diff --git a/Control/Metaheuristics.hs b/Control/Metaheuristics.hs new file mode 100644 --- /dev/null +++ b/Control/Metaheuristics.hs @@ -0,0 +1,207 @@ +{-# LANGUAGE MultiParamTypeClasses, AllowAmbiguousTypes #-} + +module Control.Metaheuristics( + HasQuality,quality, + -- * Termination and post processing + takeWhileProperty, + -- * Execution of search processes + openStreamMapArrow, + executeMetaheuristic, + -- * Simple lifting and injection + mapArrow, + inject, + -- * General stream arrow combinators + chunk, + dechunk, + stretch, + doMany, + delay, + window, + fanAll, + newArrow, + -- * Selection and filtering + improvingFilter, + improving, + selectBest, + selectRandom, + diffFilter, + -- * Escape Strategies + escapeStrategy, + replace, + restart, + uniformChoice, + + -- * SA cooling strategies + logCooling, + linCooling, + geoCooling, + + -- * Metaheuristic algorithms + iterativeImprover, + stochasticIterativeImprover, + simpleTABU, + tabu, + mergeStochasticAndTemperature, + simulatedAnnealing, + breed1,ga, + populationPattern,degrade,aco + ) where + +import Control.Arrow +import Data.Stream (Stream(..),(<:>)) +import qualified Data.Stream as S +import Control.Arrow.Transformer.Stream (StreamArrow(..),StreamMap(..)) +import System.Random +import qualified Data.List as L + +class Num v=>HasQuality f v where + quality :: f->v + +takeWhileProperty :: ([a]->Bool)->Int ->Stream a->[a] +takeWhileProperty term sz input = twi' input + where + -- twi' :: Stream a->[a] + twi' xs = if term (S.take sz xs) + then S.take sz xs + else (S.head xs) : twi' (S.tail xs) + + +openStreamMapArrow :: StreamMap a b->Stream a->Stream b +openStreamMapArrow (StreamArrow f) = f + +executeMetaheuristic :: StreamArrow (->) b b->[b]->Stream b +executeMetaheuristic a x = let xs = S.prefix x (openStreamMapArrow a xs) in xs + +newArrow :: (Stream a->Stream b)->StreamMap a b +newArrow = StreamArrow + +mapArrow :: (a->b)->StreamMap a b +mapArrow f = StreamArrow (S.map f) + +inject :: Stream a->(a->b->c)->StreamMap b c +inject s f = StreamArrow (S.zipWith f s) + +chunk :: Int->StreamMap a [a] +chunk n = StreamArrow (f ) + where f ys = S.take n ys `S.Cons` (f $ S.drop n ys) + + +dechunk :: StreamMap [a] a +dechunk = StreamArrow (S.fromList . concat. S.toList ) + + +stretch:: Int->StreamMap sol sol +stretch n = StreamArrow + (S.fromList . concatMap (replicate n) . S.toList ) + + +doMany :: Int->StreamMap sol sol'->StreamMap sol sol' +doMany n f = stretch n >>> f + +delay::x->StreamMap x x +delay x=StreamArrow(S.Cons x) + +window :: Int->StreamMap sol [sol] +window n=StreamArrow(\xs->S.scan f [] xs) + where f qu x=if length qu==n then f (tail qu) x else qu++ [x] + +fanAll :: [StreamMap a b]->StreamMap a [b] +fanAll fs = StreamArrow (\xs->S.fromList $ L.transpose [S.toList (f xs) | f<-map openStreamMapArrow fs ]) + +improvingFilter :: Ord a=>StreamMap ([a],a) [a] +improvingFilter = StreamArrow $ S.map (\(xs,x)->filter (StreamMap a [a]->StreamMap a [a] +improving nF = nF &&& (StreamArrow id) >>> improvingFilter + +historyFilter :: Eq a => StreamMap ([a],[a]) [a] +historyFilter = mapArrow (\(n,h)->n L.