combinatorial-problems (empty) → 0.0.1
raw patch · 15 files changed
+2056/−0 lines, 15 filesdep +arraydep +basedep +containerssetup-changed
Dependencies added: array, base, containers, random
Files
- CombinatorialOptimisation/SAT.hs +186/−0
- CombinatorialOptimisation/SAT.hs~ +186/−0
- CombinatorialOptimisation/TSP.hs +262/−0
- CombinatorialOptimisation/TSP.hs~ +262/−0
- FileFormat/SATLIB.hs +67/−0
- FileFormat/SATLIB.hs~ +67/−0
- FileFormat/TSPLIB.hs +104/−0
- FileFormat/TSPLIB.hs~ +105/−0
- LICENSE +674/−0
- Setup.hs +2/−0
- Test.hs~ +62/−0
- build.sh~ +3/−0
- combinatorial-problems.cabal +38/−0
- combinatorial-problems.cabal~ +38/−0
- new file~ +0/−0
+ CombinatorialOptimisation/SAT.hs view
@@ -0,0 +1,186 @@+-----------------------------------------------------------------------------+-- |+-- Module : CombinatorialOptimisation.SAT+-- Copyright : (c) Richard Senington 2011+-- License : GPL-style+-- +-- Maintainer : Richard Senington <sc06r2s@leeds.ac.uk>+-- Stability : provisional+-- Portability : portable+-- +-- A library for the representation and manipulation of satisfiability problems.+-- Currently this is expected to only be 3-SAT however I do not think the +-- code is particularly limited to 3-SAT. The approach taken is that there+-- is a complex data structure called SATProblem, which contains both the +-- problem and the solution (settings of variables). In addition it contains +-- a number additional fields that allow for making changes quickly, such +-- as a table of clause positions. This is a Map from clause index to the +-- number of variable terms that are currently set to true. +--+-- Currently the only function for quickly changing a problem is the flipping +-- of a single variable. I think some other low level operations for finding +-- clauses not currently evaluating to true and so on would be useful.+----------------------------------------------------------------------------- ++{-# LANGUAGE ScopedTypeVariables #-}++module CombinatorialOptimisation.SAT(+ SATProblem(SATProblem,numClauses,numSATEDClauses,numVariables,variableLookUp,variablePosition,clausePosition,clauseLookUp),+ numUnSATEDClauses,getTrueFalseCount,summariseSAT,makeRandomSATProblem,flipVariable,satproblem,setAllVars,randomiseVariables+)where++import qualified Data.Map as M+import qualified Data.Array as A+import Data.List+import System.Random+import System.IO.Unsafe+import Data.Char++data SATProblem = SATProblem { numClauses :: Int,+ numSATEDClauses :: Int,+ numVariables :: Int,+ variableLookUp :: Int->([Int],[Int]),+ clauseLookUp :: Int->([Int],[Int]),+ variablePosition :: M.Map Int Bool,+ clausePosition :: M.Map Int Int}++instance Eq SATProblem where+ (==) s1 s2 = (numSATEDClauses s1) == (numSATEDClauses s2) && (variablePosition s1) == (variablePosition s2)++instance Ord SATProblem where+ compare s1 s2 = compare (numSATEDClauses s2) (numSATEDClauses s1)++instance Show SATProblem where+ show s = showSATLogic s ++"\n"++ showVARPosition s ++"\n"++ summariseSAT s++"\n"++(show $ getTrueFalseCount s)++{- | For the purposes of getting a general impression of the state of the system, + it returns the number of variables in the True, and False positions. -}++getTrueFalseCount :: SATProblem->(Int,Int)+getTrueFalseCount s = let ls = M.elems $ variablePosition s+ in (length (filter (==True) ls),length (filter (==False) ls))++{- | The number of unsatisfied clauses in the problem, the inverse of @numSATEDClauses@ -}++numUnSATEDClauses :: SATProblem->Int+numUnSATEDClauses s = numClauses s - numSATEDClauses s++{- | Partial display function, for usage in show, this displays the logic of the problem. -}++showSATLogic :: SATProblem->String+showSATLogic s = concat (intersperse " /\\\n" (map writeClause [0 .. numClauses s -1])) ++ "\n"+ where+ writeClause c = let (as,bs) = clauseLookUp s c + (as',bs') = (map (\a->(a,' ')) as,map (\a->(a,'!')) bs)+ cs = sortBy (\a b->compare (fst a) (fst b)) $ as' ++ bs'+ in '(' : (concat $ intersperse " \\/ " $ [ d :'x':show c | (c,d)<-cs]) ++ ")"++{- | Partial display function, for usage in show, displays some general statistics about + the solution status. -}++summariseSAT :: SATProblem->String+summariseSAT s = concat ["number of clauses : ",show (numClauses s),"\n",+ "number of variables : ",show (numVariables s),"\n",+ "satisfied clauses : ",show (numSATEDClauses s),"\n", + satMessage,"\n"]+ where+ sat = (numSATEDClauses s) == (numClauses s)+ satMessage = if sat then "SATisfied" else "unSATisfied"++{- | Partial display function, for usage in show, displays the setting of each variable. -}++showVARPosition :: SATProblem->String+showVARPosition s = concat [concat [" x",show v," = ",show t,"\n" ] |(v,t)<- M.assocs (variablePosition s)]++{- | Alternative constructor for the data structure. Takes only those elements that can + not be derived and correctly initialises the other components, such as calculating + how many clauses are currently evaluating to true. Requires the number of clauses,+ the number of variables, the lookup function for variables (variable index + returning two lists, the first is the indexes of clauses in which this variable + is present, the second list the indexes of clauses in which the inverse of this variable + is present), the lookup table for clauses (clause index to lists of variable indexes) + and the current settings of each variable. -}++satproblem :: Int->Int->(Int->([Int],[Int]))->(Int->([Int],[Int]))->M.Map Int Bool->SATProblem+satproblem nClauses nVars varLookup claLookup varPosition+ = SATProblem nClauses satClause nVars varLookup claLookup varPosition finalClausePosition+ where+ varList = [0 .. nVars -1]+ initialClausePositions = M.fromList $ zip [0 .. nClauses -1] $ repeat 0 + finalClausePosition = foldl f M.empty [0 .. nVars -1]+ f m v = let (ords,negs) = varLookup v+ varPos = varPosition M.! v+ in if varPos then foldl (\m' c->M.adjust (+1) c m') m ords else foldl (\m' c->M.adjust (+1) c m') m negs+ satClause = sum $ map (\x->if x ==0 then 0 else 1) (M.elems finalClausePosition)++{- | For