The field of optimization and scheduling continually seeks substantial advancements in technology. Recently, two significant concepts have emerged: the application of GPUs (Graphics Processing Units) in combinatorial optimization and the potential advantages offered by quantum computing.
Federico Pagnozzi, algorithm engineer at Solvice, conducted a detailed analysis of these technologies, revealing findings that are more measured and nuanced than the prevailing excitement indicates.
Below is a summary of some of the conclusions of his research.
At first glance, GPU-based solvers seem highly attractive. Leveraging the massive parallelism of thousands of GPU cores, solutions can be generated at an unprecedented speed. NVIDIA's CUOpt, for instance, promises to explore a much broader solution space simultaneously compared to traditional metaheuristics running on CPUs. This might intuitively seem like a shortcut to better solutions.
However, the reality is more complex. The methods used to generate new solutions used by GPU cores are inherently simpler due to the architecture's "Single Instruction, Multiple Data" (SIMD) model. Each tiny core runs simplified operations, which means the candidate solutions are created by less sophisticated methods compared to those crafted by a CPU-based solver. To a certain extent it's quantity over quality.
Moreover, the hardware requirements for serious GPU-based optimization are daunting. Running CUOpt effectively demands an NVIDIA A100 GPU, which costs upward of $20,000 depending on the model — and that's without accounting for the rest of the server infrastructure. Cloud access is theoretically possible, but practical pricing remains opaque, and GPU resources are heavily contested by the AI boom. It's a high-cost, high-competition landscape, hardly ideal for scalable optimization services.
The limitations don't end there. CUOpt supports only relatively simple VRP (Vehicle Routing Problem) features: basic time windows, single shifts, capacities, pickups, deliveries, and job priorities. More complex constraints like job relations are out of scope, suggesting that while GPUs can generate many solutions quickly, they struggle with richer, real-world problem modeling.
If GPU solvers seem premature, quantum computing for optimization looks even more so. Companies are beginning to tout quantum optimization capabilities, particularly around QUBO (Quadratic Unconstrained Binary Optimization) problems, which quantum architectures are well-suited to address.
The dream is alluring: imagine translating a combinatorial optimization problem into a QUBO form, letting a quantum computer's qubits superpose and entangle their way to a global optimum, exploiting quantum tunneling to escape local minima effortlessly.
But today's reality paints a very different picture. Current "quantum solvers" largely fall back on traditional methods for anything beyond toy problems. Even companies positioning themselves as quantum pioneers recommend users solve real-world problems with classical, mixed-integer programming solvers for now. The translation of rich scheduling problems (like VRPs) into a pure QUBO formulation is not just theoretically challenging; it's practically infeasible without major simplifications that gut the original problem's nuance.
Even if theoretical formulations existed, today's quantum computers may not have enough qubits, nor the necessary fully connected architectures, to handle anything but the smallest of instances. The promise remains firmly in the "maybe 20 years from now" category — a gamble some companies are willing to make, but one that must be recognized for what it is: a gamble, not a viable production technology.
Both GPU-accelerated and quantum optimization approaches offer tantalizing visions of the future. But for businesses and practitioners working in scheduling and combinatorial optimization today, they remain solutions in search of a problem — or at least in search of hardware, theory, and economic models that can deliver real-world value.
The smart move now is to continue refining robust, adaptable optimization techniques that work on accessible hardware, with rich problem modeling capabilities and predictable performance. Future technologies will undoubtedly reshape the optimization landscape, but prudence demands we distinguish between what's possible today and what remains, for now, firmly in the realm of speculation.
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