A shrinking hypersphere PSO for engineering optimisation problems

Many real-world and engineering design problems can be formulated as constrained optimisation problems (COPs). Swarm intelligence techniques are a good approach to solve COPs. In this paper an efficient shrinking hypersphere-based particle swarm optimisation (SHPSO) algorithm is proposed for constrained optimisation. The proposed SHPSO is designed in such a way that the movement of the particle is set to move under the influence of shrinking hyperspheres. A parameter-free approach is used to handle the constraints. The performance of the SHPSO is compared against the state-of-the-art algorithms for a set of 24 benchmark problems. An exhaustive comparison of the results is provided statistically as well as graphically. Moreover three engineering design problems namely welded beam design, compressed string design and pressure vessel design problems are solved using SHPSO and the results are compared with the state-of-the-art algorithms.

[1]  Bara'a Ali Attea.  A fuzzy multi-objective particle swarm optimization for effective data clustering , 2010, Memetic Comput..

[2]  Maurice Clerc,et al.  Standard Particle Swarm Optimisation , 2012 .

[3]  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).

[4]  Xingsheng Gu,et al.  A dynamic inertia weight particle swarm optimization algorithm , 2008 .

[5]  S. Hemamalini,et al.  Emission constrained economic dispatch with valve-point effect using particle swarm optimization , 2008, TENCON 2008 - 2008 IEEE Region 10 Conference.

[6]  Zwe-Lee Gaing,et al.  Constrained dynamic economic dispatch solution using particle swarm optimization , 2004, IEEE Power Engineering Society General Meeting, 2004..

[7]  Erwie Zahara,et al.  A hybrid genetic algorithm and particle swarm optimization for multimodal functions , 2008, Appl. Soft Comput..

[8]  S. N. Kramer,et al.  An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design , 1994 .

[9]  Bo Liu,et al.  Improved particle swarm optimization combined with chaos , 2005 .

[10]  Kusum Deep,et al.  Hybridization of particle swarm optimization with quadratic approximation , 2009 .

[11]  Chun Lu,et al.  An improved GA and a novel PSO-GA-based hybrid algorithm , 2005, Inf. Process. Lett..

[12]  Ye Tian,et al.  An Improved Particle Swarm Algorithms for Global Optimization , 2010, 2010 International Conference on Machine Vision and Human-machine Interface.

[13]  Jun Zhang,et al.  A Novel Set-Based Particle Swarm Optimization Method for Discrete Optimization Problems , 2010, IEEE Transactions on Evolutionary Computation.

[14]  J. Sobieszczanski-Sobieski,et al.  Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization , 2004 .

[15]  Patrick Siarry,et al.  Particle swarm and ant colony algorithms hybridized for improved continuous optimization , 2007, Appl. Math. Comput..

[16]  Mauricio Zambrano-Bigiarini,et al.  Standard Particle Swarm Optimisation 2011 at CEC-2013: A baseline for future PSO improvements , 2013, 2013 IEEE Congress on Evolutionary Computation.

[17]  Kusum Deep,et al.  Novel Binary PSO for Continuous Global Optimization Problems , 2011, SocProS.

[18]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[19]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

[20]  Kusum Deep,et al.  Information sharing strategy among particles in Particle Swarm Optimization using Laplacian operator , 2009, 2009 IEEE Swarm Intelligence Symposium.

[21]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[22]  Yoshikazu Fukuyama,et al.  A particle swarm optimization for reactive power and voltage control considering voltage security assessment , 2000 .

[23]  Giuseppe Quaranta,et al.  Optimum design of prestressed concrete beams using constrained differential evolution algorithm , 2014 .

[24]  Michael R. Lyu,et al.  A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training , 2007, Appl. Math. Comput..

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

[26]  Ling Wang,et al.  An effective co-evolutionary differential evolution for constrained optimization , 2007, Appl. Math. Comput..

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

[28]  Michael N. Vrahatis,et al.  Particle swarm optimization for minimax problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[29]  Hazim El-Mounayri,et al.  NC end milling optimiza-tion using evolutionary computation , 2002 .

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

[31]  Ling Wang,et al.  A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization , 2007, Appl. Math. Comput..

[32]  Jiang Chuanwen,et al.  A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation , 2005, Math. Comput. Simul..

[33]  Xigang Yuan,et al.  An improved PSO algorithm for solving non-convex NLP/MINLP problems with equality constraints , 2007, Computers and Chemical Engineering.

[34]  A. Ebenezer Jeyakumar,et al.  Hybrid PSO–SQP for economic dispatch with valve-point effect , 2004 .

[35]  Ling Wang,et al.  An effective co-evolutionary particle swarm optimization for constrained engineering design problems , 2007, Eng. Appl. Artif. Intell..

[36]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[37]  Xiaodong Li,et al.  Particle swarm optimization-based schemes for resource-constrained project scheduling , 2005 .

[38]  Kusum Deep,et al.  A non-deterministic adaptive inertia weight in PSO , 2011, GECCO '11.

[39]  Kalyanmoy Deb,et al.  GeneAS: A Robust Optimal Design Technique for Mechanical Component Design , 1997 .

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

[41]  José García-Nieto,et al.  Parallel multi-swarm optimizer for gene selection in DNA microarrays , 2011, Applied Intelligence.

[42]  Qi Wu,et al.  A hybrid-forecasting model based on Gaussian support vector machine and chaotic particle swarm optimization , 2010, Expert Syst. Appl..

[43]  M. Clerc,et al.  The swarm and the queen: towards a deterministic and adaptive particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[44]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[45]  Zwe-Lee Gaing,et al.  Particle swarm optimization to solving the economic dispatch considering the generator constraints , 2003 .

[46]  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).

[47]  H. H. Balci,et al.  Scheduling electric power generators using particle swarm optimization combined with the Lagrangian relaxation method , 2004 .

[48]  Anupam Yadav,et al.  Shrinking hypersphere based trajectory of particles in PSO , 2013, Appl. Math. Comput..

[49]  Andrew Lim,et al.  Particle Swarm Optimization and Hill Climbing for the bandwidth minimization problem , 2006, Applied Intelligence.

[50]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[51]  E. Sandgren,et al.  Nonlinear Integer and Discrete Programming in Mechanical Design Optimization , 1990 .

[52]  Antonio J. Nebro,et al.  A survey of multi-objective metaheuristics applied to structural optimization , 2014 .

[53]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

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

[55]  Fei Qiao,et al.  A novel memetic algorithm and its application to data clustering , 2013, Memetic Comput..

[56]  G. Lambert-Torres,et al.  A hybrid particle swarm optimization applied to loss power minimization , 2005, IEEE Transactions on Power Systems.

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

[58]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[59]  Junyan Wang,et al.  Nonlinear Inertia Weight Variation for Dynamic Adaptation in Particle Swarm Optimization , 2011, ICSI.

[60]  Mohamed E. El-Hawary,et al.  A Survey of Particle Swarm Optimization Applications in Electric Power Systems , 2009, IEEE Transactions on Evolutionary Computation.

[61]  T. Saravanan,et al.  Optimal Power Flow Using Particle Swarm Optimization , 2014 .

[62]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[63]  Yong Wang,et al.  A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems , 2009, Frontiers of Computer Science in China.