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CivilComp Proceedings
ISSN 17593433 CCP: 93
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero
Paper 123
PseudoAdaptive Penalization to Handle Constraints in Particle Swarm Optimizers M.S. Innocente and J. Sienz
Adopt Research Group, Swansea University, United Kingdom M.S. Innocente, J. Sienz, "PseudoAdaptive Penalization to Handle Constraints in Particle Swarm Optimizers", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 123, 2010. doi:10.4203/ccp.93.123
Keywords: particle swarm optimization, pseudoadaptive tolerance relaxation, penalization method, constant coefficients.
Summary
Since particle swarm optimization is suitable for unconstrained problems only, some external technique needs to be incorporated to deal with constrained problems. One of the most popular techniques is the penalization method, where infeasible solutions are penalized by increasing the objective function value in minimization problems. The key is in the amount of penalization, which is typically linked to the amount of constraint violation. By turning the constrained problem into an unconstrained one, these methods are well suited for particle swarm optimizers because they do not disrupt the normal dynamics of the swarm. However they present the downside that problemdependent penalization coefficients are involved: an excessive penalization might lead to premature convergence, whereas too mild a penalization might lead to infeasible solutions being chosen over feasible ones.
Ideally, the penalization coefficients should be adaptive. While research on adaptive coefficients is extensive in the literature [1,3], a different adaptive scheme is proposed here where the coefficients are kept constant. The procedure consists of an initial selftuned relaxation of the constraint violation tolerances, followed by a pseudoadaptive decrease of the relaxations. The selftuning is performed so that an approximate target feasibility ratio is reached. The pseudoadaptive decrease is linked to the number of potential feasible solutions found at the current timestep. Thus, by linking the penalization to the constraint violations beyond the pseudoadaptive tolerance rather than to the actual constraint violations, a pseudoadaptive penalization is achieved. A particle swarm optimizer equipped with this constrainthandling mechanism is successfully tested on a suite of thirteen constrained problems. For comparison, the experiments are also performed without tolerance relaxations, and with the initial selftuned relaxation followed by a deterministic decrease. Comparisons to the results reported by Toscano Pulido et al. [4] and by Muñoz Zavala et al. [2] are offered as frames of reference. The pseudoadaptive tolerance relaxations scheme is successful in improving the solutions obtained for problems with low feasibility ratios and/or whose solutions are near or on the boundaries. References
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