sbx.bend source
sbx.bend on the hub · documented module
# Simulated Binary Crossover — C# Unsga3.Operators.Crossover.SimulatedBinaryCrossover.# Defaults match C#: η = 30, pair probability = 1.0 (Deb & Agrawal).# Per-variable walk peels x1 / x2 / box intervals together (guide: the# list is the shape a flat loop walks). Same RNG order as the old# index + List.get / set_var_at loop; children are built once at the end.import Baseimport ./individual.bend as Indimport ./bounds.bend as Boundsimport ./rng.bend as Rngimport ./util.bend as Utiltype Sbx is Data: MkSbx{ e: F32 p: F32 }def mk(+e: F32, +p: F32) -> Sbx: MkSbx{e, p}def default() -> Sbx: MkSbx{30.0, 1.0}def eta(op: Sbx) -> F32: match op: case MkSbx{e, p}: edef probability(op: Sbx) -> F32: match op: case MkSbx{e, p}: pdef child1(trip: Rng.State & Ind.Individual & Ind.Individual) -> Ind.Individual: (rng, c1, c2) = trip c1def child2(trip: Rng.State & Ind.Individual & Ind.Individual) -> Ind.Individual: (rng, c1, c2) = trip c2def near(+x1: F32, +x2: F32) -> Bool: F32.is_lt(F32.abs(F32.sub(x1, x2)), 1.0e-14)# C#: if rand <= 1/alpha then (rand*alpha)^(1/(η+1)) else (1/(2-rand*alpha))^(1/(η+1)).def beta.pick(+rand: F32, +alpha: F32, +inv: F32, lo: Bool) -> F32: match lo: case True{}: F32.pow(F32.mul(rand, alpha), inv) case False{}: F32.pow(F32.div(1.0, F32.sub(2.0, F32.mul(rand, alpha))), inv)def beta(+rand: F32, +alpha: F32, +inv: F32) -> F32: beta.pick(rand, alpha, inv, F32.is_le(rand, F32.div(1.0, alpha)))def close_heads(xs: List<&2, F32>, ys: List<&2, F32>) -> Bool: match xs ys: case +x <> xr +y <> yr: near(x, y) case Nil{} ys: False{} case x <> xs Nil{}: False{}# Draw the next per-var coin only when more variables remain.def advance(rng: Rng.State, rest: Nat) -> Rng.State: match rest: case 0n: rng case 1n+g: Rng.next_double(rng)def finish(+m: Nat, trip: Rng.State & List<&2, F32> & List<&2, F32>) -> Rng.State & Ind.Individual & Ind.Individual: (rng, xs, ys) = trip (rng, Ind.from_variables(xs, m), Ind.from_variables(ys, m))def done(rng: Rng.State, acc1: List<&2, F32>, acc2: List<&2, F32>) -> Rng.State & List<&2, F32> & List<&2, F32>: (rng, List.reverse(&2, F32, acc1), List.reverse(&2, F32, acc2))def skip_kind(skip: Bool, close: Bool) -> Nat: match skip: case True{}: 0n case False{}: match close: case True{}: 0n case False{}: 1n# Kind: 0n = copy heads (skip or close), 1n = SBX the heads.# One def so skip/cross are not mutually recursive with `loop`.def loop.go( fuel: Nat, kind: Nat, xs1: List<&2, F32>, xs2: List<&2, F32>, ivs: List<&2, Bounds.Interval>, +eta: F32, rng: Rng.State, acc1: List<&2, F32>, acc2: List<&2, F32>) -> Rng.State & List<&2, F32> & List<&2, F32>: match fuel kind xs1 xs2 ivs: case 0n k a b c: done(rng, acc1, acc2) case 1n++f 0n +x1 <> +rest1 +x2 <> +rest2 +iv <> ivrest: +rng2 = advance(rng, f) loop.go( f, skip_kind(F32.is_gt(Rng.last_double(rng2), 0.5), close_heads(rest1, rest2)), rest1, rest2, ivrest, eta, rng2, x1 <> acc1, x2 <> acc2 ) case 1n++f 1n+p +x1 <> +rest1 +x2 <> +rest2 +iv <> ivrest: +lo = Bounds.lo(iv) +hi = Bounds.hi(iv) +gt = F32.is_gt(x1, x2) +a = Bool.pick(F32, gt, x2, x1) +b = Bool.pick(F32, gt, x1, x2) +delta = F32.sub(b, a) +rng_a = Rng.next_double(rng) +rand = Rng.last_double(rng_a) +inv = F32.div(1.0, F32.add(eta, 1.0)) +neg = F32.neg(F32.add(eta, 1.0)) +alpha1 = F32.sub(2.0, F32.pow(F32.add(1.0, F32.div(F32.mul(2.0, F32.sub(a, lo)), delta)), neg)) +alpha2 = F32.sub(2.0, F32.pow(F32.add(1.0, F32.div(F32.mul(2.0, F32.sub(hi, b)), delta)), neg)) +c1v = F32.clamp(F32.mul(0.5, F32.sub(F32.add(a, b), F32.mul(beta(rand, alpha1, inv), delta))), lo, hi) +c2v = F32.clamp(F32.mul(0.5, F32.add(F32.add(a, b), F32.mul(beta(rand, alpha2, inv), delta))), lo, hi) +rng_b = Rng.next_double(rng_a) +sw = F32.is_gt(Rng.last_double(rng_b), 0.5) +n1 = Bool.pick(F32, sw, c2v, c1v) +n2 = Bool.pick(F32, sw, c1v, c2v) +rng_c = advance(rng_b, f) loop.go( f, skip_kind(F32.is_gt(Rng.last_double(rng_c), 0.5), close_heads(rest1, rest2)), rest1, rest2, ivrest, eta, rng_c, n1 <> acc1, n2 <> acc2 ) case 1n++f k Nil{} b c: done(rng, acc1, acc2) case 1n++f k a <> as Nil{} c: done(rng, acc1, acc2) case 1n++f k a <> as b <> bs Nil{}: done(rng, acc1, acc2)def loop( fuel: Nat, skip: Bool, close: Bool, +eta: F32, xs1: List<&2, F32>, xs2: List<&2, F32>, ivs: List<&2, Bounds.Interval>, rng: Rng.State, acc1: List<&2, F32>, acc2: List<&2, F32>) -> Rng.State & List<&2, F32> & List<&2, F32>: loop.go(fuel, skip_kind(skip, close), xs1, xs2, ivs, eta, rng, acc1, acc2)def start( +eta: F32, +x1s: List<&2, F32>, +x2s: List<&2, F32>, +box: Bounds.Box, rng: Rng.State, +m: Nat, n: Nat) -> Rng.State & Ind.Individual & Ind.Individual: match n: case 0n: (rng, Ind.from_variables(x1s, m), Ind.from_variables(x2s, m)) case 1n+f: +rng2 = Rng.next_double(rng) finish( m, loop( 1n+f, F32.is_gt(Rng.last_double(rng2), 0.5), close_heads(x1s, x2s), eta, x1s, x2s, Bounds.intervals_of(box), rng2, Nil{}, Nil{} ) )def maybe( +eta: F32, +x1s: List<&2, F32>, +x2s: List<&2, F32>, +box: Bounds.Box, rng: Rng.State, +m: Nat, +n: Nat, skip: Bool) -> Rng.State & Ind.Individual & Ind.Individual: match skip: case True{}: (rng, Ind.from_variables(x1s, m), Ind.from_variables(x2s, m)) case False{}: start(eta, x1s, x2s, box, rng, m, n)def draw( +eta: F32, +prob: F32, +x1s: List<&2, F32>, +x2s: List<&2, F32>, +box: Bounds.Box, rng: Rng.State, +m: Nat, +n: Nat) -> Rng.State & Ind.Individual & Ind.Individual: +rng2 = Rng.next_double(rng) maybe(eta, x1s, x2s, box, rng2, m, n, F32.is_gt(Rng.last_double(rng2), prob))# p=0 copies parents before any NextDouble. Matches C# children when# pair probability is 0 (every draw is > 0). Bit-zero is definitional# on the 0.0 literal; F32.is_gt stays off this path.def draw_or_copy( +eta: F32, +prob: F32, +x1s: List<&2, F32>, +x2s: List<&2, F32>, +box: Bounds.Box, rng: Rng.State, +m: Nat, +n: Nat, zero: Bool) -> Rng.State & Ind.Individual & Ind.Individual: match zero: case True{}: (rng, Ind.from_variables(x1s, m), Ind.from_variables(x2s, m)) case False{}: draw(eta, prob, x1s, x2s, box, rng, m, n)def crossover( +op: Sbx, +p1: Ind.Individual, +p2: Ind.Individual, +box: Bounds.Box, rng: Rng.State) -> Rng.State & Ind.Individual & Ind.Individual: +x1s = Ind.variables(p1) +x2s = Ind.variables(p2) +m = Bounds.n_obj(box) +prob = probability(op) draw_or_copy( eta(op), prob, x1s, x2s, box, rng, m, Bounds.n_var(box), Util.f32_is_zero(prob) )