Arjun Manoj | Searcharxiv

arXiv2026

Singularities in Multi-Objective Optimization and their Crossing during Continuation

Continuation methods help trace Pareto sets in multi-objective optimization but are inherently local: a single run traces a single connected branch, requiring multiple restarts to recover disconnected components of Pareto fronts. We show that, for unconstrained bi-objective problems under weighted-sum scalarization, these disconnects can be artifacts of singularities in the scalarization parameter, where the weight $\lambda$ diverges as the objective gradients become collinear. Recasting Pareto optimality as a nonlinear system, we apply pseudo-arclength continuation to follow the Pareto-critical set, and show that suitable singular reparameterizations allow crossing these singularities in systematically, recovering disconnected branches in a single run. A coordinate-wise projective compactification further provides a unified framework for parameter and decision-space variables. We demonstrate the approach on the ZDT3 benchmark and modifications.

math.OC↗

arXiv2025

On Some Tunable Multi-fidelity Bayesian Optimization Frameworks

Multi-fidelity optimization employs surrogate models that integrate information from varying levels of fidelity to guide efficient exploration of complex design spaces while minimizing the reliance on (expensive) high-fidelity objective function evaluations. To advance Gaussian Process (GP)-based multi-fidelity optimization, we implement a proximity-based acquisition strategy that simplifies fidelity selection by eliminating the need for separate acquisition functions at each fidelity level. We also enable multi-fidelity Upper Confidence Bound (UCB) strategies by combining them with multi-fidelity GPs rather than the standard GPs typically used. We benchmark these approaches alongside other multi-fidelity acquisition strategies (including fidelity-weighted approaches) comparing their performance, reliance on high-fidelity evaluations, and hyperparameter tunability in representative optimization tasks. The results highlight the capability of the proximity-based multi-fidelity acquisition function to deliver consistent control over high-fidelity usage while maintaining convergence efficiency. Our illustrative examples include multi-fidelity chemical kinetic models, both homogeneous and heterogeneous (dynamic catalysis for ammonia production).

cs.LG↗