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Keywords: constrained particle swarm optimisation, multi-objective optimisation.

Summary

This paper introduces a new approach for dealing with constraints when using particle swarm optimisation. The single objective constrained optimisation problem is converted into an unconstrained, bi-objective optimisation problem that is solved using a multi-objective implementation of the particle swarm optimisation algorithm. A specialised bi-objective particle swarm optimisation algorithm is presented and an engineering example is used to illustrate its performance.

The paper presents the bi-objective formulation of a constrained optimisation problem as introduced by Fletcher and Leyffer [1] (a.k.a. a filter method). In this formulation the objective function of the original problem and a measure of the constraint violation are used as the two objective functions. The multi-objective particle swarm optimisation algorithm proposed by Reyes-Sierra and Coello Coello [2] is used as a baseline that is specialised to solve the bi-objective optimisation problem of interest. The specialisation centres around the fact that while a general multi-objective optimisation algorithm will produce a Pareto front as its final product, our application only needs the point on the Pareto front with the best original objective and no constraint violation.

The design of a composite laminate for maximum stiffness subject to tight constraints on Poisson's ratio is used to illustrate the effectiveness of the new algorithm. The design variables are ply orientations and ply thicknesses. The proposed algorithm is compared to both the standard multi-objective particle swarm optimisation algorithm as well as a standard particle swarm optimisation algorithm, using a penalty function approach.

The results indicate that the specialised multi-objective particle swarm algorithm clearly outperforms the standard multi-objective particle swarm optimisation algorithm and compares favourably with the standard particle swarm optimisation algorithm for which the penalty parameter was tuned. The new algorithm is more successful at avoiding local minima that are created by the constrained design space and does not require parameter tuning.

References

1: Fletcher, R. and Leyffer, S., "Nonlinear Programming without a Penalty Function", Mathematical Programming, Vol. 91, No. 2, pp. 239-269, 2002. doi:10.1007/s101070100244
2: Reyes-Sierra, M. and Coello Coello, C. a., "Improving PSO-based Multi-Objective Optimization Using Crowding, Mutation and epsilon-dominance", Third International Conference on Evolutionary Multi-Criterion Optimization, Guanajuato, Mexico, EMO, LNCS 3410, pp. 505-519, 2005.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 89 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis and B.H.V. Topping Paper 79 Constrained Particle Swarm Optimisation Using a Multi-Objective Formulation G. Venter¹ and R.T. Haftka² ¹Department of Mechanical and Mechatronic Engineering, Stellenbosch University, South Africa ²Department of Mechanical and Aerospace Engineering, University of Florida, United States of America doi:10.4203/ccp.89.79 purchase the full-text of this paper Full Bibliographic Reference for this paper G. Venter, R.T. Haftka, "Constrained Particle Swarm Optimisation Using a Multi-Objective Formulation", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 79, 2008. doi:10.4203/ccp.89.79 Keywords: constrained particle swarm optimisation, multi-objective optimisation. Summary This paper introduces a new approach for dealing with constraints when using particle swarm optimisation. The single objective constrained optimisation problem is converted into an unconstrained, bi-objective optimisation problem that is solved using a multi-objective implementation of the particle swarm optimisation algorithm. A specialised bi-objective particle swarm optimisation algorithm is presented and an engineering example is used to illustrate its performance. The paper presents the bi-objective formulation of a constrained optimisation problem as introduced by Fletcher and Leyffer [1] (a.k.a. a filter method). In this formulation the objective function of the original problem and a measure of the constraint violation are used as the two objective functions. The multi-objective particle swarm optimisation algorithm proposed by Reyes-Sierra and Coello Coello [2] is used as a baseline that is specialised to solve the bi-objective optimisation problem of interest. The specialisation centres around the fact that while a general multi-objective optimisation algorithm will produce a Pareto front as its final product, our application only needs the point on the Pareto front with the best original objective and no constraint violation. The design of a composite laminate for maximum stiffness subject to tight constraints on Poisson's ratio is used to illustrate the effectiveness of the new algorithm. The design variables are ply orientations and ply thicknesses. The proposed algorithm is compared to both the standard multi-objective particle swarm optimisation algorithm as well as a standard particle swarm optimisation algorithm, using a penalty function approach. The results indicate that the specialised multi-objective particle swarm algorithm clearly outperforms the standard multi-objective particle swarm optimisation algorithm and compares favourably with the standard particle swarm optimisation algorithm for which the penalty parameter was tuned. The new algorithm is more successful at avoiding local minima that are created by the constrained design space and does not require parameter tuning. References 1 Fletcher, R. and Leyffer, S., "Nonlinear Programming without a Penalty Function", Mathematical Programming, Vol. 91, No. 2, pp. 239-269, 2002. doi:10.1007/s101070100244 2 Reyes-Sierra, M. and Coello Coello, C. a., "Improving PSO-based Multi-Objective Optimization Using Crowding, Mutation and epsilon-dominance", Third International Conference on Evolutionary Multi-Criterion Optimization, Guanajuato, Mexico, EMO, LNCS 3410, pp. 505-519, 2005. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £95 +P&P)
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