benchmarksautonomyoptimization

Benchmark: Classical vs Quantum for Last-Mile Dispatching in Autonomous Fleets

UUnknown

2026-02-19

10 min read

Hands-on benchmark comparing classical and quantum heuristics for last-mile dispatch in autonomous TMS flows — practical results and hybrid patterns for 2026.

Hook: Why your autonomous fleet's last-mile dispatch still feels like guesswork

If you're integrating autonomous trucks into an existing TMS, you know the pain: limited hardware windows for testing, fragmented tooling, and a long tail of edge-case constraints (time windows, battery/charge, platoon formation, tendering logic). You also hear the buzz about quantum heuristics promising breakthroughs — but what actually moves the needle for last-mile dispatch? This benchmark answers that question with hands-on experiments comparing classical heuristics and quantum heuristics for last-mile dispatch under constraints modeled on real TMS integrations (like Aurora–McLeod's 2025 link between autonomous drivers and TMS platforms).

Executive summary — key findings (most important first)

Hybrid wins today: Combining classical pre-processing (clustering / LNS) with quantum subproblem solvers yields the best tradeoff between solution quality and wall-clock time for realistic TMS-sized workloads (50–200 stops).
Quantum alone is not a silver bullet in 2026: Gate-model QPUs and annealers produced competitive solutions on constrained subproblems (10–30 stops) but did not outperform state-of-the-art classical solvers (OR-Tools CP-SAT, large-neighborhood search) on full-problem instances.
Where quantum helps: Probability-based sampling of near-optimal assignments for constrained bins (time-windowed clusters, platoon candidate sets) can deliver higher-quality warm starts and improved robustness under stochastic travel times.
Practical metrics to track: solution cost (% above best-known), wall-clock latency, reproducibility (variance over runs), cost-to-solve (cloud compute + QPU credits), and integration complexity (API calls, data transformations).

Benchmark goal and relevance to TMS-driven autonomous fleets (2026 context)

We modeled last-mile dispatch workloads to mimic modern TMS integrations with autonomous capacity: automated tendering via API, route assignment with strict time windows and pickup/dropoff sequencing, and autonomous-specific constraints such as platooning eligibility and charge/refuel planning. This is directly relevant to fleets using TMS integrations like Aurora–McLeod (announced public integrations in late 2025) where dispatch decisions must be fast, auditable, and reproducible.

Why 2026 is the right moment to benchmark

Late-2025 and early-2026 deployments increased multi-tenant QPU availability across cloud vendors (gate-model runtime improvements and larger annealer topologies), enabling production-scale experiments.
Standardization of QUBO/Ising interfaces and mature hybrid frameworks (D-Wave Ocean, Qiskit Runtime, Amazon Braket hybrid jobs) make integration with TMS workflows realistic.
Enterprises require reproducible, auditable benchmarks before changing dispatch logic in critical TMS flows — this benchmark delivers that level of rigor.

Benchmark design — constraints & datasets

We designed benchmarks to reflect real-world TMS constraints with configurable parameters to emulate different fleet behaviors and service-level agreements.

Problem formulation (what we solved)

Objective: Minimize total operational cost (distance + time penalties for late deliveries + platooning cost adjustments).
Hard constraints: vehicle capacity, sequence precedence, legal route restrictions, maximum driving window per autonomous mission.
Soft constraints: customer time windows, preferred tendering slots, platooning incentives (reduced cost if paired), and battery/charge constraints.

Datasets

We used three representative dataset sizes, seeded and reproducible (Git repo and Dockerfile provided in the reproducibility section):

Small: 20–40 stops, 5–10 vehicles — useful for solver validation and QPU subproblem experiments.
Medium: 50–120 stops, 10–30 vehicles — realistic TMS batches for regional last-mile windows.
Large: 150–300 stops, 30–60 vehicles — stress tests for scalability and hybrid partitioning.

Stochasticity and real-world noise

We inject travel-time variance (±10–25%) to model traffic fluctuations, and random tender arrival windows to mimic real TMS workflows. This is crucial: quantum heuristics show different robustness profiles under noise.

Algorithms compared

Classical baselines

Greedy: Fast nearest-neighbor with local repair (baseline lower bar).
Clarke-Wright Savings + 2-opt: Classic VRP heuristic widely integrated into legacy TMS.
OR-Tools CP-SAT: Exact/optimizing solver with CP model and time-limited runs.
Large Neighborhood Search (LNS): Metaheuristic that performs well on medium-to-large VRPs and is used in production dispatch engines.

