J.F.A. Madeira

A Two-Space Scale-Invariant Direct Multisearch Method for Mixed-Variable Multiobjective Optimization

Many multiobjective black-box problems combine continuous, ordered-discrete, and categorical variables. Direct search on such domains requires a geometry that respects each variable type and is insensitive to arbitrary scaling, spacing, and labeling. We propose DMS-SI-Mix, a dete...

Mixed-Variable Optimisation as a Metric Product Space: Transient Categorical Geometry and a Hierarchy of Local Optimality

v2, August 2026: substantially revised version — restructured into eight sections, renamed optimality hierarchy (single-ordering / visited-orderings / all-orderings), corrected algorithmic section, and a new controlled computational experiment. A version of this manuscript is und...

A Two-Space Scale-Invariant Direct Multisearch Method for Mixed-Variable Multiobjective Optimization

Many multiobjective black-box problems combine continuous, ordered-discrete, and categorical variables. Direct search on such domains requires a geometry that respects each variable type and is insensitive to arbitrary scaling, spacing, and labeling. We propose DMS-SI-Mix, a dete...