Targeting solutions in Bayesian multi-objective optimization: sequential and batch versions

Gaudrie, David; Riche, Rodolphe Le; Picheny, Victor; Enaux, Benoît; Herbert, Vincent

doi:10.1007/s10472-019-09644-8

Cited by 26 publications

(15 citation statements)

References 42 publications

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“…Both represent a trade-off between exploration and exploitation. The multiplicative EI (mEI) [12] is interesting in the context of the O-NAUTILUS method because it also takes into account a reference point provided by the DM. However, in our tests, solutions produced by mEI did not follow the DM's preferences very well.…”

Section: Expected Asfmentioning

confidence: 99%

Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

et al. 2022

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We introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires a small amount of expensive function evaluations. We share the implementation of O-NAUTILUS as open source code. Thanks to its graphical user interface, a decision maker can see in real time how the preferences provided affect the direction of the search. We demonstrate the potential and benefits of O-NAUTILUS with a problem related to the design of vehicles.

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Section: Expected Asfmentioning

confidence: 99%

Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

et al. 2022

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“…Gaudrie [33] uses the projection (intersection in case of a continuous front) of the closest non-dominated point on the line connecting the estimated ideal and nadir points as default preference. Conditional Gaussian process simulations are performed to create possible Pareto fronts, each of which defines a sample for the ideal and the nadir point, and the estimated ideal and nadir are the medians of the samples.…”

Section: Literature Reviewmentioning

confidence: 99%

Automatic Preference Based Multi-objective Evolutionary Algorithm on Vehicle Fleet Maintenance Scheduling Optimization

Wang

Limmer²,

Olhofer³

et al. 2021

Preprint

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A preference based multi-objective evolutionary algorithm is proposed for generating solutions in an automatically detected knee point region. It is named Automatic Preference based DI-MOEA (AP-DI-MOEA) where DI-MOEA stands for Diversity-Indicator based Multi-Objective Evolutionary Algorithm). AP-DI-MOEA has two main characteristics: firstly, it generates the preference region automatically during the optimization; secondly, it concentrates the solution set in this preference region. Moreover, the real-world vehicle fleet maintenance scheduling optimization (VFMSO) problem is formulated, and a customized multi-objective evolutionary algorithm (MOEA) is proposed to optimize maintenance schedules of vehicle fleets based on the predicted failure distribution of the components of cars. Furthermore, the customized MOEA for VFMSO is combined with AP-DI-MOEA to find maintenance schedules in the automatically generated preference region. Experimental results on multi-objective benchmark problems and our three-objective real-world application problems show that the newly proposed algorithm can generate the preference region accurately and that it can obtain better solutions in the preference region.

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“…Maximizing the hypervolume (HV) has been shown to produce Pareto fronts with excellent coverage [69,11,65]. However, there has been little work on EHVI in the parallel setting, and the work that has been done resorts to approximate methods [67,27,58]. Furthermore, a vast body of literature on has focused efficient EHVI computation [33,19,63], but the time complexity for computing EHVI is exponential in the number of objectives-in part due the hypervolume indicator itself incurring a time complexity that scales super-polynomially with the number of objectives [64].…”

Section: Limitations Of Current Approachesmentioning

confidence: 99%

“…Sequential greedy optimization often yields better empirical results because the optimization problem has a lower dimension: d in each step, rather than q•d in the joint problem. Most prior works in the MO setting use a sequential greedy approximation or heuristics [58,67,27,9], but impute the unobserved outcomes with the posterior mean rather than integrating over the posterior [29]. For many joint acquisition functions involving expectations, this shortcut sacrifices the theoretical error bound on the sequential greedy approximation because the exact joint acquisition function over x 1 , ..., x i , 1 ≤ i ≤ q requires integration over the joint posterior P(f (x 1 ), ..., f (x q )|D) and is not computed for i > 1.…”

Section: Related Workmentioning

confidence: 99%

Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization

Daulton,

Balandat,

Bakshy

2020

Preprint

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In many real-world scenarios, decision makers seek to efficiently optimize multiple competing objectives in a sample-efficient fashion. Multi-objective Bayesian optimization (BO) is a common approach, but many existing acquisition functions do not have known analytic gradients and suffer from high computational overhead. We leverage recent advances in programming models and hardware acceleration for multi-objective BO using Expected Hypervolume Improvement (EHVI)-an algorithm notorious for its high computational complexity. We derive a novel formulation of q-Expected Hypervolume Improvement (qEHVI), an acquisition function that extends EHVI to the parallel, constrained evaluation setting. qEHVI is an exact computation of the joint EHVI of q new candidate points (up to Monte-Carlo (MC) integration error). Whereas previous EHVI formulations rely on gradient-free acquisition optimization or approximated gradients, we compute exact gradients of the MC estimator via auto-differentiation, thereby enabling efficient and effective optimization using first-order and quasi-second-order methods. Lastly, our empirical evaluation demonstrates that qEHVI is computationally tractable in many practical scenarios and outperforms state-of-the-art multi-objective BO algorithms at a fraction of their wall time.Preprint. Under review.

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Targeting solutions in Bayesian multi-objective optimization: sequential and batch versions

Cited by 26 publications

References 42 publications

Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

Automatic Preference Based Multi-objective Evolutionary Algorithm on Vehicle Fleet Maintenance Scheduling Optimization

Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization

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