3]  James R. Wilson,et al.  Empirical Investigation of the Benefits of Partial Lamarckianism , 1997, Evolutionary Computation.

[4]  M. Tamer Ayvaz,et al.  Groundwater Parameter Estimation by Optimization and Dual Reciprocity Finite Differences Method , 2005 .

[5]  Özgür Yeniay,et al.  A comparative study on optimization methods for the constrained nonlinear programming problems. , 2005 .

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

[7]  Jiaping Yang,et al.  Structural Optimization by Genetic Algorithms with Tournament Selection , 1997 .

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

[9]  F. Glover.  HEURISTICS FOR INTEGER PROGRAMMING USING SURROGATE CONSTRAINTS , 1977 .

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

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

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

[13]  Chee Kiong Soh,et al.  Fuzzy Controlled Genetic Algorithm Search for Shape Optimization , 1996 .

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

[15]  Z. Michalewicz.  Genetic Algorithms , Numerical Optimization , and Constraints , 1995 .

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

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

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

[19]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

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

[21]  G. Di Caro,et al.  Ant colony optimization: a new meta-heuristic , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[22]  Z. Geem,et al.  PARAMETER ESTIMATION OF THE NONLINEAR MUSKINGUM MODEL USING HARMONY SEARCH 1 , 2001 .

[23]  Mehmet Polat Saka,et al.  OPTIMUM DESIGN OF PIN-JOINTED STEEL STRUCTURES WITH PRACTICAL APPLICATIONS , 1990 .

[24]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

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

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

[27]  William Prager,et al.  OPTIMAL STRUCTURAL DESIGN. , 1970 .

[28]  R. G. Fenton,et al.  A Comparison of Numerical Optimization Methods for Engineering Design , 1974 .

[29]  Mehmet Polat Saka,et al.  Optimum design of steel sway frames to BS5950 using harmony search algorithm , 2009 .

[30]  David E. Goldberg,et al.  A self adaptive hybrid genetic algorithm , 2001 .

[31]  Christopher R. Houck,et al.  Comparison of genetic algorithms, random restart and two-opt switching for solving large location-allocation problems , 1996, Comput. Oper. Res..

[32]  Makoto Ohsaki.  Configuration Optimization of Trusses , 2010 .

[33]  Z. Geem.  Optimal Design of Water Distribution Networks Using Harmony Search , 2009 .

[34]  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).

[35]  Halim Ceylan,et al.  Transport energy modeling with meta-heuristic harmony search algorithm, an application to Turkey , 2008 .

[36]  M. Mahdavi,et al.  ARTICLE IN PRESS Available online at www.sciencedirect.com , 2007 .

[37]  G. McCormick,et al.  Selected applications of nonlinear programming , 1968 .

[38]  Xi Chen,et al.  A combined global and local search method to deal with constrained optimization for continuous tabu search , 2008 .

[39]  John Holland,et al.  Adaptation in Natural and Artificial Sys-tems: An Introductory Analysis with Applications to Biology , 1975 .

[40]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[41]  David B. Fogel,et al.  A Comparison of Evolutionary Programming and Genetic Algorithms on Selected Constrained Optimization Problems , 1995, Simul..

[42]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[43]  Woo-seok Jang,et al.  Hybrid Simplex-Harmony search method for optimization problems , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[44]  M. Tamer Ayvaz,et al.  Simultaneous determination of aquifer parameters and zone structures with fuzzy c-means clustering and meta-heuristic harmony search algorithm , 2007 .

[45]  J. F. Price,et al.  On descent from local minima , 1971 .

[46]  Eugénio C. Ferreira,et al.  Can spreadsheet solvers solve demanding optimization problems? , 2001, Comput. Appl. Eng. Educ..

[47]  Reed Jacobson.  Microsoft Excel Visual Basic for applications step by step (version 5 for the Macintosh) , 1994 .

[48]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

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

[50]  K. Lee,et al.  A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice , 2005 .

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

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

[53]  R. Belew,et al.  Evolutionary algorithms with local search for combinatorial optimization , 1998 .

[54]  Erwie Zahara,et al.  Solving constrained optimization problems with hybrid particle swarm optimization , 2008 .

[55]  Leon S. Lasdon,et al.  Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming , 1978, TOMS.

[56]  Linet Özdamar,et al.  Investigating a hybrid simulated annealing and local search algorithm for constrained optimization , 2008, Eur. J. Oper. Res..

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