The design of food diets in the context of animal nutrition is a complex problem that aims to develop cost-effective formulations while balancing minimum nutritional content. Traditional approaches based on theoretical models of metabolic responses and concentrations of digestible energy in raw materials face limitations in incorporating zootechnical or environmental variables affecting the performance of animals and including multiple objectives aligned with sustainable development policies. Recently, multi-objective Bayesian optimization has been proposed as a promising heuristic alternative able to deal with the combination of multiple sources of information, multiple and diverse objectives, and with an intrinsic capacity to deal with uncertainty in the measurements that could be related to variability in the nutritional content of raw materials. However, Bayesian optimization encounters difficulties in high-dimensional search spaces, leading to exploration predominantly at the boundaries. This work analyses a strategy to split the search space into regions that provide local candidates termed multi-objective regionalized Bayesian optimization as an alternative to improve the quality of the Pareto set and Pareto front approximation provided by BO in the context of swine diet design. Results indicate that this regionalized approach produces more diverse non-dominated solutions compared to the standard multi-objective Bayesian optimization. Besides, the regionalized strategy was four times more effective in finding solutions that outperform those identified by a stochastic programming approach referenced in the literature. Experiments using batches of query candidate solutions per iteration show that the optimization process can also be accelerated without compromising the quality of the Pareto set approximation during the initial, most critical phase of optimization.

Physical simulation-based optimization is a common task in science and engineering. Many such simulations produce image- or tensor-based outputs where the desired objective is a function of those outputs, and optimization is performed over a high-dimensional parameter space. We develop a Bayesian optimization method leveraging tensor-based Gaussian process surrogates and trust region Bayesian optimization to effectively model the image outputs and to efficiently optimize these types of simulations, including a radio-frequency tower configuration problem and an optical design problem.

The ability to optimize multiple competing objective functions with high sample efficiency is imperative in many applied problems across science and industry. Multi-objective Bayesian optimization (BO) achieves strong empirical performance on such problems, but even with recent methodological advances, it has been restricted to simple, low-dimensional domains. Most existing BO methods exhibit poor performance on search spaces with more than a few dozen parameters. In this work we propose MORBO, a method for multi-objective Bayesian optimization over high-dimensional search spaces. MORBO performs local Bayesian optimization within multiple trust regions simultaneously, allowing it to explore and identify diverse solutions even when the objective functions are difficult to model globally. We show that MORBO significantly advances the state-of-the-art in sample-efficiency for several high-dimensional synthetic and real-world multi-objective problems, including a vehicle design problem with 222 parameters, demonstrating that MORBO is a practical approach for challenging and important problems that were previously out of reach for BO methods.