A family of adaptive penalty schemes for steady-state genetic algorithms

Lemonge, Afonso C. C.; Barbosa, Hélio J. C.; Bernardino, Heder S.

doi:10.1109/cec.2012.6256173

Cited by 3 publications

(4 citation statements)

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“…Although it produced good results for most of the test functions, the two-stage penalty method requires unnecessary high computation. Lemonge and Barbosa [2] proposed a simple adaptive penalty function that also uses information from the population to tune the penalty parameters. The average value of the objective function and the level of violation of each constraint during the evolution strategy are used to define the penalty parameters.…”

Section: Literature Surveymentioning

confidence: 99%

Constrained Optimization Solution Based on an Improved Genetic Algorithm

Zeng²

2012

AMM

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A hybrid adaptive genetic algorithm is proposed for solving constrained optimization problems. The algorithm combines adaptive penalty method and smoothing technique in order to get no parameter tuning and easily escaping from the local optimal solutions. Meanwhile, local line search technique is introduced and a new crossover operator is designed for getting much faster convergence. The performance of the algorithm is tested on thirteen benchmark functions and the results indicate that the proposed algorithm is robust and effective.

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Section: Literature Surveymentioning

confidence: 99%

Constrained Optimization Solution Based on an Improved Genetic Algorithm

Zeng²

2012

AMM

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“…This paper continues the work started in Lemonge et al (2012) presenting additional aspects: sensitivity analyses with respect to some parameters used in the previous algorithms are presented; additional numerical experiments are considered; and a statistical analysis using the Wilcoxon signed-rank test is provided in order to get confidence on the obtained results.…”

mentioning

confidence: 93%

“…Variants of APM for steady-state GA presented in Barbosa and Lemonge (2003) were introduced by Lemonge et al (2012). The APM, as originally proposed, computes the constraint violations in the initial population, and updates the penalty coefficient of each constraint after a pre-defined number of new individuals is inserted into the population.…”

mentioning

confidence: 99%

“…Nine values were set: 0.5, 1, 2, …, 8. Considering the best results found using Variants 3 and 4 in the computational experiments discussed in (Lemonge et al, 2012), the Variant 4 was chosen to be submitted to the sensitivity analysis of these parameters (ninser and θ) since the penalty coefficients k j vary much more than those in the Variant 3 (monotonic case). The value of ninser is incorporated in the label of the Variant 4 (Var_4); thus, Var_4-5 indicates the Variant 4 with ninser ¼ 5.…”

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confidence: 99%

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Variants of an adaptive penalty scheme for steady-state genetic algorithms in engineering optimization

Lemonge

Barbosa

Bernardino

2015

Engineering Computations

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Purpose – The purpose of this paper is to propose variants of an adaptive penalty scheme for steady-state genetic algorithms applied to constrained engineering optimization problems. Design/methodology/approach – For each constraint a penalty parameter is adaptively computed along the evolution according to information extracted from the current population such as the existence of feasible individuals and the level of violation of each constraint. The adaptive penalty method (APM), as originally proposed, computes the constraint violations of the initial population, and updates the penalty coefficient of each constraint after a given number of new individuals are inserted in the population. A second variant, called sporadic APM with constraint violation accumulation, works by accumulating the constraint violations during a given insertion of new offspring into the population, updating the penalty coefficients, and fixing the penalty coefficients for the next generations. The APM with monotonic penalty coefficients is the third variation, where the penalty coefficients are calculated as in the original method, but no penalty coefficient is allowed to have its value reduced along the evolutionary process. Finally, the penalty coefficients are defined by using a weighted average between the current value of a coefficient and the new value predicted by the method. This variant is called the APM with damping. Findings – The paper checks new variants of an APM for evolutionary algorithms; variants of an APM, for a steady-state genetic algorithm based on an APM for a generational genetic algorithm, largely used in the literature previously proposed by two co-authors of this manuscript; good performance of the proposed APM in comparison with other techniques found in the literature; innovative and general strategies to handle constraints in the field of evolutionary computation. Research limitations/implications – The proposed algorithm has no limitations and can be applied in a large number of evolutionary algorithms used to solve constrained optimization problems. Practical implications – The proposed algorithm can be used to solve real world problems in engineering as can be viewed in the references, presented in this manuscript, that use the original (APM) strategy. The performance of these variants is examined using benchmark problems of mechanical and structural engineering frequently discussed in the literature. Originality/value – It is the first extended analysis of the variants of the APM submitted for possible publication in the literature, applied to real world engineering optimization problems.

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