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Inverse multi-objective robust evolutionary design

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Abstract

In this paper, we present an Inverse Multi-Objective Robust Evolutionary (IMORE) design methodology that handles the presence of uncertainty without making assumptions about the uncertainty structure. We model the clustering of uncertain events in families of nested sets using a multi-level optimization search. To reduce the high computational costs of the proposed methodology we proposed schemes for (1) adapting the step-size in estimating the uncertainty, and (2) trimming down the number of calls to the objective function in the nested search. Both offline and online adaptation strategies are considered in conjunction with the IMORE design algorithm. Design of Experiments (DOE) approaches further reduce the number of objective function calls in the online adaptive IMORE algorithm. Empirical studies conducted on a series of test functions having diverse complexities show that the proposed algorithms converge to a set of Pareto-optimal design solutions with non-dominated nominal and robustness performances efficiently.

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Notes

  1. There are two basic strategies for using Memetic Algorithms [15–17]:

    • Lamarckian learning forces the genotype to reflect the result of improvement in local search by placing the locally improved individual back into the population to compete for reproductive opportunities.

    • Baldwinian learning only alters the fitness of the individuals and the improved genotype is not encoded back into the population.

  2. Based on the central limit theorem, random samples from a given distribution with mean μ and variance σ 2 will approach a Gaussian/Normal distribution N(μ, σ 2) when the sample size increases.

  3. Note that x * represents the nominal global optimum (maximum).

  4. Note that x^ represents the robust global optimum (maximum).

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Acknowledgment

This work was funded by Honda Research Institute Germany. The authors would like to thank E. Körner at Honda Research Institute Europe, and the Parallel and Distributed Computing Centre of Nanyang Technological University for their support in this work.

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Authors and Affiliations

  1. School of Computer Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore

    Dudy Lim, Yew-Soon Ong & Bu Sung Lee

  2. Honda Research Institute Europe GmbH, Carl-Legien-Strasse 30, 63073, Offenbach, Germany

    Yaochu Jin & Bernhard Sendhoff

Authors
  1. Dudy Lim
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  2. Yew-Soon Ong
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  3. Yaochu Jin
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  4. Bernhard Sendhoff
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  5. Bu Sung Lee
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Correspondence to Dudy Lim.

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Lim, D., Ong, YS., Jin, Y. et al. Inverse multi-objective robust evolutionary design. Genet Program Evolvable Mach 7, 383–404 (2006). https://doi.org/10.1007/s10710-006-9013-7

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