rapid initialisation of problem instances. This fixes the setting of + all variables to either true or false. The effect this has on the number + of clauses that evaluate to true is unknown until it is carried out. -}++setAllVars :: Bool->SATProblem->SATProblem+setAllVars b s = satproblem (numClauses s) (numVariables s) (variableLookUp s) (clauseLookUp s) initialVarPosition+ where+ initialVarPosition = M.fromList $ zip [0 .. numVariables s -1] $ repeat b++{- | For rapid initialisation of problem instances for usage in stochastic algorithms. + Specifically expected to be used for genetic algorithms and other forms of + stochastic meta-heuristic. -}++randomiseVariables :: RandomGen g=>g->SATProblem->SATProblem+randomiseVariables g s = satproblem (numClauses s) (numVariables s) (variableLookUp s) (clauseLookUp s) varpos + where+ varpos = M.fromList $ zip [0 .. (numVariables s) -1] $ (randoms g :: [Bool])++{- | I am not sure how often this will be used in practice, as randomly created problems+ often seem to be quite easy to solve. Requires a source of random numbers, the number+ of variables and the number of clauses to create, in that order. It is assumed + that 3-SAT problems are the type wanted. -} ++makeRandomSATProblem :: RandomGen g=>g->Int->Int->SATProblem+makeRandomSATProblem gen numVariables numClauses + = satproblem numClauses numVariables varLookup claLookup initialVarPosition + where+ initialVarPosition = M.fromList $ zip [0 .. numVariables -1] $ repeat False+ clauses = take numClauses $ nub (unfoldr generateRandomClause gen)+ generateRandomClause g = let f (ms,ns) gen'+ | length ms + length ns == 3 = (ms,ns,gen')+ | otherwise = let (l :: Int,gen'') = randomR (0,1) gen' + (n :: Int,gen''') = randomR (0,numVariables -1) gen''+ already = elem n ms || elem n ns+ in if already then f (ms,ns) gen'''+ else if l ==0 then f (n:ms,ns) gen'''+ else f (ms,n:ns) gen'''+ (ords,negs,g') = f ([],[]) g+ in Just ((sort ords,sort negs),g')+ emptyClauseData = M.fromList $ zip [0 .. numVariables -1] (repeat ([],[]))+ basicClauseLookup = foldl constructClauseLookup emptyClauseData $ zip [0..] clauses+ varLookup = ((A.listArray (0,numVariables-1) (M.elems basicClauseLookup)) A.!)+ constructClauseLookup m (clauseIndex,(ords,negs)) = let addNeg m' x = M.adjust (\(as,bs)->(as,clauseIndex:bs)) x m'+ addOrd m' x = M.adjust (\(as,bs)->(clauseIndex:as,bs)) x m'+ in foldl addNeg (foldl addOrd m ords) negs+ claLookup = ((A.listArray (0,numVariables-1) clauses) A.!)++{- | The first low level operation. Takes a problem and changes the + setting of the indexed variable from true to false. This is + expected to be used in conjunction with other program logic+ to select which index to flip. -}+ +flipVariable :: Int->SATProblem->(SATProblem,Int)+flipVariable v s + = let modifiedVarPos = M.insert v changedVar (variablePosition s)+ in (s{numSATEDClauses=numSATEDClauses s + overAllChange,variablePosition=modifiedVarPos,clausePosition=modifiedClausePos},overAllChange)+ where+ overAllChange = ordChange + negChange+ changedVar = not $ (variablePosition s) M.! v+ (ords,negs) = (variableLookUp s) v+ cp = clausePosition s+ (cp',ordChange) = if changedVar then foldl countInc (cp,0) ords else foldl countDec (cp,0) ords+ (modifiedClausePos,negChange) = if changedVar then foldl countDec (cp',0) negs else foldl countInc (cp',0) negs+ countInc (positions,counter) i = let current = positions M.! i+ counter' = if current == 0 then counter+1 else counter+ in (M.insert i (current+1) positions,counter')+ countDec (positions,counter) i = let current = positions M.! i+ counter' = if current == 1 then counter-1 else counter+ in (M.insert i (current-1) positions,counter')++
+ CombinatorialOptimisation/SAT.hs~ view
@@ -0,0 +1,186 @@+-----------------------------------------------------------------------------+-- |+-- Module : CombinatorialOptimisation.SAT+-- Copyright : (c) Richard Senington 2011+-- License : GPL-style+-- +-- Maintainer : Richard Senington <sc06r2s@leeds.ac.uk>+-- Stability : provisional+-- Portability : portable+-- +-- A library for the representation and manipulation of satisfiability problems.+-- Currently this is expected to only be 3-SAT however I do not think the +-- code is particularly limited to 3-SAT. The approach taken is that there+-- is a complex data structure called SATProblem, which contains both the +-- problem and the solution (settings of variables). In addition it contains +-- a number additional fields that allow for making changes quickly, such +-- as a table of clause positions. This is a Map from clause index to the +-- number of variable terms that are currently set to true. +--+-- Currently the only function for quickly changing a problem is the flipping +-- of a single variable. I think some other low level operations for finding +-- clauses not currently evaluating to true and so on would be useful.+----------------------------------------------------------------------------- ++{-# LANGUAGE ScopedTypeVariables #-}++module CombinatorialOptimisation.SAT(+ SATProblem(SATProblem,numClauses,numSATEDClauses,numVariables,variableLookUp,variablePosition,clausePosition,clauseLookUp),+ numUnSATEDClauses,getTrueFalseCount,summariseSAT,makeRandomSATProblem,flipVariable,satproblem,setAllVars,randomiseVariables+)where++import qualified Data.Map as M+import qualified Data.Array as A+import Data.List+import System.Random+import System.IO.Unsafe+import Data.Char++data SATProblem = SATProblem { numClauses :: Int,+ numSATEDClauses :: Int,+ numVariables :: Int,+ variableLookUp :: Int->([Int],[Int]),+ clauseLookUp :: Int->([Int],[Int]),+ variablePosition :: M.Map Int Bool,+ clausePosition :: M.Map Int Int}++instance Eq SATProblem where+ (==) s1 s2 = (numSATEDClauses s1) == (numSATEDClauses s2) && (variablePosition s1) == (variablePosition s2)++instance Ord SATProblem where+ compare s1 s2 = compare (numSATEDClauses s2) (numSATEDClauses s1)++instance Show SATProblem where+ show s = showSATLogic s ++"\n"++ showVARPosition s ++"\n"++ summariseSAT s++"\n"++(show $ getTrueFalseCount s)++{- | For the purposes of getting a general impression of the state of the system, + it returns the number of variables in the True, and False positions. -}++getTrueFalseCount :: SATProblem->(Int,Int)+getTrueFalseCount s = let ls = M.elems $ variablePosition s+ in (length (filter (==True) ls),length (filter (==False) ls))++{- | The number of unsatisfied clauses in the problem, the inverse of numSATEDClauses -}++numUnSATEDClauses :: SATProblem->Int+numUnSATEDClauses s = numClauses s - numSATEDClauses s++{- | Partial display function, for usage in show, this displays the logic of the problem. -}++showSATLogic :: SATProblem->String+showSATLogic s = concat (intersperse " /\\\n" (map writeClause [0 .. numClauses s -1])) ++ "\n"+ where+ writeClause c = let (as,bs) = clauseLookUp s c + (as',bs') = (map (\a->(a,' ')) as,map (\a->(a,'!')) bs)+ cs = sortBy (\a b->compare (fst a) (fst b)) $ as' ++ bs'+ in '(' : (concat $ intersperse " \\/ " $ [ d :'x':show c | (c,d)<-cs]) ++ ")"++{- | Partial display function, for usage in show, displays some general statistics about + the solution status. -}++summariseSAT :: SATProblem->String+summariseSAT s = concat ["number of clauses : ",show (numClauses s),"\n",+ "number of variables : ",show (numVariables s),"\n",+ "satisfied clauses : ",show (numSATEDClauses s),"\n", + satMessage,"\n"]+ where+ sat = (numSATEDClauses s) == (numClauses s)+ satMessage = if sat then "SATisfied" else "unSATisfied"++{- | Partial display function, for usage in show, displays the setting of each variable. -}++showVARPosition :: SATProblem->String+showVARPosition s = concat [concat [" x",show v," = ",show t,"\n" ] |(v,t)<- M.assocs (variablePosition s)]++{- | Alternative constructor for the data structure. Takes only those elements that can + not be derived and correctly initialises the other components, such as calculating + how many clauses are currently evaluating to true. Requires the number of clauses,+ the number of variables, the lookup function for variables (variable index + returning two lists, the first is the indexes of clauses in which this variable + is present, the second list the indexes of clauses in which the inverse of this variable + is present), the lookup table for clauses (clause index to lists of variable indexes) + and the current settings of each variable. -}++satproblem :: Int->Int->(Int->([Int],[Int]))->(Int->([Int],[Int]))->M.Map Int Bool->SATProblem+satproblem nClauses nVars varLookup claLookup varPosition+ = SATProblem nClauses satClause nVars varLookup claLookup varPosition finalClausePosition+ where+ varList = [0 .. nVars -1]+ initialClausePositions = M.fromList $ zip [0 .. nClauses -1] $ repeat 0 + finalClausePosition = foldl f M.empty [0 .. nVars -1]+ f m v = let (ords,negs) = varLookup v+ varPos = varPosition M.! v+ in if varPos then foldl (\m' c->M.adjust (+1) c m') m ords else foldl (\m' c->M.adjust (+1) c m') m negs+ satClause = sum $ map (\x->if x ==0 then 0 else 1) (M.elems finalClausePosition)++{- | For rapid initialisation of problem instances. This fixes the setting of + all variables to either true or false. The effect this has on the number + of clauses that evaluate to true is unknown until it is carried out. -}++setAllVars :: Bool->SATProblem->SATProblem+setAllVars b s = satproblem (numClauses s) (numVariables s) (variableLookUp s) (clauseLookUp s) initialVarPosition+ where+ initialVarPosition = M.fromList $ zip [0 .. numVariables s -1] $ repeat b++{- | For rapid initialisation of problem instances for usage in stochastic algorithms. + Specifically expected to be used for genetic algorithms and other forms of + stochastic meta-heuristic. -}++randomiseVariables :: RandomGen g=>g->SATProblem->SATProblem+randomiseVariables g s = satproblem (numClauses s) (numVariables s) (variableLookUp s) (clauseLookUp s) varpos + where+ varpos = M.fromList $ zip [0 .. (numVariables s) -1] $ (randoms g :: [Bool])++{- | I am not sure how often this will be used in practice, as randomly created problems+ often seem to be quite easy to solve. Requires a source of random numbers, the number+ of variables and the number of clauses to create, in that order. It is assumed + that 3-SAT problems are the type wanted. -} ++makeRandomSATProblem :: RandomGen g=>g->Int->Int->SATProblem+makeRandomSATProblem gen numVariables numClauses + = satproblem numClauses numVariables varLookup claLookup initialVarPosition + where+ initialVarPosition = M.fromList $ zip [0 .. numVariables -1] $ repeat False+ clauses = take numClauses $ nub (unfoldr generateRandomClause gen)+ generateRandomClause g = let f (ms,ns) gen'+ | length ms + length ns == 3 = (ms,ns,gen')+ | otherwise = let (l :: Int,gen'') = randomR (0,1) gen' + (n :: Int,gen''') = randomR (0,numVariables -1) gen''+ already = elem n ms || elem n ns+ in if already then f (ms,ns) gen'''+ else if l ==0 then f (n:ms,ns) gen'''+ else f (ms,n:ns) gen'''+ (ords,negs,g') = f ([],[]) g+ in Just ((sort ords,sort negs),g')+ emptyClauseData = M.fromList $ zip [0 .. numVariables -1] (repeat ([],[]))+ basicClauseLookup = foldl constructClauseLookup emptyClauseData $ zip [0..] clauses+ varLookup = ((A.listArray (0,numVariables-1) (M.elems basicClauseLookup)) A.!)+ constructClauseLookup m (clauseIndex,(ords,negs)) = let addNeg m' x = M.adjust (\(as,bs)->(as,clauseIndex:bs)) x m'+ addOrd m' x = M.adjust (\(as,bs)->(clauseIndex:as,bs)) x m'+ in foldl addNeg (foldl addOrd m ords) negs+ claLookup = ((A.listArray (0,numVariables-1) clauses) A.!)++{- | The first low level operation. Takes a problem and changes the + setting of the indexed variable from true to false. This is + expected to be used in conjunction with other program logic+ to select which index to flip. -}+ +flipVariable :: Int->SATProblem->(SATProblem,Int)+flipVariable v s + = let modifiedVarPos = M.insert v changedVar (variablePosition s)+ in (s{numSATEDClauses=numSATEDClauses s + overAllChange,variablePosition=modifiedVarPos,clausePosition=modifiedClausePos},overAllChange)+ where+ overAllChange = ordChange + negChange+ changedVar = not $ (variablePosition s) M.! v+ (ords,negs) = (variableLookUp s) v+ cp = clausePosition s+ (cp',ordChange) = if changedVar then foldl countInc (cp,0) ords else foldl countDec (cp,0) ords+ (modifiedClausePos,negChange) = if changedVar then foldl countDec (cp',0) negs else foldl countInc (cp',0) negs+ countInc (positions,counter) i = let current = positions M.! i+ counter' = if current == 0 then counter+1 else counter+ in (M.insert i (current+1) positions,counter')+ countDec (positions,counter) i = let current = positions M.! i+ counter' = if current == 1 then counter-1 else counter+ in (M.insert i (current-1) positions,counter')++