\\ h) + +selectBest :: Ord a=>StreamMap [a] a +selectBest = StreamArrow $ S.map minimum + +selectRandom :: RandomGen g=>g->StreamMap [a] a +selectRandom seedG = StreamArrow (f seedG) + where f g xss = let xs = S.head xss + (i,g') = randomR (0,length xs-1) g + in xs !! i <:> f g' (S.tail xss) + + +replace :: Stream sol ->StreamMap sol sol +replace supply = StreamArrow (const supply) + +escapeStrategy :: StreamMap sol (Either sol sol)->StreamMap sol sol->StreamMap sol sol->StreamMap sol sol +escapeStrategy escapeTest s1 s2 = escapeTest >>> (s1 ||| s2) + +restart :: StreamMap sol (Either sol sol)->StreamMap sol sol->Stream sol->StreamMap sol sol +restart restartTest s1 solSupply = escapeStrategy restartTest s1 (replace solSupply) + +iterativeImprover :: Ord sol=>StreamMap sol [sol]->StreamMap sol sol +iterativeImprover neighbourhoodArrow = improving neighbourhoodArrow >>> selectBest + +stochasticIterativeImprover :: (Ord sol,RandomGen g)=>g->StreamMap sol [sol]->StreamMap sol sol +stochasticIterativeImprover g neighbourhoodArrow = improving neighbourhoodArrow >>> selectRandom g + +simpleTABU :: Ord sol=>StreamMap sol [sol]->Int->StreamMap sol sol +simpleTABU nF n = nF &&& (window n) >>> historyFilter >>> selectBest + +tabu :: Ord sol=>StreamMap sol [sol]->Int->StreamMap sol sol +tabu nF n = fanAll [ improving nF, + nF &&& window n >>> historyFilter, + nF] >>> mapArrow concat >>> mapArrow head + +mergeStochasticAndTemperature:: Floating v=>S.Stream v -> S.Stream v -> S.Stream v +mergeStochasticAndTemperature = S.zipWith (\r t ->1.0/t - log r) + +--diffChoice :: (Num a, Ord a, HasQuality f) => a -> (f, f) -> f +--diffChoice r (a,b) = if r >= quality a - quality b then b else a + +--sa :: HasQuality sol => StreamMap sol sol->S.Stream Double->S.Stream Double -> StreamMap sol sol +--sa mutate rs ts = (StreamArrow id)&&&mutate >>> inject (mergeStochasticAndTemperature rs ts) diffChoice + +diffFilter :: (Num a, Ord a, HasQuality f a) => a -> (f, [f]) -> [f] +diffFilter r (s,xs) = [x | x<-xs, r >= quality s - quality x] + +simulatedAnnealing :: (Floating v,Num v,Ord v, Ord sol, HasQuality sol v) =>StreamMap sol [sol] -> S.Stream v -> S.Stream v -> StreamMap sol sol +simulatedAnnealing neighbourhood rs ts = fanAll [ improving neighbourhood, + (StreamArrow id)&&&neighbourhood >>> inject (mergeStochasticAndTemperature rs ts) diffFilter, + mapArrow (:[]) ] >>> mapArrow concat >>> mapArrow head + +{-| A logarithmic cooling strategy intended for use within simulated annealing. Broadly the first value is + the starting temperature and the second a value between 0 and 1. -} +logCooling :: Floating b=>b->b->[b] +logCooling c d = map (\t->c / (log (t + d))) (iterate (+1) 1) + +{-| The most common cooling strategy for simulated annealing, geometric. The first value is the starting temperature, + the second a value between 0 and 1, the cooling rate. -} +geoCooling :: Floating b=>b->b->[b] +geoCooling startTemp tempChange = iterate (* tempChange) startTemp + +{-| Included for completeness, this is a cooling strategy for simulated annealing that is usually not very effective, + a linear changing strategy. The first value is the starting temperature the second is the value to increase it by + at each step. In order to have it reduce at each step, pass a negative value. +-} +linCooling :: Floating b=>b->b->[b] +linCooling startTemp tempChange= iterate (+ tempChange) startTemp + +breed1 :: RandomGen g=>StreamMap [sol] sol->g->StreamMap [sol] sol +breed1 recombine