Admissible Operator Optimisation: Selection and Efficiency Within Constraint Boundaries

This paper defines admissible operator optimisation within the Paton System, establishing how execution paths are selected and evaluated under constraint. Building on the Paton Operator Calculus and Operator Stability frameworks, this work formalises how systems choose among multiple admissible paths while preserving viability. The framework introduces efficiency as a constrained measure, where optimisation is permitted only within admissible regions and must not compromise continuation. The approach is non-interfering and introduces no new domain-specific dynamics or optimisation laws. Instead, it provides a structural method for ranking execution paths according to admissibility, efficiency, and stability, enabling viable decision-making across complex systems. This paper forms part of the Paton Operator Layer and is structurally linked with: The Paton Operator Calculus: Composition, Sequencing, and Admissible Execution Paths Operator Stability and Failure: Admissibility Breakdown Under Sequential Constraint DOI 19605231