Quantum-inspired evolutionary optimization (QIEO) is a new class of population-based metaheuristic optimization algorithms which represents design variables as a set of qubits and searches a continuous, multi-dimensional landscape through rotation of the qubit's amplitude pair. Every generation rotates those amplitudes toward a single elite, which corresponds to that generation's best. The per-generation cost scales as O(Nₚ N_g) for Nₚ chromosomes and N_g genes (decision variables). Production use of such solvers is rarely confined to a single machine class. Prototypes are run on laboratory servers- before moving to rented cloud workstations for more involved campaigns. The largest problems are reserved for leadership-class accelerators. This paper asks whether a single OpenMP 5 source of QIEO, offloaded with #pragma omp target, is a viable production path in each of those settings. We report three independent, campaigns of the 0/1 knapsack problem against a same-source multi-core Intel CPU baseline. The study comprises approximately 3,000 runs spanning varying chromosome and gene counts, evaluated using both chromosome-level and gene-level offload strategies on the NVIDIA Tesla V100 SXM2, NVIDIA A100 80GB, and AMD Instinct MI300X GPUs. Deployment-specific nuances such as Volta's constant-memory cliffs, Ampere's L2 persistence and cp.async, CDNA 3's Infinity Cache and XCD occupancy are addressed to ensure high performance of these platforms. Results reveal gene-parallel offload achieved geometric-mean speedups of 90×, 136×, and 155× over a single CPU core on the V100, A100, and MI300X, respectively, and 12×, 17×, and 16.6× over 72 host threads. Furthermore DetermineElite, the O(Nₚ) selection of the generation-best chromosome, is found to be better suited to the host than to the device.