Structural Admissibility as a Foundation for Optimization

This paper argues that a significant source of difficulty in optimization does not arise from evaluation mechanisms or search strategies, but from the uncontrolled inclusion of structurally illegitimate configurations. We introduce the notion of structural admissibility as a non-evaluative criterion that determines whether a configuration, partial or complete, constitutes a coherent instantiation of an optimization problem. Admissibility is defined solely by intrinsic structural conditions and is invariant under changes in objective functions or search procedures. The admissibility criterion induces a structurally reduced configuration space that preserves all feasible and optimal solutions. By excluding inadmissible configurations prior to evaluation, redundancy, non-extendability, and logical inconsistency are eliminated without introducing algorithmic bias. The framework is independent of specific optimization methods and applies uniformly to incremental and complete search processes. Representative examples, including the knapsack problem, graph coloring, and the traveling salesman problem, demonstrate how diverse sources of search space inflation can be treated within a unified structural perspective. Rather than accelerating computation, structural admissibility clarifies and reorganizes optimization around the intrinsic structure of the problem itself.