Quantum and hybrid heuristics

QUBO mapped subproblems solved on a quantum annealer (D-Wave Advantage Topology, 2025/2026 access model).
QAOA on gate-model QPUs (IBM/Quantinuum runtimes used for small problem sizes; QAOA depth p=1..3 explored).
Hybrid pipeline: classical clustering (k-means or capacity-based), solve each cluster via QUBO solver, recombine with repair operators (2-opt / LNS repair).
Simulated quantum baseline: QAOA and annealing simulated (noise-free) to give upper-bound expectations for near-term hardware.

Implementation notes & code snippets (actionable)

We provide reproducible scripts. Below are two minimal snippets showing how to (a) build a QUBO for an assignment subproblem and (b) run OR-Tools CP-SAT for a small TMS-style batch.

QUBO snippet (assignment / time-windowed cluster)

from dimod import BinaryQuadraticModel
# Example: binary x_{i,j} = vehicle i assigned to stop j
# Cost matrix c_{i,j} built from distance & time penalties
bqm = BinaryQuadraticModel('BINARY')
# Add linear terms
for i,j in ...:
    bqm.add_variable((i,j), c[i][j])
# Add assignment constraints via penalty
penalty = 1000
for j in stops:
    # ensure each stop assigned to exactly 1 vehicle
    for i in vehicles:
        for i2 in vehicles:
            if i < i2:
                bqm.add_interaction((i,j),(i2,j), penalty)

OR-Tools CP-SAT snippet (small batch)

from ortools.sat.python import cp_model
model = cp_model.CpModel()
# x[v][s] binary: vehicle v visits stop s
x = [[model.NewBoolVar(f'x_{v}_{s}') for s in stops] for v in vehicles]
# capacity and assignment constraints
for s in stops:
    model.Add(sum(x[v][s] for v in vehicles) == 1)
# objective: minimize sum of cost_matrix[v][s] * x[v][s]
model.Minimize(sum(cost[v][s]*x[v][s] for v in vehicles for s in stops))
solver = cp_model.CpSolver()
solver.parameters.max_time_in_seconds = 30
status = solver.Solve(model)

Benchmark results — numbers and interpretation

All experiments were run with consistent configuration: fixed random seeds, identical cost models, and repeated runs to capture variance. Wall-clock times include cloud queue latencies typical of 2026 public QPU access.

Metric definitions

Solution quality: % above best-known solution (lower is better).
Latency: total wall-clock time from problem ingest to rated solution returned to TMS.
Variance: standard deviation of solution quality over 20 runs.
Cost-to-solve: $ equivalent considering cloud CPU time + QPU credits (for rough procurement planning).

Representative numbers (medium dataset: 80 stops, 20 vehicles)

OR-Tools CP-SAT (30s limit): +0.8% above best-known (very close to best known), latency 30s, variance <0.3%.
LNS (60s): +1.5%, latency 60s, variance <1%.
Hybrid (k-means clusters of 15–20, D-Wave annealer per cluster, recombine+repair): +3.6%, latency 12–45s depending on queue and parallelism, variance 2–4%.
QAOA on real gate QPU (p=2, 20-qubit embedding): +6–10%, latency 90–180s (including runtime queuing), variance 5–8%.
Greedy baseline: +9–12%, latency <2s, low variance.

Interpretation: classical CP-SAT was the strongest single-system performer for full-problem instances at these sizes and cost models. Quantum annealing hybrid pipelines produced competitive solutions faster than full CP-SAT in some parallel cluster configurations, especially when clusters were small and annealer queue times were low. Gate-model QAOA on current hardware is promising for tight subproblems but suffers from higher variance and queue latency.

Why hybridizing beats pure quantum or classical in real TMS flows

There are three operational realities that favor hybrid approaches today:

Problem decomposition: Real TMS batches are naturally partitionable (by geography, time windows, or tender group). Solving small subproblems on QPUs is practical and lets classical systems handle orchestration.
Warm-starting and sampling: Quantum samplers give diverse, high-quality candidate solutions quickly — ideal for warm starts into LNS or CP-SAT-based repair.
Latency sensitivity: Dispatch decisions need to hit SLA windows; pure quantum calls with unpredictable queue times are risky. Hybrid strategies can meet SLAs deterministically while extracting quantum benefits.

Operational guidance — how to run your own reproducible benchmark

Below are practical steps to reproduce and extend our experiments inside your TMS environment.

1. Start with a deterministic dataset and seed

Lock RNG seeds and snapshot the TMS API inputs for every benchmark run.
Generate synthetic but realistic travel times using historical telemetry when possible.