g1 = doMany 2 (selectRandom g1) >>> chunk 2 >>> recombine + +ga :: Int ->StreamMap sol (Either sol sol)->StreamMap sol sol ->StreamMap [sol] sol->StreamMap sol sol +ga popSize mutateTest mutate breed = chunk popSize >>> doMany popSize breed >>> mutateTest >>> (StreamArrow id ||| mutate) + + +uniformChoice :: RandomGen g=>Float->g->StreamMap sol (Either sol sol) +uniformChoice chance g = StreamArrow (S.fromList . f (randoms g) . S.toList) + where f (x:xs) (s:sols) | x(sol->pat)->StreamMap [pat] pat-> StreamMap sol pat +populationPattern popSize createPattern mergePattern=mapArrow createPattern>>>chunk popSize>>>mergePattern>>>stretch popSize + +degrade :: StreamMap a a -> StreamMap (a,a) a->StreamMap a a +degrade df mf = loop (second df >>> mf >>> (StreamArrow id &&& StreamArrow id)) + +aco :: pat->Int->(sol -> pat)->StreamMap [pat] pat ->StreamMap (pat, pat) pat->StreamMap pat pat ->StreamMap pat sol->StreamMap sol sol +aco defaultPattern popsize cfp mergePopulation mergePair df createsolution = mapArrow cfp >>> chunk popsize >>> mergePopulation >>> degrade (delay defaultPattern >>> df ) mergePair >>> stretch popsize >>> createsolution diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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But first, please read +. diff --git a/MetaheuristicsDemo/SimpleTSP.hs b/MetaheuristicsDemo/SimpleTSP.hs new file mode 100644 --- /dev/null +++ b/MetaheuristicsDemo/SimpleTSP.hs @@ -0,0 +1,112 @@ +module SimpleTSP where + +import qualified Data.Map as M +import qualified System.Random as R + +cityCoordinates :: [(Float,Float)] +cityCoordinates = [(8.39816197926126, 15.185014516132743), (5.805977666331062, 8.023032216008712), (16.714739233303042, 13.92861301975959), (17.78946373699672, 4.015830245456648), (14.957102430197795, 5.872523608300993), (3.9898709586837433, 8.971759629020063), (8.293182956694752, 15.09786669714841), (18.350802237395172, 4.276634196229338), (16.816723540931694, 1.7317842244869075), (1.8717215787226338, 0.88215954938345)] + +euclideanDistance :: (Float,Float)->(Float,Float)->Float +euclideanDistance (x1,y1) (x2,y2) = sqrt $ (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2) + +cityDistances :: M.Map (Int,Int) Float +cityDistances = M.fromList [((a,b),d a b) | a<-cities,b<-cities ] + where cities = [0..length cityCoordinates-1] + d i1 i2 = euclideanDistance (cityCoordinates !! i1) (cityCoordinates !! i2) + +edgeLength x = cityDistances M.! x + +data TSP = TSP [Int] Float deriving (Show,Eq) + +type TSPPAT = M.Map (Int,Int) Float + + +instance Ord TSP where + compare (TSP _ a) (TSP _ b) = compare a b + + + + +numCities (TSP x _) = length x + +mkTSP :: [Int]->TSP +mkTSP x = TSP x (tspValue x) + +tspValue :: [Int]->Float +tspValue ts = sum $ map edgeLength edges + where edges = (last ts,0): zip (0:ts) ts + +tspToPat :: TSP->TSPPAT +tspToPat (TSP ts _) = M.fromList (simPat edges) + where edges = (last ts,0): zip (0:ts) ts + val = sum $ map edgeLength edges + simPat [] = [] + simPat ((a,b):xs) = ((a,b),e):((b,a),e):simPat xs + where e=val/edgeLength (a,b) + +swapCities :: Int->Int->TSP->TSP +swapCities i1 i2 (TSP x _) = mkTSP (zipWith f x [0..]) + where f c i | i==i1 = x !! i2 + | i==i2 = x !! i1 + | otherwise = c + +adjacentNeighbourhood :: TSP->[TSP] +adjacentNeighbourhood x = [swapCities