Sebastian Rojas Gonzalez

Sebastian Rojas Gonzalez, Juergen Branke, Inneke van Nieuwenhuyse

We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto optimal solutions among a finite set of candidates for which the two objective outcomes have been observed with uncertainty (e.g., after running a multiobjective stochastic simulation optimization procedure). When identifying these solutions, the noise perturbing the observed performance may lead to two types of errors: solutions that are truly Pareto-optimal can be wrongly considered dominated, and solutions that are truly dominated can be wrongly considered Pareto-optimal. We propose a novel Bayesian bi-objective ranking and selection method that sequentially allocates extra samples to competitive solutions, in view of reducing the misclassification errors when identifying the solutions with the best expected performance. The approach uses stochastic kriging to build reliable predictive distributions of the objective outcomes, and exploits this information to decide how to resample. Experimental results show that the proposed method outperforms the standard allocation method, as well as a well-known the state-of-the-art algorithm. Moreover, we show that the other competing algorithms also benefit from the use of stochastic kriging information; yet, the proposed method remains superior.

Jack M. Buckingham, Sebastian Rojas Gonzalez, Juergen Branke

Multi-objective Bayesian optimization aims to find the Pareto front of trade-offs between a set of expensive objectives while collecting as few samples as possible. In some cases, it is possible to evaluate the objectives separately, and a different latency or evaluation cost can be associated with each objective. This decoupling of the objectives presents an opportunity to learn the Pareto front faster by avoiding unnecessary, expensive evaluations. We propose a scalarization based knowledge gradient acquisition function which accounts for the different evaluation costs of the objectives. We prove asymptotic consistency of the estimator of the optimum for an arbitrary, D-dimensional, real compact search space and show empirically that the algorithm performs comparably with the state of the art and significantly outperforms versions which always evaluate both objectives.

Felix Huber, Sebastian Rojas Gonzalez, Raul Astudillo

We present a novel approach to help decision-makers efficiently identify preferred solutions from the Pareto set of a multi-objective optimization problem. Our method uses a Bayesian model to estimate the decision-maker's utility function based on pairwise comparisons. Aided by this model, a principled elicitation strategy selects queries interactively to balance exploration and exploitation, guiding the discovery of high-utility solutions. The approach is flexible: it can be used interactively or a posteriori after estimating the Pareto front through standard multi-objective optimization techniques. Additionally, at the end of the elicitation phase, it generates a reduced menu of high-quality solutions, simplifying the decision-making process. Through experiments on test problems with up to nine objectives, our method demonstrates superior performance in finding high-utility solutions with a small number of queries. We also provide an open-source implementation of our method to support its adoption by the broader community.

Alejandro Morales-Hernández, Sebastian Rojas Gonzalez, Inneke Van Nieuwenhuyse et al.

Adhesive joints are increasingly used in industry for a wide variety of applications because of their favorable characteristics such as high strength-to-weight ratio, design flexibility, limited stress concentrations, planar force transfer, good damage tolerance, and fatigue resistance. Finding the optimal process parameters for an adhesive bonding process is challenging: the optimization is inherently multi-objective (aiming to maximize break strength while minimizing cost), constrained (the process should not result in any visual damage to the materials, and stress tests should not result in failures that are adhesion-related), and uncertain (testing the same process parameters several times may lead to different break strengths). Real-life physical experiments in the lab are expensive to perform. Traditional evolutionary approaches (such as genetic algorithms) are then ill-suited to solve the problem, due to the prohibitive amount of experiments required for evaluation. Although Bayesian optimization-based algorithms are preferred to solve such expensive problems, few methods consider the optimization of more than one (noisy) objective and several constraints at the same time. In this research, we successfully applied specific machine learning techniques (Gaussian Process Regression) to emulate the objective and constraint functions based on a limited amount of experimental data. The techniques are embedded in a Bayesian optimization algorithm, which succeeds in detecting Pareto-optimal process settings in a highly efficient way (i.e., requiring a limited number of physical experiments).

Alejandro Morales-Hernández, Inneke Van Nieuwenhuyse, Sebastian Rojas Gonzalez et al.

Automotive companies are increasingly looking for ways to make their products lighter, using novel materials and novel bonding processes to join these materials together. Finding the optimal process parameters for such adhesive bonding process is challenging. In this research, we successfully applied Bayesian optimization using Gaussian Process Regression and Logistic Regression, to efficiently (i.e., requiring few experiments) guide the design of experiments to the Pareto-optimal process parameter settings.

Alejandro Morales-Hernández, Inneke Van Nieuwenhuyse, Sebastian Rojas Gonzalez

Hyperparameter optimization (HPO) is a necessary step to ensure the best possible performance of Machine Learning (ML) algorithms. Several methods have been developed to perform HPO; most of these are focused on optimizing one performance measure (usually an error-based measure), and the literature on such single-objective HPO problems is vast. Recently, though, algorithms have appeared that focus on optimizing multiple conflicting objectives simultaneously. This article presents a systematic survey of the literature published between 2014 and 2020 on multi-objective HPO algorithms, distinguishing between metaheuristic-based algorithms, metamodel-based algorithms, and approaches using a mixture of both. We also discuss the quality metrics used to compare multi-objective HPO procedures and present future research directions.