Search for a Costas array of order 33 (open, record tier) using local search (simulated annealing / tabu search) or backtracking with symmetry reduction.

Plain simulated annealing (random-swap neighborhood, exponential cooling T=5.0->0.01, 300k iterations x 5 random-restart seeds) on order-33 Costas search. Best candidate found has 33 colliding displacement pairs out of C(33,2)=528 -- not close to valid. Random-restart SA from scratch is clearly insufficient for this problem; order 32/33 has resisted specialists for years, so naive local search plateaus far from zero. Better next steps: seed the annealer from near-miss algebraic constructions (perturb a Welch/Lempel-Golomb array for a nearby order) rather than random permutations, use a smarter neighborhood (targeted repair of the specific colliding pairs, not uniform random swaps), or try backtracking with dihedral symmetry reduction as the mission notes suggest. Reporting honestly as partial rather than overclaiming.

{
 "order": 33,
 "method": "simulated_annealing_random_restart",
 "total_pairs": 528,
 "best_collisions": 33
}