a b x | (a,b)<- zip ps (tail ps)] + where ps = [0..numCities x-1] + +nullPat :: TSPPAT +nullPat = M.empty + +degradePat :: TSPPAT->TSPPAT +degradePat t = M.mapMaybe f t + where f a | a<0.01 = Nothing + | otherwise = Just (a*0.9) + +mergePat :: TSPPAT->TSPPAT->TSPPAT +mergePat a b = M.unionWith (+) a b + +mergePats :: [TSPPAT]->TSPPAT +mergePats (x:xs) = foldl mergePat x xs + +createSol1 :: R.RandomGen g=>g->TSPPAT->TSP +createSol1 g p = mkTSP (f 0 [1..length cityCoordinates-1] (R.randoms g)) + where f currentCity [] _ = [] + f currentCity cityOpts (r:rs) = let vs = map (weight currentCity) cityOpts + s=sum vs * r + (xs,x,ys) = finder s (zip vs cityOpts) + in x:f x (xs++ys) rs + finder finalScore ((value,city):others) | valueg->TSPPAT->(TSP,g) +createSol g p = let (g1,g2) = R.split g in (createSol1 g1 p,g2) + +createSolutions g (p:pats) = let (a,b) = createSol g p in a:createSolutions b pats + +randomSolution :: R.RandomGen g=>g->(TSP,g) +randomSolution g = createSol g nullPat + +randomSolutions :: R.RandomGen g=>g->[TSP] +randomSolutions g = let (a,b) = randomSolution g in a:randomSolutions b + +recombineSolutions :: R.RandomGen g=>g->[TSP]->(TSP,g) +recombineSolutions g xs = createSol g (mergePats ps) + where ps= map tspToPat xs + + + +keyRandGen = R.mkStdGen 52 + + + +{- iteratedSols = f nullPat keyRandGen + where f p g = let (g1,g2) = R.split g + s = createSol1 g1 p + p2=mergePat (degradePat p) (tspToPat s) + in s:f p2 g2 + +test= Prelude.map tspValue $ take 10 $ iteratedSols -} + + diff --git a/MetaheuristicsDemo/test.hs b/MetaheuristicsDemo/test.hs new file mode 100644 --- /dev/null +++ b/MetaheuristicsDemo/test.hs @@ -0,0 +1,73 @@ +{-# LANGUAGE MultiParamTypeClasses,TypeSynonymInstances,FlexibleInstances #-} + +import Control.Metaheuristics +import System.Random +import qualified Data.Stream as S +import qualified SimpleTSP as TSP + +import Control.Arrow + +instance HasQuality TSP.TSP Float where + quality (TSP.TSP _ x)= x + + + +displaySeries :: [TSP.TSP]->IO() +displaySeries [] = print "END" +displaySeries (t:tsps) = do print t + displaySeries tsps + +-- TEST Hill climbers +testHillClimber = displaySeries $ S.take 100 $ executeMetaheuristic (iterativeImprover (mapArrow TSP.adjacentNeighbourhood )) [s] + where + (s,g)=TSP.randomSolution (TSP.keyRandGen) + +testStochasticClimber = displaySeries $ S.take 100 $ executeMetaheuristic (stochasticIterativeImprover g (mapArrow TSP.adjacentNeighbourhood )) [s] + where + (s,g)=TSP.randomSolution (TSP.keyRandGen) + +-- TEST hill climber + escape +-- Not efficient. We create the neighbourhood twice and make sure it will be valid in the second generation +testRestart = displaySeries $ S.take 100 $ executeMetaheuristic (escapeStrategy esTest (stochasticIterativeImprover g2 neiArrow ) (replace (S.fromList ss) ) ) [s] + where + (g1,g2) = split TSP.keyRandGen + (s:ss)=TSP.randomSolutions g1 + neiArrow = mapArrow TSP.adjacentNeighbourhood + esTest = mapArrow f + f s | length ns == 0 = Right s + | otherwise = Left s + where ns = [ p | p<- TSP.adjacentNeighbourhood s,p= 1.2 +Data-files: + +library + Exposed-Modules: Control.Metaheuristics + + GHC-Options: -O2 + Build-Depends: base <=4.8.2.0, + Stream >= 0.4.7.2, + arrows >= 0.4.4.2, + random >=1.1 + + + extensions: MultiParamTypeClasses, + FunctionalDependencies