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Lean: - OptimizedRoute.lean: 2-opt route shorter than exactishRoute optimizedRoute cost: 345147 vs exactishRoute: 401666 (14.1% shorter) Proofs: optimizedRoute_length, optimizedRoute_shorter, costSavings_positive All via native_decide. lake build: 3571 jobs, 0 errors. Python: - scale_space_solver.py: replaced Gaussian cost smoothing with cluster-based multi-scale optimization. Single-linkage clustering at each sigma, reduced TSP on representatives, expand + 2-opt polish. Fixed voltage/scale mapping.
42 lines
1.4 KiB
Text
42 lines
1.4 KiB
Text
import Semantics.RouteCost
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/-!
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# Optimized Route Proof
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2-opt local search over exactishRoute finds a strictly cheaper permutation
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of the same 39 nodes. The cost comparison is over `Nat` (Q16.16-scaled
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fixed-point arithmetic), so `native_decide` closes the inequality gate.
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Route discovered by 2-opt: cost 345147 < 401666 (exactishRoute).
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-/
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namespace Semantics.RouteCost
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/-- The 2-opt optimized route: same 39 nodes, different order. -/
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def optimizedRoute : List RouteNode :=
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[ nF01, nF02, nF03, nS1, nB2, nS2, nF04, nF05, nF06, nF07
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, nM2, nM3, nF12, nF11, nM5, nM1, nB3, nB1, nS4, nB4
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, nS3, nF08, nF09, nF10, nM4, nF37, nF34, nF24, nF17, nF16
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, nG0, nB5, nB8, nB7, nB6, nS5, nX3, nX2, nX1
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]
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/-- Both routes visit 39 nodes. -/
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theorem optimizedRoute_length :
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optimizedRoute.length = exactishRoute.length := by
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native_decide
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/-- The optimized route is strictly cheaper than the exactish route.
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Cost: 345147 < 401666 (Q16.16-scaled Nat). -/
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theorem optimizedRoute_shorter :
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routeCostSum optimizedRoute < routeCostSum exactishRoute := by
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native_decide
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/-- Cost savings from 2-opt optimization (Q16.16-scaled Nat). -/
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def costSavings : Nat :=
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routeCostSum exactishRoute - routeCostSum optimizedRoute
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theorem costSavings_positive : costSavings > 0 := by
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unfold costSavings
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exact Nat.sub_pos_of_lt optimizedRoute_shorter
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end Semantics.RouteCost
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