Theoretical and Practical Convergence of a Self-Adaptive Penalty Algorithm for Constrained Global Optimization

M. Fernanda P. Costa (), Rogério B. Francisco (), Ana Maria A. C. Rocha () and Edite M. G. P. Fernandes ()
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M. Fernanda P. Costa: University of Minho
Rogério B. Francisco: Polytechnic of Porto
Ana Maria A. C. Rocha: University of Minho
Edite M. G. P. Fernandes: University of Minho

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 3, No 15, 875-893

Abstract: Abstract This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems.

Keywords: Global optimization; Self-adaptive penalty; Firefly algorithm; 90C30; 90C26; 90C59 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-016-1042-7

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