Quantum-inspired algorithms emulate quantum mechanical principles, such as, superposition, interference, and probabilistic amplitude evolution, on classical hardware by representing candidate solutions as qubit vectors and evolving them through rotation-gate operators. This approach offers higher optimization performance without physical qubits, and has been shown to achieve order-of-magnitude speedups (10--80$\times$) over traditional solvers on combinatorial, high-dimensional NP-hard problems. A critical barrier to adoption, however, is the lack of a unified execution framework that delivers both algorithmic performance and hardware portability. We present \textbf{Cross-Backend Quantum Inspired Evolutionary Optimizer (QIEO)}, the runtime core of BQP's BQPhy solver, which addresses this gap through a \emph{single-source-of-truth} architecture. One C++ implementation of the QIEO algorithm is compiled once per hardware target and exposed to multiple high-level languages via thin binding layers. The framework dispatches to CPU (sequential), OpenMP~5 (multi-core), CUDA (NVIDIA), and HIP (AMD) backends at runtime, adapting kernels to each device's memory hierarchy and warp/wavefront execution model. The framework's real-world utility is validated through binding demonstrations that share the identical C++ runtime. BQPhy's Python library is demonstrated on a neural network hyperparameter optimisation achieving 88.60\% test accuracy on MNIST. BQPhy's MATLAB's Toolkit is tested on wind farm layout optimisation attaining $365\,399 \pm 4\,552$~MWh/yr, which is statistically indistinguishable from particle swarm optimisation and $+7.6\%$ above genetic algorithms on a 32-variable constrained engineering problem. The Julia package tackles the Lotka--Volterra parameter estimation where BQPhy replaces native Julia solvers on the same residual, cutting mean SSE by $2.1\times$.

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