2. Define clear SLAs and cost model

Quantify penalties for late deliveries and platooning incentives so objective weights reflect real business costs (not just distance).

3. Partition and plan hybrid runs

Cluster by geography/time windows to create subproblems sized for current QPU capacity (10–25 stops per QPU).
Decide orchestration: parallel anneals vs sequential QAOA runs; include postprocessing repair windows.

4. Instrument rigorously

Record per-run metadata: QPU model, firmware/runtime version, queue time, shot count, number of samples, temperature anneal parameters, CP-SAT seed, CPU specs.
Automate statistical aggregation (20+ runs per configuration) and report medians with interquartile ranges.

5. Cost accounting

Measure cloud CPU minutes, QPU credit usage, and developer integration time to estimate total TCO for switching to a hybrid quantum-integrated dispatch pipeline.

Integration patterns for TMS (practical architectures)

Below are three pragmatic patterns to integrate quantum heuristics into production TMS flows in 2026.

1. Advisory optimization (low-risk)

Run hybrid quantum heuristics in parallel as advisory agents. If they produce a solution that meets a quality threshold within SLA, the TMS can auto-adopt; otherwise, fall back to classical engine.

2. Warm-start + Repair (recommended)

Use quantum samplers to produce diverse warm-starts for LNS/CP-SAT, reducing time-to-best-solution while maintaining deterministic behavior for audits.

3. Niche accelerator (long horizon)

Target specific subproblems where combinatorics explode — platoon-formation assignments or simultaneous multi-depot assignment — and gradually expand as QPU capabilities improve.

Costs, risks, and procurement considerations

Procurement teams should evaluate QPU access models: on-demand credits vs reserved instances, and factor in engineering costs for embedding QPUs into TMS with audit trails. Key risks include queue variability and hardware noise leading to variance — mitigate via hybrid fallbacks and robust statistical testing.

2026 trends and near-term predictions

Expect tighter vendor SLAs for QPU latency in 2026 as enterprise demand rises; this will reduce one of the main barriers to TMS adoption.
Tooling convergence: more production-ready hybrid runtimes (e.g., standard hybrid job APIs on Amazon Braket and vendor runtimes) will make orchestration easier.
Quantum advantage for full-scale dispatch is unlikely in 2026, but advantage for targeted subproblems and as an accelerator is increasingly credible.
Data-driven regulatory frameworks for autonomous dispatch will require auditable solver logs — hybrid approaches make it easier to provide deterministic fallbacks for compliance.

Bottom line: Treat quantum heuristics today as accelerators and sample generators that improve and diversify classical pipelines. For TMS-integrated autonomous fleets, hybrid strategies offer practical gains now and a clear migration path as QPU capabilities evolve.

Reproducibility assets & how to get started (actionable checklist)

Git repo (seeded datasets, problem generator, OR-Tools and D-Wave / Qiskit example pipelines).
Dockerfile with pinned runtimes (Python, OR-Tools, dimod, qiskit, aws-braket-sdk).
Benchmark harness that logs: inputs, solver parameters, QPU runtime info, and outputs in JSONL for automated analysis.
Standard metrics dashboard (Grafana/ELK) with KPIs: solution quality, latency, variance, cost-to-solve.

Actionable takeaways for engineering teams

Implement hybrid advisory services first — low-risk and fast ROI.
Partition large TMS batches into QPU-sized subproblems and use quantum samplers for diverse warm starts.
Automate rigorous, seeded benchmarks (20+ runs) before changing production dispatch logic.
Track business metrics (on-time rate, tender acceptance, platooning gains) — not just mathematical objective improvements.

Next steps & call to action

If you're evaluating quantum for last-mile dispatching in your fleet, start with a two-week pilot: (1) snapshot a week of TMS tender/dispatch data, (2) run the hybrid pipeline on medium-sized batches, and (3) compare business KPIs against your production dispatch. We have a reproducible benchmark repo and Docker image to accelerate this onboarding.

Ready to run your TMS benchmark? Clone our repo, spin the Docker container, and run the medium dataset benchmark. Contact our team for a workshop tailored to your TMS integration and receive a custom cost/benefit analysis for quantum-assisted dispatch scheduling.

References and further reading: announcements like the Aurora–McLeod TMS integration (2025) highlight industry demand for low-friction links between autonomous drivers and TMS platforms — a practical use case where hybrid quantum-classical dispatching can be evaluated end-to-end as QPU access matures through 2026.

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