Multi-objective constrained black-box optimization using radial basis function surrogates

Regis, Rommel G.

doi:10.1016/j.jocs.2016.05.013

Cited by 42 publications

(8 citation statements)

References 50 publications

(75 reference statements)

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“…We believe that it should also be possible to propagate multiple solutions and combine the TRM method with non-dominance testing as has been done [31] and in [56]. One can think of other globalization strategies as well: RBF models have been used in multiobjective Stochastic Search algorithms [57] and trust region ideas have been included into population based strategies [26]. It will thus be interesting to see whether the theoretical convergence properties can be maintained within these contexts…”

Section: Discussionmentioning

confidence: 99%

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Berkemeier

Peitz

2021

MCA

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We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point is proven. The method is derivative-free in the sense that derivative information need not be available for the expensive objectives. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar counterparts and complements multiobjective line-search algorithms. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points needed per iteration scales linearly with the decision space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives.

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Section: Discussionmentioning

confidence: 99%

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Berkemeier

Peitz

2021

MCA

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“…Several works describe the construction of data profiles for multiobjective blackbox optimization, based on the use of quality indicators (see [2,30] for surveys on quality indicators). Since the works of [22], which to the best of our knowledge, introduced data and performance profiles for multiobjective blackbox optimization, many researchers have adopted this framework to assess the performance of their methods [17,31,34]. However, these frameworks rely on spread and cardinality metrics, which are not Pareto compliant [2] with the dominance order for multiobjective optimization.…”

Section: Data Profiles For Multiobjective Blackbox Optimizationmentioning

confidence: 99%

DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization

2021

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The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to multiobjective derivative-free optimization with bound constraints. This method does not aggregate objectives and keeps a list of non dominated points which converges to a (local) Pareto set as long as the algorithm unfolds. As in the single-objective optimization MADS algorithm, this method is built around a search step and a poll step. Under classical direct search assumptions, it is proved that the so-called DMulti-MADS algorithm generates multiple subsequences of iterates which converge to a set of local Pareto stationary points.Finally, computational experiments suggest that this approach is competitive compared to the state-of-the-art algorithms for multiobjective blackbox optimization.

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“…In [114], RBF was used as a metamodel for each objective and constraint function. It was assumed that at least one feasible solution is available to train the metamodels in step 5.…”

Section: Non-kriging Based Algorithmsmentioning

confidence: 99%

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

et al. 2017

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Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008-2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation based algorithms. We also compare these algorithms based on different criteria such as metamodelling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive mmultiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

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Multi-objective constrained black-box optimization using radial basis function surrogates

Cited by 42 publications

References 50 publications

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

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