+ CombinatorialOptimisation/TSP.hs view
@@ -0,0 +1,262 @@+-----------------------------------------------------------------------------+-- |+-- Module : CombinatorialOptimisation.TSP+-- Copyright : (c) Richard Senington 2011+-- License : GPL-style+-- +-- Maintainer : Richard Senington <sc06r2s@leeds.ac.uk>+-- Stability : provisional+-- Portability : portable+-- +-- A library for the representation and manipulation of travelling salesperson+-- problems.+-- The approach taken is the creation of a complex data structure called +-- TSPProblem which contains both the problem, the current solution and +-- the current value of the route.+-- The route is stored as a dictionary (@Data.Map@) of vertex indexes+-- to a pair of values, the previous vertex and the next vertex in the+-- sequence. This is to facilitate changing the route quickly, and+-- avoid searching for data in lists.+--+-- The data structure also contains two additional fields, the +-- @routeElementToIndex@ and @indexToRouteElement@ components.+-- These exist to allow manipulation either by the vertex number+-- or the position in the current solution. +-- Solutions are hamiltonian cycles.+-- For ease of reasoning it is recommended that users do not +-- attempt to move vertex 0, or index 0, so that solutions+-- are cycles from 0 to 0. I may change this in the future to +-- lock this down a bit. In the meantime, there is no+-- actual problem with making these changes, however +-- later manipulations may not match up clearly with +-- the way the show routines work.+--+-- Currently only two functions are provided for manipulating routes,+-- either by position in the sequence (@exchangeCitiesOnIndex@) or +-- by vertex name (@exchangeCities@).+--+-- I am not sure how this will clearly support meta-heuristics that+-- work by deleting edges and recombining subsequences. However +-- since I am storing association lists I think it should be possible +-- to make this work, I will worry about it later.+----------------------------------------------------------------------------- ++module CombinatorialOptimisation.TSP(+ TSPProblem(TSPProblem,currentPrice,routeMap,edgePrices,numCities,routeElementToIndex,indexToRouteElement),+ InternalStorage(ExplicitMatrix,TriangularMatrix,Recomputation),+ showEdgeWeights,+ exchangeCities,+ exchangeCitiesOnIndex,+ evaluateRouteNaive,+ randomiseRoute,+ setRoute,+ makeASymmetricTSPMap,+ makeSymmetricTSPMap,+ makeEuclideanTSPMap+)where++import qualified Data.Map as M+import qualified Data.Array as A+import System.Random+import Data.List++{- | The data type for carrying the combination problem and solution to + the TSP. The route is stored as a dictionary of associations + from vertex name to a pair of values, the name of the preceding + vertex and the next vertex. This forms an infinite loop, so + use carefully.++ The @routeElementToIndex@\/@indexToRouteElement@ pair store + fixed indexes to the cities. This is intended to allow + a dumb heuristic to decide to switch elements 0 and 2, + knowing they must be separated by 1 element, rather than+ vertices 0 and 2, which may be next to each other, or + very different parts of the cycle.+-}++data TSPProblem = TSPProblem { currentPrice :: Float,+ routeMap :: M.Map Int (Int,Int),+ edgePrices :: (Int->Int->Float),+ numCities :: Int,+ routeElementToIndex :: M.Map Int Int,+ indexToRouteElement :: M.Map Int Int+ }++{- | There are three possible internal storage forms. A full explicit matrix, an upper triangular matrix or recomputation + from data points. The advantage of full explicit is speed, but it takes more memory. It is also the only option for + asymmetric TSP problems. The triangular matrix is also fast, but can only be used in symmetric problems, and also + still requires quite a bit of memory. Recomputation is the last option, it is slow because it is no longer a lookup+ table, but will take much less room. Can only be used with problems where the distance between two points can be+ calculated. Currently I am only supporting symmetric TSPs for this.+-}++data InternalStorage = ExplicitMatrix | TriangularMatrix | Recomputation deriving (Show,Eq) -- just in case I need these++instance Show TSPProblem where+ show t = concat ["TSPProblem of ",show . numCities $ t,+ " cities\n Current Solution ",show r,+ "\n Costing ",show . currentPrice $ t,"\n"]+ where+ rm = snd . ((M.!) (routeMap t))+ r = 0:(takeWhile (\x->x/=0) $ iterate rm (rm 0))++[0]++{- | Converts the lookup table of a problem into a comma and newline delimited+ string. This should facilitate copying into spreadsheets for checking the + problem being used and validating solutions by hand. -}++showEdgeWeights :: TSPProblem->String+showEdgeWeights t = headerRow ++ concatMap makeRow nc+ where+ ep = edgePrices t+ nc = [0 .. numCities t-1]+ headerRow = ',': concat (intersperse "," $ map show [0..numCities t-1]) ++ "\n"+ makeRow i = show i ++ "," ++ concat (intersperse "," [ show (ep i' i) | i'<-nc]) ++"\n"++{- | Will perform a switch of 2 cities in the path. This is by city name, not current index+ in the path. It looks up the current indexes by city name and passes the work off to + @exchangeCitiesOnIndex@. -}++exchangeCities :: Int->Int->TSPProblem->TSPProblem+exchangeCities a b t = exchangeCitiesOnIndex (min i1 i2) (max i1 i2) t + where+ i1 = routeElementToIndex t M.! a+ i2 = routeElementToIndex t M.! b+ +{- | Performs the bulk of the work for exchanging elements of the cycle.