Necessary and Sufficient Conditions for Surrogate Functions of Pareto Frontiers and Their Synthesis Using Gaussian Processes
This work addresses the challenge of accurately synthesizing Pareto frontiers in multi-objective optimization, which is important for decision-makers in fields like engineering and design, though it appears incremental as it builds on existing surrogate methods with new theoretical conditions.
The paper tackled the problem of defining surrogate functions for Pareto frontiers in multi-objective optimization by introducing necessary and sufficient conditions that work directly in objective space, allowing real or user-designed surrogates. Results showed that Gaussian processes with monotonicity constraints managed these conditions well, producing high-quality frontier approximations, while an existing method without this theory violated the conditions significantly.
This paper introduces the necessary and sufficient conditions that surrogate functions must satisfy to properly define frontiers of non-dominated solutions in multi-objective optimization problems. These new conditions work directly on the objective space, thus being agnostic about how the solutions are evaluated. Therefore, real objectives or user-designed objectives' surrogates are allowed, opening the possibility of linking independent objective surrogates. To illustrate the practical consequences of adopting the proposed conditions, we use Gaussian processes as surrogates endowed with monotonicity soft constraints and with an adjustable degree of flexibility, and compare them to regular Gaussian processes and to a frontier surrogate method in the literature that is the closest to the method proposed in this paper. Results show that the necessary and sufficient conditions proposed here are finely managed by the constrained Gaussian process, guiding to high-quality surrogates capable of suitably synthesizing an approximation to the Pareto frontier in challenging instances of multi-objective optimization, while an existing approach that does not take the theory proposed in consideration defines surrogates which greatly violate the conditions to describe a valid frontier.