Kaifeng Yang

Faster Exact Algorithms for Computing Expected Hypervolume Improvement

This paper is about computing the expected improvement of the hypervolume indicator given a Pareto front approximation and a predictive multivariate Gaussian distribution of a new candidate point. It is frequently used as an infill or prescreening criterion in multiobjective optimization with expensive function evaluations where predictions are provided by Kriging or Gaussian process surrogate models. The expected hypervolume improvement has good properties as an infill criterion, but exact algorithms for its computation have so far been very time consuming even for the two and three objective case. This paper introduces faster exact algorithms for computing the expected hypervolume improvement for independent Gaussian distributions. A new general computation scheme is introduced and a lower bound for the time complexity. By providing new algorithms, upper bounds for the time complexity for problems with two as well as three objectives are improved. For the 2-D case the time complexity bound is reduced from previously \(O(n^3 \log n)\) to \(O(n^2)\). For the 3-D case the new upper bound of \(O(n^3)\) is established; previously \(O(n^4 \log n)\). It is also shown how an efficient implementation of these new algorithms can lead to a further reduction of running time. Moreover it is shown how to process batches of multiple predictive distributions efficiently. The theoretical analysis is complemented by empirical speed comparisons of C++ implementations of the new algorithms to existing implementations of other exact algorithms.

A Multicriteria Generalization of Bayesian Global Optimization

This chapter discusses a generalization of the expected improvement used in Bayesian global optimization to the multicriteria optimization domain, where the goal is to find an approximation to the Pareto front. The expected hypervolume improvement (EHVI) measures improvement as the gain in dominated hypervolume relative to a given approximation to the Pareto front. We will review known properties of the EHVI, applications in practice and propose a new exact algorithm for computing EHVI. The new algorithm has asymptotically optimal time complexity O(nlogn). This improves existing computation schemes by a factor of n∕logn. It shows that this measure, at least for a small number of objective functions, is as fast as other simpler measures of multicriteria expected improvement that were considered in recent years.

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

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 in

Expected hypervolume improvement algorithm for PID controller tuning and the multiobjective dynamical control of a biogas plant

On^d

A new approach to target region based multiobjective evolutionary algorithms

for

Multi-objective aerodynamic design with user preference using truncated expected hypervolume improvement

d\ge 3