+ It assumes that the order of the indexes is increasing (e.g. 0 2 not 2 0).+ While changing the order it will also calculate the change in value of the + route and update this. This is performed fairly efficiently by finding the + edges being removed, and the edges being created and adding the difference + between the two to the current price. -}++exchangeCitiesOnIndex :: Int->Int->TSPProblem->TSPProblem+exchangeCitiesOnIndex i1 i2 t + | d == 0 = t+ | d == 1 = t{routeMap=rAdj,currentPrice=currentPrice t + priceChangeAdj,routeElementToIndex=t2',indexToRouteElement=t1'}+ | otherwise = t{routeMap=r',currentPrice=currentPrice t + priceChange,routeElementToIndex=t2',indexToRouteElement=t1'}+ where + d = abs (i1 - i2)++ -- basic setup+ r = (routeMap t)+ a = indexToRouteElement t M.! i1+ b = indexToRouteElement t M.! i2+ p = edgePrices t+ ((a1,a2),(b1,b2)) = (r M.! a,r M.! b)++ -- usual code+ priceChange = sum [p a1 b,p b a2,p b1 a,p a b2] - sum [p a a2,p b b2,p a1 a,p b1 b]+ r' = foldl' (\m (k,f) -> M.adjust f k m) r [(a,\_->(b1,b2)),(b,\_->(a1,a2)),(a1,\(x,y)->(x,b)),(a2,\(x,y)->(b,y)),(b1,\(x,y)->(x,a)),(b2,\(x,y)->(a,y))]++ -- index exchange+ t1 = indexToRouteElement t+ t2 = routeElementToIndex t+ t2' = M.insert b i1 (M.insert a i2 t2) + t1' = M.insert i1 b (M.insert i2 a t1) + + -- adjacent exchange, special case+ priceChangeAdj = sum [p a1 b,p b a,p a b2] - sum [p a1 a,p a b,p b b2]+ rAdj = foldl' (\m (k,f) -> M.adjust f k m) r [(a1,\(x,y)->(x,b)),(b2,\(x,y)->(a,y)),(a,\_->(b,b2)),(b,\_->(a1,a))]++{- | A brute force recalculation of the current length of the path. Use sparingly.-}++evaluateRouteNaive :: TSPProblem->TSPProblem+evaluateRouteNaive t = t{currentPrice=evalRoute 0}+ where+ ep = edgePrices t+ rm = snd . ((M.!) (routeMap t))+ evalRoute x = let n = rm x+ in if n==0 then ep x n + else ep x n + evalRoute n++{- | Take a path through the system and a problem, insert the path into the system, + calculating distances and setting up appropriate look up tables. It does not+ validate the list in terms of going through all the cities, or going through + a city more than once (though this is likely to break other parts of the system + very very fast). It does organise the list so that the starting node is vertex 0. ++ Uses the @evaluateRouteNaive@ to calculate the length of the path via a brute+ force method. This is not expected to be used frequently. -}++setRoute :: [Int]->TSPProblem->TSPProblem+setRoute path t = evaluateRouteNaive t{routeMap=newRoute,indexToRouteElement=in1,routeElementToIndex=in2} + where+ l = dropWhile (/=0) $ cycle path + l' = tail l+ l'' = tail l'+ (k,k':_) = span (\(_,x,_)->x/=0) $ zip3 l l' l''+ newRoute = foldl' (\m (a,b,c) -> M.insert b (a,c) m) M.empty (k':k)+ in1 = M.fromList $ zip [0..] (take (numCities t) l)+ in2 = M.fromList . (map swap) . M.assocs $ in1+ swap (a,b) = (b,a)++{- | Shuffles a simple list of cities and then passes off the work to setRoute. -}++randomiseRoute :: RandomGen g=>g->TSPProblem->TSPProblem+randomiseRoute g t = setRoute (0:map snd (sort (zip (randoms g :: [Float]) [1 .. numCities t -1]))) t ++{- | Construct a TSPProblem instance for an Asymmetric TSP. That is, the distance+ from A-B is the not necessarily the same as B-A. The actual route will + not be set up initially, the dictionaries will be empty. This could be + used directly for a global search system (branch and bound), or use in + conjunction with @setRoute@ or @randomiseRoute@ to initialise for local search. + Internal data structure is always fully explicit matrix.-}++makeASymmetricTSPMap :: RandomGen g=>(Float,Float)->Int->g->TSPProblem+makeASymmetricTSPMap distanceLimits numCities g + = let cities = [0 ..(numCities-1)]+ cityCoords = [(a,b) | a<-cities,b<-cities,a/=b]+ matrix = M.fromList $ zip cityCoords (randomRs distanceLimits g)+ -- p' = (\x y->M.findWithDefault 0 (x,y) matrix)+ explicit = A.listArray (0,numCities*numCities-1) [M.findWithDefault 0 (a,b) matrix | a<-cities,b<-cities]+ in TSPProblem 0 M.empty (\x y->explicit A.! (x * numCities + y)) numCities M.empty M.empty+ -- TSPProblem 0 M.empty p numCities M.empty M.empty++{- | Construct a TSPProblem instance for a Symmetric TSP. That is, the distance+ from A-B is the same as B-A. The actual route will not be set up initially,+ the dictionaries will be empty. This could be used directly for a global + search system (branch and bound), or use in conjunction with @setRoute@ or + @randomiseRoute@ to initialise for local search. Should be noted that this+ does not create locations and calculate distances, but rather randomly + assigns distances to each edge, making them symmetric. -}++makeSymmetricTSPMap :: RandomGen g=>InternalStorage->(Float,Float)->Int->g->TSPProblem+makeSymmetricTSPMap Recomputation _ _ _ = error "Cannot support recomputation, please use alternative storage, or makeEuclideanTSPMap"+makeSymmetricTSPMap storageType distanceLimits numCities g + = let cities = [0 ..(numCities-1)]+ cityCoords = [(a,b) | a<-cities,b<-take (a+1) cities,a/=b ]+ f e ((a,b),c) = M.insert (b,a) c (M.insert (a,b) c e)+ matrix = foldl f M.empty (zip cityCoords (randomRs distanceLimits g))+ explicit = A.listArray (0,numCities*numCities-1) [M.findWithDefault 0 (a,b) matrix | a<-cities,b<-cities]+ triangular = A.listArray (0,sum [0..numCities]) [M.findWithDefault 0 (a,b) matrix | a<-cities,b<-[0..a]]+ p = if storageType == ExplicitMatrix then (\x y->explicit A.! (x * numCities + y))+ else (\x y->let x' = min x y; y' = max x y in triangular A.! (div (y'*y'+y') 2 + x'))+ in TSPProblem 0 M.empty p numCities M.empty M.empty++{- | Construct a TSPProblem instance for a Symmetric TSP. The route will not be+ initially set up, the dictionaries will be empty. This does create the + vertices of the graph as points in a 2d space, and the lengths of edges + are calculated, so this supports all internal storage types. +-}++makeEuclideanTSPMap :: RandomGen g=>InternalStorage->(Float,Float)->(Float,Float)->Int->g->TSPProblem+makeEuclideanTSPMap storageType xRange yRange numCities g + = let cities = [0 ..