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

Bigeon, Jean; Digabel, Sébastien Le; Salomon, Ludovic

doi:10.1007/s10589-021-00272-9

Cited by 13 publications

(28 citation statements)

References 40 publications

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“…DMulti-MADS [17] is a direct search iterative method designed to solve constrained multiobjective blackbox optimization problems. It is an extension of the MADS [7] algorithm to multiobjective optimization, strongly inspired by the DMS [26] and BiMADS algorithms [13].…”

Section: The Dmulti-mads Algorithmmentioning

confidence: 99%

“…In all cases, the iterate list L k F is filtered to keep only best non-dominated feasible points found until the end of this iteration. More details can be found in [17].…”

Section: The Dmulti-mads Algorithmmentioning

confidence: 99%

“…Based on these remarks, this work proposes two other ways to handle blackbox constraints, based on the DMulti-MADS algorithm [17,17]. DMulti-MADS is an extension of the MADS algorithm to multiobjective optimization, strongly inspired by the DMS and BiMADS algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…At the same time, experiments have shown its competitiveness according to state-of-the-art solvers on synthetic bound-constrained problems [17]. Similarly to DMS, the first version of DMulti-MADS, described in [17] requires a feasible starting point. The two extensions described below remove this limitation.…”

Section: Introductionmentioning

confidence: 99%

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Handling of constraints in multiobjective blackbox optimization

Bigeon¹,

Digabel²,

Salomon³

2022

Preprint

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This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where research of a feasible point is prioritized if not available before improving the current solution set, or in a progressive barrier approach, where any trial point whose constraint violation function values are above a threshold are rejected. This threshold is progressively decreased along the iterations. As in the singleobjective case, it is proved that these two variants generate feasible and/or infeasible sequences which converge either in the feasible case to a set of local Pareto optimal points or in the infeasible case to Clarke stationary points according to the constraint violation function. Computational experiments show that these two approaches are competitive with other state-of-the-art algorithms.

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Section: The Dmulti-mads Algorithmmentioning

confidence: 99%

“…In all cases, the iterate list L k F is filtered to keep only best non-dominated feasible points found until the end of this iteration. More details can be found in [17].…”

Section: The Dmulti-mads Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Handling of constraints in multiobjective blackbox optimization

Bigeon¹,

Digabel²,

Salomon³

2022

Preprint

Self Cite

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show abstract

“…The imfil method can be heuristically modified in such a way to produce a set of non-dominated points. More recently, in [4] a new MADS-type algorithm has been proposed for multiobjective problems, namely DMulti-MADS. This method does not aggregate objectives and keeps a list of non dominated points which converges to a (local) Pareto set.…”

Section: Introductionmentioning

confidence: 99%

A derivative-free approach to mixed integer constrained multiobjective nonsmooth optimization

Liuzzi¹,

Lucidi²

2022

Preprint

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In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. Furthermore, we consider the case where a subset of the variables can only take integer values. We propose a new linesearchbased solution method and show that it converges to a set of stationary points for the problem. For what concerns the continuous variables, we employ a strategy for the estimation of the Pareto frontier recently proposed in the literature and which takes advantage of dense seuqnces of search directions. The subset of variables that must assume dicrete values are dealt with using primitive directions appropriately modified to take into account the presence of more than one objective functions. Numerical results obtained with the proposed method on a set of test problems and comparison with other solution methods show the viability and efficiency of the proposed approach.

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Algorithm Switching for Multiobjective Predictions in Renewable Energy Markets

Li,

Kannan

2025

Lecture Notes in Computer Science

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

Cited by 13 publications

References 40 publications

Handling of constraints in multiobjective blackbox optimization

Handling of constraints in multiobjective blackbox optimization

A derivative-free approach to mixed integer constrained multiobjective nonsmooth optimization

Algorithm Switching for Multiobjective Predictions in Renewable Energy Markets

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