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Surrogate-assisted multi-objective design of complex multibody systems

Augustina C. Amakor, Manuel B. Berkemeier, Meike Wohlleben, Walter Sextro, Sebastian Peitz

TL;DR

Efficiently solving expensive multi-objective design problems for complex multibody systems is challenging due to the high cost of evaluating multiple conflicting criteria. The authors propose an adaptive surrogate-based optimization framework that alternates surrogate modeling (ANN or RBF) with multi-objective optimization (notably NSGA-II) and uses Pareto-informed sampling guided by the Hausdorff distance to converge toward the true Pareto front within a fixed evaluation budget. The approach is demonstrated on an expensive rear-suspension multibody model, showing that interactive coupling yields near-optimal fronts with orders-of-magnitude speedups compared to full evaluations, and that ANN surrogates generally outperform RBFs in this setting. The work provides a practical pathway to scalable, high-quality Pareto front estimation for large, costly MBS analyses and points to future extensions with more objectives and smarter sampling strategies.

Abstract

The optimization of large-scale multibody systems is a numerically challenging task, in particular when considering multiple conflicting criteria at the same time. In this situation, we need to approximate the Pareto set of optimal compromises, which is significantly more expensive than finding a single optimum in single-objective optimization. To prevent large costs, the usage of surrogate models, constructed from a small but informative number of expensive model evaluations, is a very popular and widely studied approach. The central challenge then is to ensure a high quality (that is, near-optimality) of the solutions that were obtained using the surrogate model, which can be hard to guarantee with a single pre-computed surrogate. We present a back-and-forth approach between surrogate modeling and multi-objective optimization to improve the quality of the obtained solutions. Using the example of an expensive-to-evaluate multibody system, we compare different strategies regarding multi-objective optimization, sampling and also surrogate modeling, to identify the most promising approach in terms of computational efficiency and solution quality.

Surrogate-assisted multi-objective design of complex multibody systems

TL;DR

Efficiently solving expensive multi-objective design problems for complex multibody systems is challenging due to the high cost of evaluating multiple conflicting criteria. The authors propose an adaptive surrogate-based optimization framework that alternates surrogate modeling (ANN or RBF) with multi-objective optimization (notably NSGA-II) and uses Pareto-informed sampling guided by the Hausdorff distance to converge toward the true Pareto front within a fixed evaluation budget. The approach is demonstrated on an expensive rear-suspension multibody model, showing that interactive coupling yields near-optimal fronts with orders-of-magnitude speedups compared to full evaluations, and that ANN surrogates generally outperform RBFs in this setting. The work provides a practical pathway to scalable, high-quality Pareto front estimation for large, costly MBS analyses and points to future extensions with more objectives and smarter sampling strategies.

Abstract

The optimization of large-scale multibody systems is a numerically challenging task, in particular when considering multiple conflicting criteria at the same time. In this situation, we need to approximate the Pareto set of optimal compromises, which is significantly more expensive than finding a single optimum in single-objective optimization. To prevent large costs, the usage of surrogate models, constructed from a small but informative number of expensive model evaluations, is a very popular and widely studied approach. The central challenge then is to ensure a high quality (that is, near-optimality) of the solutions that were obtained using the surrogate model, which can be hard to guarantee with a single pre-computed surrogate. We present a back-and-forth approach between surrogate modeling and multi-objective optimization to improve the quality of the obtained solutions. Using the example of an expensive-to-evaluate multibody system, we compare different strategies regarding multi-objective optimization, sampling and also surrogate modeling, to identify the most promising approach in terms of computational efficiency and solution quality.

Paper Structure

This paper contains 12 sections, 14 equations, 10 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Multibody systems
  4. Multi-objective optimization
  5. Surrogate modeling
  6. Methodology
  7. Experiment
  8. Results
  9. NSGA-II optimizer with ANN surrogate models
  10. NSGA-II with RBF
  11. Different sample sizes
  12. Conclusion

Figures (10)

  • Figure 1: MOEA example, where a population of individuals is improved from one generation to the next ($\blacksquare\rightarrow\bigcirc\rightarrow\triangle\rightarrow\square$).
  • Figure 2: Sketch of the methodology.
  • Figure 3: Latin hypercube sampling for 20 points (in green) for the Branin function.
  • Figure 4: Example for the Hausdorff distance (adapted from https://en.wikipedia.org/wiki/Hausdorff_distance).
  • Figure 5: Trapezoidal link rear suspension system under consideration.
  • ...and 5 more figures