(numCities-1)]+ (genA,genB) = split g+ positions = take numCities $ zip (randomRs xRange genA) (randomRs yRange genB)+ posArr = A.listArray (0 , numCities-1) positions++ explicit = A.listArray (0,numCities*numCities-1) [euclidianDistance (posArr A.! a) (posArr A.! b) | a<-cities,b<-cities]+ triangular = A.listArray (0,sum [0..numCities]) [euclidianDistance (posArr A.! a) (posArr A.! b) | a<-cities,b<-[0..a]]++ p = case storageType of+ ExplicitMatrix -> \x y->explicit A.! (x * numCities + y)+ TriangularMatrix -> (\x y->let x' = min x y; y' = max x y in triangular A.! (div (y'*y'+y') 2 + x'))+ Recomputation -> \a b->if a == b then 0 else euclidianDistance (posArr A.! a) (posArr A.! b)+ in TSPProblem 0 M.empty p numCities M.empty M.empty+ where+ euclidianDistance :: (Float,Float)->(Float,Float)->Float+ euclidianDistance (a,b) (c,d) = sqrt ((a-c)*(a-c)+(b-d)*(b-d))+ ++
+ CombinatorialOptimisation/TSP.hs~ view
@@ -0,0 +1,262 @@+-----------------------------------------------------------------------------+-- |+-- Module : CombinatorialOptimisation.TSP+-- Copyright : (c) Richard Senington 2011+-- License : GPL-style+-- +-- Maintainer : Richard Senington <sc06r2s@leeds.ac.uk>+-- Stability : provisional+-- Portability : portable+-- +-- A library for the representation and manipulation of traveling salesperson+-- problems.+-- The approach taken is the creation of a complex data structure called +-- TSPProblem which contains both the problem, the current solution and +-- the current value of the route.+-- The route is stored as a dictionary (@Data.Map@) of vertex indexes+-- to a pair of values, the previous vertex and the next vertex in the+-- sequence. This is to facilitate changing the route quickly, and+-- avoid searching for data in lists.+--+-- The data structure also contains two additonal fields, the +-- @routeElementToIndex@ and @indexToRouteElement@ components.+-- These exist to allow manipulation either by the vertex number+-- or the position in the current solution. +-- Solutions are hamiltonian cycles.+-- For ease of reasoning it is recomended that users do not +-- attempt to move vertex 0, or index 0, so that solutions+-- are cycles from 0 to 0. I may change this in the future to +-- lock this down a bit. In the meantime, there is no+-- actual problem with making these changes, however +-- later manipulations may not match up clearly with +-- the way the show routines work.+--+-- Currently only two functions are provided for manipulating routes,+-- either by position in the sequence (@exchangeCitiesOnIndex@) or +-- by vertex name (@exchangeCities@).+--+-- I am not sure how this will clearly support meta-heuristics that+-- work by deleting edges and recombining subsequences. However +-- since I am storing association lists I think it should be possible +-- to make this work, I will worry about it later.+----------------------------------------------------------------------------- ++module CombinatorialOptimisation.TSP(+ TSPProblem(TSPProblem,currentPrice,routeMap,edgePrices,numCities,routeElementToIndex,indexToRouteElement),+ InternalStorage(ExplicitMatrix,TriangularMatrix,Recomputation),+ showEdgeWeights,+ exchangeCities,+ exchangeCitiesOnIndex,+ evaluateRouteNaive,+ randomiseRoute,+ setRoute,+ makeASymmetricTSPMap,+ makeSymmetricTSPMap,+ makeEuclideanTSPMap+)where++import qualified Data.Map as M+import qualified Data.Array as A+import System.Random+import Data.List++{- | The data type for carrying the combination problem and solution to + the TSP. The route is stored as a dictionary of associations + from vertex name to a pair of values, the name of the preceding + vertex and the next vertex. This forms an infinite loop, so + use carefully.++ The @routeElementToIndex@\/@indexToRouteElement@ pair store + fixed indexes to the cities. This is intended to allow + a dumb heuristic to decide to switch elements 0 and 2, + knowing they must be separated by 1 element, rather than+ vertices 0 and 2, which may be next to each other, or + very different parts of the cycle.+-}++data TSPProblem = TSPProblem { currentPrice :: Float,+ routeMap :: M.Map Int (Int,Int),+ edgePrices :: (Int->Int->Float),+ numCities :: Int,+ routeElementToIndex :: M.Map Int Int,+ indexToRouteElement :: M.Map Int Int+ }++{- | There are three possible internal storage forms. A full explicit matrix, an upper triangular matrix or recomputation + from data points. The advantage of full explicit is speed, but it takes more memory. It is also the only option for + asymmetric TSP problems. The triangular matrix is also fast, but can only be used in symmetric problems, and also + still requires quite a bit of memory. Recomputation is the last option, it is slow because it is no longer a lookup+ table, but will take much less room. Can only be used with problems where the distance between two points can be+ calculated. Currently I am only supporting symmetric TSPs for this.+-}++data InternalStorage = ExplicitMatrix | TriangularMatrix | Recomputation deriving (Show,Eq) -- just in case I need these++instance Show TSPProblem where+ show t = concat ["TSPProblem of ",show . numCities $ t,+ " cities\n Current Solution ",show r,+ "\n Costing ",show . currentPrice $ t,"\n"]+ where+ rm = snd . ((M.!) (routeMap t))+ r = 0:(takeWhile (\x->x/=0) $ iterate rm (rm 0))++[0]++{- | Converts the lookup table of a problem into a comma and newline deliminated+ string. This should facilitate copying into spreadsheets for checking the + problem being used and validating solutions by hand. -}++showEdgeWeights :: TSPProblem->String+showEdgeWeights t = headerRow ++ concatMap makeRow nc+ where+ ep = edgePrices t+ nc = [0 .. numCities t-1]+ headerRow = ',': concat (intersperse "," $ map show [0..numCities t-1]) ++ "\n"+ makeRow i = show i ++ "," ++ concat (intersperse "," [ show (ep i' i) | i'<-nc]) ++"\n"++{- | Will perform a switch of 2 cities in the path. This is by city name, not current index+ in the path. It looks up the current indexes by city name and passes the work off to + @exchangeCitiesOnIndex@. -}++exchangeCities :: Int->Int->TSPProblem->TSPProblem+exchangeCities a b t = exchangeCitiesOnIndex (min i1 i2) (max i1 i2) t + where+ i1 = routeElementToIndex t M.! a+ i2 = routeElementToIndex t M.! b+ +{- | Performs the bulk of the work for exchanging elements of the cycle.