Global optimality and completeness of finite grammar-based topology searches

Determine whether a globally optimal reconfigurable integrated photonic spectrometer topology and continuous parameter configuration exist beyond the finite topology reservoirs and parameter budgets evaluated by the grammar-based optimization, and establish whether any superior circuit or continuous solution was missed.

Background

The paper searches reconfigurable integrated photonic spectrometer architectures by combining a finite grammar-generated topology reservoir with bounded continuous optimization of coupler, phase-shifter, and delay-line parameters. The reported dFT and dFT-variant winners are therefore best-performing designs within the evaluated search spaces rather than mathematically established global optima.

Because the search is finite, an unresolved issue is whether a topology outside the sampled reservoir, or a continuous parameter configuration outside the explored optimization budget, could achieve a lower architecture-screening objective or better reconstruction performance. Resolving this would require a completeness argument, an exhaustive search over a sufficiently defined design space, or a method capable of establishing global optimality.