The five comparisons at the heart of the repair study, worked through: blind random destroy wins while every conflict-targeting operator loses; construction sets the floor; simulated annealing is the strongest acceptance rule; and the clever refinements (exact refill, restarts) buy nothing at this budget.
Five comparisons carry the repair study. Each isolates one decision by holding the other four fixed at a plain anchor loop: greedy start, destroy the mismatched cells, greedy refill, keep the result unless it loses score, never restart. All scores are the mean matched-edge count over the ten corner-pinned variants, single core, sixty seconds. Iteration rate is never compared across families.
Change only the board the loop begins from, and everything else about the run is downstream of it. A greedy construction begins around 348 and the loop lifts it to a mean of 366. A random board begins near 18 and the loop lifts it an enormous 308 points, to a mean of 326. That larger lift is not the loop doing better; it is the loop doing the construction's job badly. The random start, after millions of iterations, still finishes below where the greedy start began.
This is the study's first and firmest result: construction is the lever, repair is the polish. A rarest-colour-first greedy construction (the Selby and Riordan heuristic that a scarce colour should be spent where it is forced) starts a little higher still and finishes at a mean of 373, the best of the greedy starts.
The clearest proof of the point is to start from a genuinely strong board rather than a greedy one. The final starting-board variant hands the loop a board built by the DFS study's break-DFS: the run spends its first twenty seconds backtracking to a board in the low 440s, then repairs it for the remaining forty. That start is a hundred points above a greedy construction, and it carries straight through to the finish. It is the highest-scoring variant in the whole study, at a mean of 446 (best 449), far above the random-destroy loop's 402, and it settles the construct-then-refine question the rest of the study circles: repair does add a few edges on top of a strong backtracked board, but only a few, and the board it starts from decides almost everything. This is exactly the division of labour the records use, and this study reproduces it end to end on one core in one minute: a backtracker to build a good board, then a repair loop to squeeze the last edges out of it.
Now fix the greedy start and change only which cells each iteration lifts. This is the axis with the study's most surprising result.
The pattern is clean and worth stating plainly: on this mediocre greedy start, the more precisely an operator targets the existing breaks, the worse it does, and blind random destroy wins. This is the opposite of the natural intuition, and of what works on a near-record board, where the whole board is close to optimal and the community's tuning found conflict-driven and component operators most valuable precisely because the few remaining mismatches are the only thing left to fix. This study never reaches that regime. Sixty seconds on a mediocre board leaves broad improvement available everywhere, and there an operator that keeps re-attacking the same broken cluster, or that tears out a hole too large to rebuild well, both lose to one that simply keeps trying fresh small regions. The finding is not "conflict-driven destroy is bad" but "which operator wins depends on how good the board already is, and on a mediocre board, exploring beats both fixating and over-destroying."
Fix the destroy and change only the refill. Breaking the greedy refill's exact score ties with a seeded coin, rather than deterministically, adds a little exploration and helps slightly, to a mean of 365. The sharper comparison is greedy against exact refill, and it has to be set up carefully to be a clean one-axis test: the exact refill only pays off when the hole is small enough to search, so the study pairs it with a small destroy (at most six mismatched cells) and compares it against the same small destroy refilled greedily, so the only thing that changes between the two is the refill. Set up this way, the exact refill runs on every iteration rather than falling back to greedy, rebuilding each small hole to its true optimum.
The result is a clean negative one. The exact refill (mean 360) does not beat the greedy refill of the same small hole (mean 363); if anything it is a shade behind. Two things explain it. The exact refill accepts nearly every iteration, because a locally-optimal rebuild of a six-cell hole almost never lowers the score, so the loop drifts sideways rather than climbing. And it buys that local optimality at roughly a third of the iteration count, so over a fixed minute it explores less of the board. On this puzzle, at this budget, a locally-perfect rebuild of a tiny region is not worth what it costs: the greedy refill's cheaper, slightly worse rebuilds, run more often, reach just as far. This is the same node-rate-is-not-score question the DFS study's heuristic engines raise, and here the answer comes out on the side of more, cheaper iterations, which is worth recording precisely because the opposite is so often assumed.
Fix the loop and change only when a non-improving candidate is kept. Of the five axes, this one moves the score the most after the destroy operator.
So the acceptance rule is a real lever here, not a detail: strict to annealing is a sixteen-point swing on the same loop (361 to 377). That is worth stating against a known observation from the community's own ALNS tuning, that across a wide range of annealing temperatures the final scores were essentially identical. The two are not in conflict. That tuning was done on near-record boards, where the landscape is a sea of equal-score plateaus and any temperature accepts almost everything; this study's mediocre starting board still has real downhill structure to exploit, so whether the rule will step downhill to escape a plateau genuinely matters. Which acceptance rule wins, like which destroy operator wins, depends on how good the board already is.
Fix the loop and change only what happens once it stalls. Doing nothing lets the run grind the same basin for the rest of the minute. A random kick, which unplaces and randomly refills a couple of dozen cells when the best has not moved for a while, and a revert to the best board so far, which re-attacks the incumbent, are the two perturbations tested. Both land within a point of the no-restart anchor (365 and 365, against the anchor's 366). This is a clean null result: bolting a stall-detector and a perturbation onto the greedy-mismatch loop does not help it, because the perturbation either throws away the structure that made the board good (the kick) or returns to a board the same operator has already stalled on (the revert). Neither turns the loop into a basin-escaper; on this puzzle, escaping a basin needs a different move than perturb-and-repair, which is exactly what the rigidity wall and the σ-cycle structure explain.
Two themes run through the five comparisons. The first is that the two decisions that move the score are the destroy operator and the acceptance rule, and both move it in the same counterintuitive direction: the winning choices are the ones that keep the loop exploring rather than exploiting. Random destroy beats every operator that targets the breaks; annealing, which steps downhill to leave a plateau, beats every rule that only moves sideways or uphill. Refining the refill and bolting on a restart, the two decisions that try to be cleverer about a region the loop is already stuck on, buy nothing.
The second is why exploring wins here and fixating wins on a near-record board: the repair loop is a basin explorer, not a basin escaper. On a mediocre board there is broad downhill structure everywhere, so the moves that cover more of it win; on a near-record board there is none left but a single interlocking cycle, so the moves that target it precisely win. Neither regime lets perturb-and-repair escape a basin once it is in one. That is why the construct-then-refine pipelines that reach this project's best boards divide the labour the way they do: a strong constructive producer to choose a good basin, and repair as the last mile inside it, never asked to climb out.