+ It assumes that the order of the indexes is increasing (e.g. 0 2 not 2 0).+ While changing the order it will also calculate the change in value of the + route and update this. This is performed fairly efficiently by finding the + edges being removed, and the edges being created and adding the difference + between the two to the current price. -}++exchangeCitiesOnIndex :: Int->Int->TSPProblem->TSPProblem+exchangeCitiesOnIndex i1 i2 t + | d == 0 = t+ | d == 1 = t{routeMap=rAdj,currentPrice=currentPrice t + priceChangeAdj,routeElementToIndex=t2',indexToRouteElement=t1'}+ | otherwise = t{routeMap=r',currentPrice=currentPrice t + priceChange,routeElementToIndex=t2',indexToRouteElement=t1'}+ where + d = abs (i1 - i2)++ -- basic setup+ r = (routeMap t)+ a = indexToRouteElement t M.! i1+ b = indexToRouteElement t M.! i2+ p = edgePrices t+ ((a1,a2),(b1,b2)) = (r M.! a,r M.! b)++ -- usual code+ priceChange = sum [p a1 b,p b a2,p b1 a,p a b2] - sum [p a a2,p b b2,p a1 a,p b1 b]+ r' = foldl' (\m (k,f) -> M.adjust f k m) r [(a,\_->(b1,b2)),(b,\_->(a1,a2)),(a1,\(x,y)->(x,b)),(a2,\(x,y)->(b,y)),(b1,\(x,y)->(x,a)),(b2,\(x,y)->(a,y))]++ -- index exchange+ t1 = indexToRouteElement t+ t2 = routeElementToIndex t+ t2' = M.insert b i1 (M.insert a i2 t2) + t1' = M.insert i1 b (M.insert i2 a t1) + + -- adjacent exchange, special case+ priceChangeAdj = sum [p a1 b,p b a,p a b2] - sum [p a1 a,p a b,p b b2]+ rAdj = foldl' (\m (k,f) -> M.adjust f k m) r [(a1,\(x,y)->(x,b)),(b2,\(x,y)->(a,y)),(a,\_->(b,b2)),(b,\_->(a1,a))]++{- | A brute force recalculation of the current length of the path. Use sparingly.-}++evaluateRouteNaive :: TSPProblem->TSPProblem+evaluateRouteNaive t = t{currentPrice=evalRoute 0}+ where+ ep = edgePrices t+ rm = snd . ((M.!) (routeMap t))+ evalRoute x = let n = rm x+ in if n==0 then ep x n + else ep x n + evalRoute n++{- | Take a path through the system and a problem, insert the path into the system, + calculating distances and setting up appropriate look up tables. It does not+ validate the list in terms of going through all the cities, or going through + a city more than once (though this is likely to break other parts of the system + very very fast). It does organise the list so that the starting node is vertex 0. ++ Uses the @evaluateRouteNaive@ to calculate the length of the path via a brute+ force method. This is not expected to be used frequently. -}++setRoute :: [Int]->TSPProblem->TSPProblem+setRoute path t = evaluateRouteNaive t{routeMap=newRoute,indexToRouteElement=in1,routeElementToIndex=in2} + where+ l = dropWhile (/=0) $ cycle path + l' = tail l+ l'' = tail l'+ (k,k':_) = span (\(_,x,_)->x/=0) $ zip3 l l' l''+ newRoute = foldl' (\m (a,b,c) -> M.insert b (a,c) m) M.empty (k':k)+ in1 = M.fromList $ zip [0..] (take (numCities t) l)+ in2 = M.fromList . (map swap) . M.assocs $ in1+ swap (a,b) = (b,a)++{- | Shuffles a simple list of cities and then passes off the work to setRoute. -}++randomiseRoute :: RandomGen g=>g->TSPProblem->TSPProblem+randomiseRoute g t = setRoute (0:map snd (sort (zip (randoms g :: [Float]) [1 .. numCities t -1]))) t ++{- | Construct a TSPProblem instance for an Asymmetric TSP. That is, the distance+ from A-B is the not necessarily the same as B-A. The actual route will + not be set up initially, the dictionaries will be empty. This could be + used directly for a global search system (branch and bound), or use in + conjunction with @setRoute@ or @randomiseRoute@ to initialise for local search. + Internal data structure is always fully explicit matrix.-}++makeASymmetricTSPMap :: RandomGen g=>(Float,Float)->Int->g->TSPProblem+makeASymmetricTSPMap distanceLimits numCities g + = let cities = [0 ..(numCities-1)]+ cityCoords = [(a,b) | a<-cities,b<-cities,a/=b]+ matrix = M.fromList $ zip cityCoords (randomRs distanceLimits g)+ -- p' = (\x y->M.findWithDefault 0 (x,y) matrix)+ explicit = A.listArray (0,numCities*numCities-1) [M.findWithDefault 0 (a,b) matrix | a<-cities,b<-cities]+ in TSPProblem 0 M.empty (\x y->explicit A.! (x * numCities + y)) numCities M.empty M.empty+ -- TSPProblem 0 M.empty p numCities M.empty M.empty++{- | Construct a TSPProblem instance for a Symmetric TSP. That is, the distance+ from A-B is the same as B-A. The actual route will not be set up initially,+ the dictionaries will be empty. This could be used directly for a global + search system (branch and bound), or use in conjunction with @setRoute@ or + @randomiseRoute@ to initialise for local search. Should be noted that this+ does not create locations and calculate distances, but rather randomly + assigns distances to each edge, making them symmetric. -}++makeSymmetricTSPMap :: RandomGen g=>InternalStorage->(Float,Float)->Int->g->TSPProblem+makeSymmetricTSPMap Recomputation _ _ _ = error "Cannot support recomputation, please use alternative storage, or makeEuclideanTSPMap"+makeSymmetricTSPMap storageType distanceLimits numCities g + = let cities = [0 ..(numCities-1)]+ cityCoords = [(a,b) | a<-cities,b<-take (a+1) cities,a/=b ]+ f e ((a,b),c) = M.insert (b,a) c (M.insert (a,b) c e)+ matrix = foldl f M.empty (zip cityCoords (randomRs distanceLimits g))+ explicit = A.listArray (0,numCities*numCities-1) [M.findWithDefault 0 (a,b) matrix | a<-cities,b<-cities]+ triangular = A.listArray (0,sum [0..numCities]) [M.findWithDefault 0 (a,b) matrix | a<-cities,b<-[0..a]]+ p = if storageType == ExplicitMatrix then (\x y->explicit A.! (x * numCities + y))+ else (\x y->let x' = min x y; y' = max x y in triangular A.! (div (y'*y'+y') 2 + x'))+ in TSPProblem 0 M.empty p numCities M.empty M.empty++{- | Construct a TSPProblem instance for a Symmetric TSP. The route will not be+ initially set up, the dictionaries will be empty. This does create the + vertices of the graph as points in a 2d space, and the lengths of edges + are calculated, so this supports all internal storage types. +-}++makeEuclideanTSPMap :: RandomGen g=>InternalStorage->(Float,Float)->(Float,Float)->Int->g->TSPProblem+makeEuclideanTSPMap storageType xRange yRange numCities g + = let cities = [0 ..