# Gradient Based Biobjective Shape Optimization to Improve Reliability and Cost of Ceramic Components

## TL;DR

This paper presents a gradient-based biobjective shape optimization approach for ceramic components, balancing reliability and cost using PDE constraints and adjoint methods, demonstrated through 2D test cases.

## Contribution

It introduces two gradient-based optimization methods for biobjective shape optimization with PDE constraints, utilizing efficient adjoint gradient computations and demonstrating trade-offs in 2D ceramic component design.

## Key findings

- Pareto fronts effectively illustrate reliability-cost trade-offs
- Innovative shapes emerge balancing conflicting objectives
- Methods outperform traditional approaches in efficiency

## Abstract

We consider the simultaneous optimization of the reliability and the cost of a ceramic component in a biobjective PDE constrained shape optimization problem. A probabilistic Weibull-type model is used to assess the probability of failure of the component under tensile load, while the cost is assumed to be proportional to the volume of the component. Two different gradient-based optimization methods are suggested and compared at 2D test cases. The numerical implementation is based on a first discretize then optimize strategy and benefits from efficient gradient computations using adjoint equations. The resulting approximations of the Pareto front nicely exhibit the trade-off between reliability and cost and give rise to innovative shapes that compromise between these conflicting objectives.