A Critical Review of Adaptive Penalty Techniques in Evolutionary Computation

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

doi:10.1007/978-81-322-2184-5_1

Cited by 14 publications

(8 citation statements)

References 39 publications

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“…(7), the distance |λ−λopt| of the Lagrange factor from its optimal value given in Eq. (6), and the value of the penalty parameter µ. For comparison, the distance x − xopt from the optimal solution for corresponding runs on unconstrained sphere functions is included as well.…”

Section: Discussionmentioning

confidence: 99%

“…Most often, the modified objective is the sum of the original one and as many penalty terms as there are constraints, each weighted with its own penalty parameter. Barbosa et al [6] provide a recent review of adaptive penalty techniques (i.e., of penalty techniques that adapt their penalty parameters in response to the candidate solutions generated during the search).…”

Section: Background and Related Workmentioning

confidence: 99%

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Towards an Augmented Lagrangian Constraint Handling Approach for the (1+1)-ES

Arnold

Porter

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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We consider the problem of devising an approach for handling inequality constraints in evolution strategies that allows converging linearly to optimal solutions on sphere functions with a single linear constraint. An analysis of the single-step behaviour of the (1 + 1)-ES shows that the task of balancing improvements in the objective with those in the constraint function is quite delicate, and that adaptive approaches need to be carefully designed in order to avoid failure. Based on the understanding gained, we propose a simple augmented Lagrangian approach and experimentally demonstrate good performance on a broad range of sphere functions as well as on moderately ill-conditioned ellipsoids with a single linear constraint.

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Section: Discussionmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

Towards an Augmented Lagrangian Constraint Handling Approach for the (1+1)-ES

Arnold

Porter

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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“…Penalty functions, the basic idea of this strategy is to refine the fitness functions by extending the objective function with a penalty term. Penalty functions are the most commonly used approaches for evolutionary algorithm, in particular for handling inequality constraints (Barbosa et al 2015).…”

Section: Optimisation Objective Functionmentioning

confidence: 99%

Application of permutation genetic algorithm for sequential model building–model validation design of experiments

2015

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The work presented in this paper is motivated by a complex multivariate engineering problem associated with engine mapping experiments, which require efficient design of experiments (DoE) strategies to minimise expensive testing. The paper describes the development and evaluation of a Permutation Genetic Algorithm (PermGA) to enable an exploration-based sequential DoE strategy for complex reallife engineering problems. A known PermGA was implemented to generate uniform OLH DoEs, and substantially extended to support generation of model building-model validation (MB-MV) sequences, by generating optimal infill sets of test points as OLH DoEs that preserve good spacefilling and projection properties for the merged MB + MV test plan. The algorithm was further extended to address issues with non-orthogonal design spaces, which is a common problem in engineering applications. The effectiveness of the PermGA algorithm for the MB-MV OLH DoE sequence was evaluated through a theoretical benchmark problem based on the Six-Hump-Camel-Back function, as well as the Gasoline Direct Injection engine steady-state engine mapping problem that motivated this research. The case studies show that the algorithm is effective in delivering quasi-orthogonal spacefilling DoEs with good properties even after several MB-MV iterations, while the improvement in model adequacy and accuracy can be monitored by the engineering analyst. The Communicated by

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“…However, more effective approaches have looked at dynamically changing the penalty function depending on the current and past state of the search, which are called adaptive penalties. A review of adaptive penalties has been presented by Barbosa et al [34]. Adaptive penalties have the advantage of automatically changing the penalty function to adapt to the current search, thus reducing (or even eliminating) any user required input of penalty parameters.…”

Section: Introductionmentioning

confidence: 99%

Constrained niching using differential evolution

Poole

Allen

2019

Swarm and Evolutionary Computation

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The work presented here involves development and detailed investigations of niching methods for multimodal optimization of constrained functions. There is a lack of investigations in the literature on constrained multimodal optimization, hence a number of constrained niching algorithms have been developed here that leverage existing differential evolution-based niching methods with a feasibility rules-domination selection procedure. Furthermore, a suite of 18 benchmark functions has been developed and are presented in this paper; nine newly developed functions are incorporated with nine existing functions from the literature. Optimization results on these analytical functions using the constrained niching algorithms are presented, with analysis provided on the ability to locate multiple global optima, the convergence speed and constraint handling nature of the methods. The differential evolution strategy is also investigated, with SHADE and L-SHADE strategies considered. Finally, a dimensionality study also compares against the only other known constrained niching algorithm. Results indicate that all of the algorithms developed and tested generally perform well for low dimensional, low modality problems, but that local neighbourhood-based methods show the best results across the suite of functions tested. When high-dimensional problems are considered, using the L-SHADE strategy yields excellent results. An accompanying supplementary data file is provided with the manuscript.has also been successfully applied to DE [51]. The ensemble approach takes any number of constraint handling techniques and adaptively applies them to exploit the individual performance of each technique. Mezura-Montes et al.[52] investigated the effect of different mutation strategies in DE on constrained optimization. They highlighted the fact that much work in solving CNOPs using DE uses the feasibility rules of Deb [14], and as such, used this to handle the constraints.Commonly, population diversity is a requirement of EAs, such that design space exploration is achieved, with diversity decreasing through the optimization to exploit the global optimum within the space. On the other hand, while diversity is important for unimodal optimization, this is not necessarily the main driver of niching techniques. Niching requires a more careful balance of diversity to be able to locate and maintain strong and stable niches, and therefore exploit all the optima in the design space. Comprehensive reviews on niching techniques have been provided by Das et al.[53] and more recently by Li et al. [25] (the reader is particularly guided to the review of Li et al. for discussions of niching using SIAs as well as EAs), and a short review is presented here with particular attention paid to niching using EAs.One of the earliest bodies of work on maintaining population diversity, and therefore implicitly also multimodal optimization, was by de Jong [17], who introduced the classical idea of crowding. Crowding compares the fitness of close individuals and attemp...

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A Critical Review of Adaptive Penalty Techniques in Evolutionary Computation

Cited by 14 publications

References 39 publications

Towards an Augmented Lagrangian Constraint Handling Approach for the (1+1)-ES

Towards an Augmented Lagrangian Constraint Handling Approach for the (1+1)-ES

Application of permutation genetic algorithm for sequential model building–model validation design of experiments

Constrained niching using differential evolution

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