Faster Exact Algorithms for Computing Expected Hypervolume Improvement

Hupkens, Iris; Deutz, André H.; Yang, Kaifeng; Emmerich, Michael

doi:10.1007/978-3-319-15892-1_5

Cited by 55 publications

(48 citation statements)

References 29 publications

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“…Couckuyt et al [8] provided an exact EHVI calculation algorithm for d > 2, and, according to experimental data, this algorithm was typically much faster than the one introduced in [12], but it still had a high worst-case time complexity. Hupkens et al [14] found algorithms for computing EHVI with the then lowest worst-case time complexity of O(n 2 ) and O(n 3 ), for two and three objectives, respectively. Recently, Emmerich et al [13] proposed an asymptotically optimal algorithm for the bi-objective case, with a computational time complexity of Θ(n log n).…”

Section: Relevance and Related Workmentioning

confidence: 99%

“…Three algorithms, IRS fast [14], CDD13 [8] and KMAC, which is short for the authors given name, in this paper are compared via the same benchmarks. The test benchmarks from Emmerich and Fonseca [28] are used to generated the Pareto fronts.…”

Section: Empirical Comparisonmentioning

confidence: 99%

“…This is a problem, as many SAMCO algorithms require a large number of EHVI computations to be performed in every iteration. Since the announcement of exact computation schemes [12], significant progress has been made, resulting in faster computation schemes [8,13,14]. Notably, in 2-D, the computation time could be improved from O(n 3 log n)-using a straightforward integration scheme, with a grid partitioning and repeated hypervolume computations for each grid cell -to asymptotically optimal Θ(n log n) in [13] using a stripe partitioning and a multi-layered integration scheme.…”

Section: Introductionmentioning

confidence: 99%

“…Notably, in 2-D, the computation time could be improved from O(n 3 log n)-using a straightforward integration scheme, with a grid partitioning and repeated hypervolume computations for each grid cell -to asymptotically optimal Θ(n log n) in [13] using a stripe partitioning and a multi-layered integration scheme. However, despite significant efficiency improvements [8,14], the running time of the best-known algorithms for d ≥ 3 has remained in O(n d ). This paper shows that the new integration technique proposed in [13] can be generalized to d ≥ 3, yielding a new algorithm with asymptotically optimal time complexity in Θ(n log n).…”

Section: Introductionmentioning

confidence: 99%

“…Experimental results on test data are reported in Sect. 5, including a speed comparison to other algorithms proposed in the literature [8,14]. Section 6 discusses how the new algorithm can be modified for solving the related problems of PoI and TEHVI.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Yang

Emmerich

Deutz

et al. 2017

Lecture Notes in Computer Science

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Abstract. The Expected Hypervolume Improvement (EHVI) is a frequently used infill criterion in surrogate-assisted multi-criterion optimization. It needs to be frequently called during the execution of such algorithms. Despite recent advances in improving computational efficiency, its running time for three or more objectives has remained inwhere d is the number of objective functions and n is the size of the incumbent Pareto-front approximation. This paper proposes a new integration scheme, which makes it possible to compute the EHVI in Θ(n log n) optimal time for the important three-objective case (d = 3). The new scheme allows for a generalization to higher dimensions and for computing the Probability of Improvement (PoI) integral efficiently. It is shown, both theoretically and empirically, that the hidden constant in the asymptotic notation is small. Empirical speed comparisons were designed between the C++ implementations of the new algorithm (which will be in the public domain) and those recently published by competitors, on randomly-generated non-dominated fronts of size 10, 100, and 1000. The experiments include the analysis of batch computations, in which only the parameters of the probability distribution change but the incumbent Pareto-front approximation stays the same. Experimental results show that the new algorithm is always faster than the other algorithms, sometimes over 10 4 times faster.

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Section: Relevance and Related Workmentioning

confidence: 99%

Section: Empirical Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Yang

Emmerich

Deutz

et al. 2017

Lecture Notes in Computer Science

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Multi‐objective global optimization (MOGO): Algorithm and case study in gradient elution chromatography

Freier

Lieres

2017

Biotechnology Journal

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Biotechnological separation processes are routinely designed and optimized using parallel high-throughput experiments and/or serial experiments. Well-characterized processes can further be optimized using mechanistic models. In all these cases - serial/parallel experiments and modeling - iterative strategies are customarily applied for planning novel experiments/simulations based on the previously acquired knowledge. Process optimization is typically complicated by conflicting design targets, such as productivity and yield. We address these issues by introducing a novel algorithm that combines recently developed approaches for utilizing statistical regression models in multi-objective optimization. The proposed algorithm is demonstrated by simultaneous optimization of elution gradient and pooling strategy for chromatographic separation of a three-component system with respect to purity, yield, and processing time. Gaussian Process Regression Models (GPM) are used for estimating functional relationships between design variables (gradient, pooling) and performance indicators (purity, yield, time). The Pareto front is iteratively approximated by planning new experiments such as to maximize the Expected Hypervolume Improvement (EHVI) as determined from the GPM by Markov Chain Monte Carlo (MCMC) sampling. A comprehensive Monte-Carlo study with in-silico data illustrates efficiency, effectiveness and robustness of the presented Multi-Objective Global Optimization (MOGO) algorithm in determining best compromises between conflicting objectives with comparably very low experimental effort.

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Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case

Allmendinger

Emmerich

Hakanen

et al. 2017

J. Multi-Crit. Decis. Anal.

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Complexity in solving real-world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time-consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate-assisted optimization.For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive training time of surrogate models, or the optimal use of many-core computers to approximate efficiently multiple objectives simultaneously. Thinking out of the box, complexity can also be shifted from approximating the individual objective functions to approximating the entire Pareto front. This leads to further complexities, namely, how to validate statistically and apply the techniques developed to real-world problems. In this paper, we discuss emerging complexity-related topics in surrogate-assisted multicriteria optimization that may not be prevalent in nonsurrogate-assisted single-objective optimization. These complexities are motivated using several real-world problems in which the authors were involved. We then discuss several promising future research directions and prospective solutions to tackle emerging complexities in surrogate-assisted multicriteria optimization. Finally, we provide insights from an industrial point of view into how surrogate-assisted multicriteria optimization techniques can be developed and applied within a collaborative business environment to tackle real-world problems.

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Faster Exact Algorithms for Computing Expected Hypervolume Improvement

Cited by 55 publications

References 29 publications

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

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

Multi‐objective global optimization (MOGO): Algorithm and case study in gradient elution chromatography

Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case

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