An efficient multi-objective optimization method for black-box functions using sequential approximate technique

Chen, Guodong; Han, Xu; Liu, Guiping; Jiang, Chao; Zhao, Ziqi

doi:10.1016/j.asoc.2011.09.011

Cited by 41 publications

(23 citation statements)

References 21 publications

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“…Type 2 of the adaptive framework has been inspired by this paper. In [95] also an optimization-based method similar to the idea in [42] is introduced. Without loss of generality, we summarize these methods together.…”

Section: Summary Of Methods In the Adaptive Framework: Typementioning

confidence: 99%

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A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods

Tabatabaei

Hakanen

Hartikainen

et al. 2015

Struct Multidisc Optim

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A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods Tabatabaei, Mohammad; Hakanen, Jussi; Hartikainen, Markus; Miettinen, Kaisa; Sindhya, Karthik Tabatabaei, M., Hakanen, J., Hartikainen, M., Miettinen, K., & Sindhya, K. (2015). A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods. Structural and Multidisciplinary Optimization, 52 (1) AbstractComputationally expensive multiobjective optimization problems arise, e.g. in many engineering applications, where several conflicting objectives are to be optimized simultaneously while satisfying constraints. In many cases, the lack of explicit mathematical formulas of the objectives and constraints may necessitate conducting computationally expensive and time-consuming experiments and/or simulations. As another challenge, these problems may have either convex or nonconvex or even disconnected Pareto frontier consisting of Pareto optimal solutions. Because of the existence of many such solutions, typically, a decision maker is required to select the most preferred one. In order to deal with the high computational cost, surrogate-based methods are commonly used in the literature. This paper surveys surrogate-based methods proposed in the literature, where the methods are independent of the underlying optimization algorithm and mitigate the computational burden to capture different types of Pareto frontiers. The methods considered are classified, discussed and then compared. These methods are divided into two frameworks: the sequential and the adaptive frameworks. Based on the comparison, we recommend the adaptive framework to tackle the aforementioned challenges.

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Section: Summary Of Methods In the Adaptive Framework: Typementioning

confidence: 99%

“…After initializing the trust region, in [42,95] initial points are sampled using OLHS and LHS, respectively, within the trust region in Step 1, and evaluated with the computationally expensive functions in Step 2. Each computationally expensive function is approximated in…”

Section: Summary Of Methods In the Adaptive Framework: Typementioning

confidence: 99%

A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods

Tabatabaei

Hakanen

Hartikainen

et al. 2015

Struct Multidisc Optim

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“…Some of the earliest studies are those of Schaffer (1985) who invented in VectorEvaluated Genetic Algorithm (VEGA) and Goldberg (1989) who pioneered in Multi-Objective optimization Evolution (DE). Rangavajhala et al (2006;Chen et al, 2012) suggested on Robust Design Optimization (RDO) and a new efficient sequential approximate MultiObjective Optimization (MOO) method for by obtaining the Pareto-optimal points respectively. Mosavi and Vaezipour (2012) developed a method on the basis of Reactive Search Optimization (RSO) algorithms in solving engineering optimal design and compared this method with Interactive Multi-objective Optimization and Decision-making method.…”

Section: Introductionmentioning

confidence: 99%

Multi-Objective Evolutionary Optimization of Sandwich Structures: An Evaluation by Elitist Non-dominated Sorting Evolution Strategy

Akmar¹,

Krämer²,

Rabczuk³

2015

American Journal of Engineering and Applied Sciences

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Abstract:In this study, an application of evolutionary multi-objective optimization algorithms on the optimization of sandwich structures is presented. The solution strategy is known as Elitist Non-Dominated Sorting Evolution Strategy (ENSES) wherein Evolution Strategies (ES) as Evolutionary Algorithm (EA) in the elitist Non-dominated Sorting Genetic algorithm (NSGA-II) procedure. Evolutionary algorithm seems a compatible approach to resolve multi-objective optimization problems because it is inspired by natural evolution, which closely linked to Artificial Intelligence (AI) techniques and elitism has shown an important factor for improving evolutionary multi-objective search. In order to evaluate the notion of performance by ENSES, the well-known study case of sandwich structures are reconsidered. For Case 1, the goals of the multi-objective optimization are minimization of the deflection and the weight of the sandwich structures. The length, the core and skin thicknesses are the design variables of Case 1. For Case 2, the objective functions are the fabrication cost, the beam weight and the end deflection of the sandwich structures. There are four design variables i.e., the weld height, the weld length, the beam depth and the beam width in Case 2. Numerical results are presented in terms of Paretooptimal solutions for both evaluated cases.

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“…For updating the surrogate, in [4], all feasible nondominated solutions from the latest generation were re-evaluated and added to the training data set. In [5], all nondominated solutions after using surrogates were reevaluated without considering the feasibility of the solutions. In [6,7], the probability of feasibility was used for selecting individuals to update the surrogates.…”

Section: Introductionmentioning

confidence: 99%

“…In [4][5][6], initial training of surrogates was performed without considering any information from infeasible solutions, while in [7] a prefixed number of feasible solutions was used to train Kriging models. For updating the surrogate, in [4], all feasible nondominated solutions from the latest generation were re-evaluated and added to the training data set.…”

Section: Introductionmentioning

confidence: 99%

On Constraint Handling in Surrogate-Assisted Evolutionary Many-Objective Optimization

Chugh

Sindhya

Miettinen

et al. 2016

Parallel Problem Solving From Nature – PPSN XIV

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Abstract. Surrogate-assisted evolutionary multiobjective optimization algorithms are often used to solve computationally expensive problems. But their efficacy on handling constrained optimization problems having more than three objectives has not been widely studied. Particularly the issue of how feasible and infeasible solutions are handled in generating a data set for training a surrogate has not received much attention. In this paper, we use a recently proposed Kriging-assisted evolutionary algorithm for many-objective optimization and investigate the effect of infeasible solutions on the performance of the surrogates. We assume that constraint functions are computationally inexpensive and consider different ways of handling feasible and infeasible solutions for training the surrogate and examine them on different benchmark problems. Results on the comparison with a reference vector guided evolutionary algorithm show that it is vital for the success of the surrogate to properly deal with infeasible solutions.

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An efficient multi-objective optimization method for black-box functions using sequential approximate technique

Cited by 41 publications

References 21 publications

A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods

A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods

Multi-Objective Evolutionary Optimization of Sandwich Structures: An Evaluation by Elitist Non-dominated Sorting Evolution Strategy

On Constraint Handling in Surrogate-Assisted Evolutionary Many-Objective Optimization

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