--orders: route several connection orders in parallel, keep the best

The default order is always one of the candidates, so the result is
never worse than a plain run; ties go to the earlier candidate.

src/freeroute/route/orders.py

@@ -0,0 +1,67 @@
+"""Route one board in several connection orders at once and keep the best.
+
+Which connection routes first moves the result on a crowded board by several
+connections either way, and no single order wins everywhere. Routing a few
+orders in parallel processes and keeping the one that leaves the fewest
+connections unrouted costs cores, not wall time.
+
+Without a seed the candidates are the default order and seeds 0 to N-2, so the
+result is never worse than a plain run. With seed S they are seeds S to S+N-1.
+Ties go to the earlier candidate, so the choice is deterministic.
+"""
+
+from __future__ import annotations
+
+from concurrent.futures import ProcessPoolExecutor
+import os
+
+from freeroute.dsn import parse_dsn
+from freeroute.ses import RoutingResult
+
+from .pipeline import build_exact_routing_result, build_routing_result
+
+
+def candidate_seeds(orders: int, seed: int | None = None) -> list[int | None]:
+    orders = max(int(orders), 1)
+    if seed is None:
+        return [None, *range(orders - 1)]
+    return list(range(seed, seed + orders))
+
+
+def score(result: RoutingResult) -> tuple[int, int]:
+    """Connections left open, then those left to a zone fill: lower is better."""
+    missing = sum(1 for u in result.unrouted if not u[3])
+    return missing, len(result.unrouted) - missing
+
+
+def route_once(dsn_text: str, engine: str, options: dict, seed: int | None) -> RoutingResult:
+    dsn = parse_dsn(dsn_text)
+    if engine == "exact":
+        return build_exact_routing_result(dsn, seed=seed, **options)
+    if engine == "grid":
+        return build_routing_result(dsn, seed=seed, **options)
+    raise ValueError(f"routing orders are not supported by the {engine} engine")
+
+
+def best_of_orders(
+    dsn_text: str,
+    engine: str,
+    options: dict,
+    *,
+    orders: int,
+    seed: int | None = None,
+    jobs: int | None = None,
+) -> tuple[RoutingResult, int | None, list[tuple[int | None, tuple[int, int]]]]:
+    """Route ``orders`` orders and return the best result, the seed that made
+    it (None for the default order), and every candidate's seed and score."""
+    seeds = candidate_seeds(orders, seed)
+    if len(seeds) == 1:
+        result = route_once(dsn_text, engine, options, seeds[0])
+        return result, seeds[0], [(seeds[0], score(result))]
+    jobs = max(1, min(jobs or os.cpu_count() or 1, len(seeds)))
+    with ProcessPoolExecutor(jobs) as pool:
+        futures = [pool.submit(route_once, dsn_text, engine, options, s) for s in seeds]
+        results = [f.result() for f in futures]
+    scores = [score(r) for r in results]
+    best = min(range(len(seeds)), key=lambda i: (scores[i], i))
+    return results[best], seeds[best], list(zip(seeds, scores, strict=True))