A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach

Deb, Kalyanmoy; Datta, Rituparna

doi:10.1080/0305215x.2012.685074

Cited by 54 publications

(41 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some of the most common techniques use penalty functions (e.g., Mezura-Montes et al 2003;Runarsson and Yao 2000;Tessema and Yen 2006), multi-objective optimization (Wang and Cai 2012), a combination of a bi-objective optimization and a penalty approach Deb and Datta 2013), the epsilon constrained method (Takahama and Sakai 2012), cultural algorithms (Coello Coello and Landa-Becerra 2004), and those that distinguish between feasible and infeasible solutions (MezuraMontes and Coello Coello 2005). A recent survey on constraint-handling techniques in evolutionary and swarm algorithms is given by Mezura-Montes and Coello Coello (2011) and a tutorial is given by Coello Coello (2012).…”

Section: Review Of Literaturementioning

confidence: 99%

Trust Regions in Surrogate-Assisted Evolutionary Programming for Constrained Expensive Black-Box Optimization

Regis

2014

Infosys Science Foundation Series

View full text Add to dashboard Cite

This paper develops a new surrogate-assisted evolutionary programming (EP) algorithm for computationally expensive constrained black-box optimization. The proposed algorithm, TRICEPS (Trust Regions In Constrained Evolutionary Programming using Surrogates) builds surrogates for the black-box objective function and inequality constraint functions in every generation of the EP and uses a trustregion-like approach to refine the best solution at the end of each generation. Each parent produces a large number of trial offspring in each generation, and then the surrogates are used to identify promising trial offspring, which become the actual offspring where the objective and constraint functions are evaluated. After the function evaluations at these offspring, TRICEPS finds a minimizer of the surrogate of the objective function within a trust region centered at the current best solution and subject to surrogate inequality constraints with a small margin and with a distance requirement from previously evaluated points. The trust region is either expanded or reduced depending on whether the subproblem solution turned out to be feasible and whether the ratio of the actual improvement to the predicted improvement exceeds or falls below certain thresholds. TRICEPS is implemented using a cubic radial basis function (RBF) model with a linear polynomial tail and is compared to an RBF-assisted EP called CEP-RBF (Regis 2014b) and to other alternatives on 18 benchmark problems and on an automotive application with 124 decision variables and 68 black-box inequality constraints. Performance and data profiles show that TRICEPS is a substantial improvement over CEP-RBF and it is much better than the other alternatives on the test problems used. Keywords IntroductionIn many real-world engineering optimization problems, the values of the objective and constraint functions are outputs of computationally expensive simulations. These types of optimization problems are found in the automotive and aerospace industries (e.g., Jones 2008;Ong et al. 2003) and in various parameter estimation problems (e.g., Mugunthan et al. 2005;Tolson and Shoemaker 2007). A reasonable strategy for solving these problems is to use surrogate-based or surrogate-assisted optimization methods, including surrogate-assisted evolutionary algorithms (EAs) Jin (2011), where the algorithm uses surrogate models to approximate the black-box objective and constraint functions. For instance, Regis (2014b) successfully developed a surrogate-assisted Evolutionary Programming (EP) algorithm and applied it to a large-scale automotive optimization application with 124 decision variables and 68 black-box inequality constraints given a severely limited computational budget of only 1,000 simulations, where one simulation yields the objective function value and each of the constraint function values at a given input vector. The purpose of this paper is two-fold: (1) To develop a new surrogate-assisted EP for constrained black-box optimization that improves on the algorithm ...

show abstract

Section: Review Of Literaturementioning

confidence: 99%

Trust Regions in Surrogate-Assisted Evolutionary Programming for Constrained Expensive Black-Box Optimization

Regis

2014

Infosys Science Foundation Series

View full text Add to dashboard Cite

show abstract

“…However, once λ increases beyond R 0 (see figure inset), then the minimum value of f + λv occurs at the desired optimum "A" regardless of further increases in λ. R 0 is the lower bound of penalty parameter. With this view (and following Deb and Datta 2013), our approach in this paper is to seek an estimated upper bound for R 0 , as described further below.…”

Section: Introductionmentioning

confidence: 98%

“…1, and change R 0 . In prior work, such scaling has been done manually by inspection and user's judgment (Deb and Datta 2013) to obtain better numerical conditioning and efficient performance. In this paper, we will present a simple adaptive and algorithmic method of choosing these c i (i.e., of normalizing the constraints), and investigate its performance on 22 standard problems from the literature (Liang et al 2006).…”

Section: Introductionmentioning

confidence: 99%

“…In this context, a method for rationally selecting an appropriate λ that is large enough, and yet not too large, has been proposed recently (Deb and Datta 2013). The essential idea is summarized in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we will present a simple adaptive and algorithmic method of choosing these c i (i.e., of normalizing the constraints), and investigate its performance on 22 standard problems from the literature (Liang et al 2006). Additionally, we adopt and improve the hybrid approach of Deb and Datta (2013), wherein multi-objective evolutionary optimization is used for several generations to get a reasonable estimate of R 0 as well as a good starting guess, followed by classical local search in Matlab to refine the best guess. This alternating hybrid strategy is continued until convergence.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Uniform adaptive scaling of equality and inequality constraints within hybrid evolutionary-cum-classical optimization

Datta

Deb

2015

Soft Comput

Self Cite

View full text Add to dashboard Cite

The holy grail of constrained optimization is the development of an efficient, scale invariant and generic constraint handling procedure. To address these, the present paper proposes a unified approach of constraint handling, which is capable of handling all inequality, equality and hybrid constraints in a coherent manner. The proposed method also automatically resolves the issue of constraint scaling which is critical in real world and engineering optimization problems. The proposed unified approach converts the single-objective constrained optimization problem into a multi-objective problem. Evolutionary multi-objective optimization is used to solve the modified bi-objective problem and to estimate the penalty parameter automatically. The constrained optimum is further improved using classical optimization. The efficiency of the proposed method is validated on a set of well-studied constrained test problems and compared against without using normalization technique to show the necessity of normalization. The results establish the importance of scaling , especially in constrained optimization and call for further investigation into its use in constrained optimization research.

show abstract

Use of Infeasible Solutions During Constrained Evolutionary Search: A Short Survey

Singh

Alam

Ray

2016

Lecture Notes in Computer Science

View full text Add to dashboard Cite

A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach

Cited by 54 publications

References 30 publications

Trust Regions in Surrogate-Assisted Evolutionary Programming for Constrained Expensive Black-Box Optimization

Trust Regions in Surrogate-Assisted Evolutionary Programming for Constrained Expensive Black-Box Optimization

Uniform adaptive scaling of equality and inequality constraints within hybrid evolutionary-cum-classical optimization

Use of Infeasible Solutions During Constrained Evolutionary Search: A Short Survey

Contact Info

Product

Resources

About