Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints
This addresses the challenge of efficiently finding Pareto-optimal solutions under constraints in domains like aviation power system design, where evaluations are costly, though it appears incremental as it builds on existing entropy search methods.
The paper tackles the problem of constrained multi-objective blackbox optimization with expensive evaluations by proposing MESMOC, an output-space entropy based acquisition function, which demonstrates effectiveness over state-of-the-art algorithms in real-world engineering design applications.
We consider the problem of constrained multi-objective blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number of function evaluations. For example, in aviation power system design applications, we need to find the designs that trade-off total energy and the mass while satisfying specific thresholds for motor temperature and voltage of cells. This optimization requires performing expensive computational simulations to evaluate designs. In this paper, we propose a new approach referred as {\em Max-value Entropy Search for Multi-objective Optimization with Constraints (MESMOC)} to solve this problem. MESMOC employs an output-space entropy based acquisition function to efficiently select the sequence of inputs for evaluation to uncover high-quality pareto-set solutions while satisfying constraints. We apply MESMOC to two real-world engineering design applications to demonstrate its effectiveness over state-of-the-art algorithms.