QAOA for Fleet Maintenance Scheduling

Scheduling maintenance across a breeder fleet is an NP-hard constraint problem; we map it to Ising form and benchmark QAOA against classical solvers.

The scheduling problem

A fleet of breeder units (FOAK, then NOAK, then BOAK and beyond) must schedule maintenance windows subject to coupled constraints: keep enough units available for firm output, respect crew and spare-part limits, and avoid clustering outages of tritium-producing units. This is a constrained combinatorial optimization, NP-hard in general and solved today by classical mixed-integer and heuristic methods.

# Binary var x_{u,w} = 1 if unit u takes maintenance in window w
minimize  sum_{u,w} c_{u,w} x_{u,w}         # preference / risk cost
s.t.  sum_w x_{u,w} = 1        for all u    # each unit serviced once
      sum_u x_{u,w} <= K_w                  # crew capacity per window
      availability(w) >= A_min  for all w   # firm-output floor

Mapping to Ising for QAOA

Hard constraints become quadratic penalty terms so the whole objective is a single Ising/QUBO cost, the form QAOA and annealers consume. Penalty weights must dominate the objective scale so violating a constraint is never favorable.

H = sum_{u,w} c_{u,w} x_{u,w}
  + P1 * sum_u ( sum_w x_{u,w} - 1 )^2        # one-window penalty
  + P2 * sum_w ( relu( sum_u x_{u,w} - K_w ) )^2  # capacity penalty
# choose P1,P2 >> max cost; then substitute x = (1 - z)/2 for spins z

Honest evaluation protocol

• Every instance is solved classically (MILP / simulated annealing) to get a baseline and, where feasible, a proven optimum.
• QAOA is scored on approximation ratio and wall-clock against that baseline, at matched problem sizes.
• Constraint satisfaction is checked exactly; a physically infeasible schedule is discarded regardless of cost.

To date, classical solvers handle realistic fleet sizes comfortably, so QAOA here is exploratory. Its interest grows only if fleet and constraint counts scale past where classical methods degrade, an open empirical question we test rather than assume. See campaign scheduling for the intra-machine analogue.