Computing 3-D Expected Hypervolume Improvement and Related Integrals in Asymptotically Optimal Time

Yang, Kaifeng; Emmerich, Michael; Deutz, André H.; Fonseca, Carlos M.

doi:10.1007/978-3-319-54157-0_46

Cited by 31 publications

(25 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There have been propositions to speed up this process [26]. In particular, the fastest known methods to calculate EHV have been proposed in Emmerich et al [27] for two objectives and in Yang et al [28] for three objectives. Another disadvantage of the EHV is the selection of the reference point, which is non-trivial and greatly affects the performance of the method.…”

Section: Related Workmentioning

confidence: 99%

“…In the case that the Pareto front approximation is sorted by a coordinate, the complexity can be reduced to (ℓ), which can be easily achieved in Bayesian optimization. In Yang et al [28] the approach is extended to three objectives with a time complexity of (ℓ (ℓ)), which we consequently implemented. A summary for the efficient computation of ∆ is given in Emmerich, Fonseca [51].…”

Section: Select Point From Candidate Setmentioning

confidence: 99%

See 1 more Smart Citation

Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm

2018

View full text Add to dashboard Cite

Many engineering problems require the optimization of expensive, black-box functions involving multiple conflicting criteria, such that commonly used methods like multiobjective genetic algorithms are inadequate. To tackle this problem several algorithms have been developed using surrogates. However, these often have disadvantages such as the requirement of a priori knowledge of the output functions or exponentially scaling computational cost with respect to the number of objectives. In this paper a new algorithm is proposed, TSEMO, which uses Gaussian processes as surrogates. The Gaussian processes are sampled using spectral sampling techniques to make use of Thompson sampling in conjunction with the hypervolume quality indicator and NSGA-II to choose a new evaluation point at each iteration. The reference point required for the hypervolume calculation is estimated within TSEMO. Further, a simple extension was proposed to carry out batch-sequential design. TSEMO was compared to ParEGO, an expected hypervolume implementation, and NSGA-II on 9 test problems with a budget of 150 function evaluations. Overall, TSEMO shows promising performance, while giving a simple algorithm without the requirement of a priori knowledge, reduced hypervolume calculations to approach linear scaling with respect to the number of objectives, the capacity to handle noise and lastly the ability for batch-sequential usage.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Select Point From Candidate Setmentioning

confidence: 99%

Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm

2018

View full text Add to dashboard Cite

show abstract

“…Similar to the derivation of the term (35), the terms (36), (37) and (38) can be written as follows:…”

Section: -D Ehvi Calculationmentioning

confidence: 99%

Efficient computation of expected hypervolume improvement using box decomposition algorithms

et al. 2019

Self Cite

View full text Add to dashboard Cite

In the field of multi-objective optimization algorithms, multi-objective Bayesian Global Optimization (MOBGO) is an important branch, in addition to evolutionary multiobjective optimization algorithms (EMOAs). MOBGO utilizes Gaussian Process models learned from previous objective function evaluations to decide the next evaluation site by maximizing or minimizing an infill criterion. A commonly used criterion in MOBGO is the Expected Hypervolume Improvement (EHVI), which shows a good performance on a wide range of problems, with respect to exploration and exploitation. However, so far, it has been a challenge to calculate exact EHVI values efficiently. This paper proposes an efficient algorithm for the exact calculation of the EHVI for in a generic case. This efficient algorithm is based on partitioning the integration volume into a set of axis-parallel slices. Theoretically, the upper bound time complexities can be improved from previously O(n 2 ) and O(n 3 ), for two-and three-objective problems respectively, to Θ(n log n), which is asymptotically optimal. This article generalizes the scheme in higher dimensional cases by utilizing a new hyperbox decomposition technique, which is proposed by Dächert et al., EJOR, 2017. It also utilizes a generalization of the multilayered integration scheme that scales linearly in the number of hyperboxes of the decomposition. The speed comparison shows that the proposed algorithm in this paper significantly reduces computation time. Finally, this decomposition technique is applied in the calculation of the Probability of Improvement (PoI).

show abstract

“…While exact algorithms for the computation of EHVI have been developed recently (Hupkens et al, 2015;Yang et al, 2017), such algorithms are difficult to be extended to problems with more than 3 objectives. Recently, a subset of the present authors (Zhao et al, 2018) developed a fast exact framework for the computation of EHVI with arbitrary number of objectives by integrating a closed-formulation for computing the (hyper)volume of hyperrectangles with existing approaches (While et al, 2012;Couckuyt et al, 2014) to decompose hypervolumes.…”

Section: Multi-objective Bayesian Optimizationmentioning

confidence: 99%

Experiment Design Frameworks for Accelerated Discovery of Targeted Materials Across Scales

et al. 2019

View full text Add to dashboard Cite

Over the last decade, there has been a paradigm shift away from labor-intensive and time-consuming materials discovery methods, and materials exploration through informatics approaches is gaining traction at present. Current approaches are typically centered around the idea of achieving this exploration through high-throughput (HT) experimentation/computation. Such approaches, however, do not account for the practicalities of resource constraints which eventually result in bottlenecks at various stage of the workflow. Regardless of how many bottlenecks are eliminated, the fact that ultimately a human must make decisions about what to do with the acquired information implies that HT frameworks face hard limits that will be extremely difficult to overcome. Recently, this problem has been addressed by framing the materials discovery process as an optimal experiment design problem. In this article, we discuss the need for optimal experiment design, the challenges in it's implementation and finally discuss some successful examples of materials discovery via experiment design.

show abstract

Computing 3-D Expected Hypervolume Improvement and Related Integrals in Asymptotically Optimal Time

Cited by 31 publications

References 28 publications

Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm

Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm

Efficient computation of expected hypervolume improvement using box decomposition algorithms

Experiment Design Frameworks for Accelerated Discovery of Targeted Materials Across Scales

Contact Info

Product

Resources

About