(numCities-1)]+ (genA,genB) = split g+ positions = take numCities $ zip (randomRs xRange genA) (randomRs yRange genB)+ posArr = A.listArray (0 , numCities-1) positions++ explicit = A.listArray (0,numCities*numCities-1) [euclidianDistance (posArr A.! a) (posArr A.! b) | a<-cities,b<-cities]+ triangular = A.listArray (0,sum [0..numCities]) [euclidianDistance (posArr A.! a) (posArr A.! b) | a<-cities,b<-[0..a]]++ p = case storageType of+ ExplicitMatrix -> \x y->explicit A.! (x * numCities + y)+ TriangularMatrix -> (\x y->let x' = min x y; y' = max x y in triangular A.! (div (y'*y'+y') 2 + x'))+ Recomputation -> \a b->if a == b then 0 else euclidianDistance (posArr A.! a) (posArr A.! b)+ in TSPProblem 0 M.empty p numCities M.empty M.empty+ where+ euclidianDistance :: (Float,Float)->(Float,Float)->Float+ euclidianDistance (a,b) (c,d) = sqrt ((a-c)*(a-c)+(b-d)*(b-d))+ ++
+ FileFormat/SATLIB.hs view
@@ -0,0 +1,67 @@+-----------------------------------------------------------------------------+-- |+-- Module : FileFormat.SATLIB+-- Copyright : (c) Richard Senington 2011+-- License : GPL-style+-- +-- Maintainer : Richard Senington <sc06r2s@leeds.ac.uk>+-- Stability : provisional+-- Portability : portable+-- +-- The loading routines for the Conjunctive Normal Form (cnf) styled files+-- that can be found on the SATLIB website. Relies upon the+-- @CombinatorialOptimisation.SAT@ library for the data structures.+----------------------------------------------------------------------------- ++module FileFormat.SATLIB(loadCNFFile,saveAsCNF)where++import CombinatorialOptimisation.SAT++import Data.List+import qualified Data.Map as M+import qualified Data.Array as A++{- | Loading routine that takes the file path and returns a SATProblem. All variables will be set to false in the initial +setup, and the truth values of all clauses set appropriately. -}++loadCNFFile :: FilePath->IO(SATProblem)+loadCNFFile fName + = do rawContents<-readFile fName+ let ls = (filter (\x->head x /= 'c')) $ lines rawContents+ let problemLine = words $ head $ filter (\x->head x == 'p') ls+ let (varCount,clauseCount) = if problemLine !! 1 /= "cnf" then error "This is not a CNF file"+ else (read $ problemLine !! 2,read $ problemLine !! 3) :: (Int,Int)+ let clauseLines = (map processClause) . (mySplit 0) . (map read) . (concatMap words) . tail $ ls + let clauseMap = foldl f (M.fromList (zip [0 .. varCount -1] $ repeat ([],[]))) (zip [0..] clauseLines)+ let varLook = ((A.listArray (0,varCount -1) (M.elems clauseMap)) A.!)+ let claLook = ((A.listArray (0,clauseCount -1) clauseLines) A.!)+ return $ satproblem clauseCount varCount varLook claLook (M.fromList $ zip [0 .. varCount -1] $ repeat False)+ where+ mySplit target xs = mySplit' [] xs+ where + mySplit' [] [] =[]+ mySplit' ns [] = [reverse ns]+ mySplit' ns (x:xs) | x == target = (reverse ns) : mySplit' [] xs+ | otherwise = mySplit' (x:ns) xs+ processClause cs = let (as,bs) = partition (>0) cs in (map ((+) (-1)) as,map ((+) (-1)) $ map abs bs)+ f m (clauseIndex,(ords,negs)) = let addNeg m' x = M.adjust (\(as,bs)->(as,clauseIndex:bs)) x m'+ addOrd m' x = M.adjust (\(as,bs)->(clauseIndex:as,bs)) x m'+ in foldl addNeg (foldl addOrd m ords) negs ++{- | Save routine for SATProblem, outputs back into SATLIB cnf format. The code @(loadCNFFile f) >>= (saveAsCNF f)@ should +have no effect upon the file. All information such as variable settings and the truth values of clauses is lost.+To save extra information use standard prelude write file function with show. I will try to improve on that +at some point. -}++saveAsCNF :: FilePath->SATProblem->IO ()+saveAsCNF fName s = writeFile fName $ fixedHeader++problemHeader++concatMap prepareClause [0.. (numClauses s)-1]+ where+ fixedHeader = concat ["c\n","c SAT instance in DIMACS CNF input format.\n","c\n"]+ problemHeader = concat ["p cnf ",show . numVariables $ s," ",show . numClauses $ s,"\n"]+ prepareClause c = let (as,bs) = clauseLookUp s c+ (as',bs') = (map (\a->(a,a+1)) as,map (\a->(a,-(a+1))) bs)+ cs = map snd (sortBy (\a b->compare (fst a) (fst b)) $ as' ++ bs')+ in (init . init . concat $ [show k++" " | k<-cs ++ [0]]) ++ "\n"+ ++
+ FileFormat/SATLIB.hs~ view
@@ -0,0 +1,67 @@+-----------------------------------------------------------------------------+-- |+-- Module : FileFormat.SATLIB+-- Copyright : (c) Richard Senington 2011+-- License : GPL-style+-- +-- Maintainer : Richard Senington <sc06r2s@leeds.ac.uk>+-- Stability : provisional+-- Portability : portable+-- +-- The loading routines for the Conjuntive Normal Form (cnf) styled files+-- that can be found on the SATLIB website. Relies upon the+-- @CombinatorialOptimisation.SAT@ library for the data structures.+----------------------------------------------------------------------------- ++module FileFormat.SATLIB(loadCNFFile,saveAsCNF)where++import CombinatorialOptimisation.SAT++import Data.List+import qualified Data.Map as M+import qualified Data.Array as A++{- | Loading routine that takes the file path and returns a SATProblem. All variables will be set to false in the initial +setup, and the truth values of all clauses set appropriately. -}++loadCNFFile :: FilePath->IO(SATProblem)+loadCNFFile fName + = do rawContents<-readFile fName+ let ls = (filter (\x->head x /= 'c')) $ lines rawContents+ let problemLine = words $ head $ filter (\x->head x == 'p') ls+ let (varCount,clauseCount) = if problemLine !! 1 /= "cnf" then error "This is not a CNF file"+ else (read $ problemLine !! 2,read $ problemLine !! 3) :: (Int,Int)+ let clauseLines = (map processClause) . (mySplit 0) . (map read) . (concatMap words) . tail $ ls + let clauseMap = foldl f (M.fromList (zip [0 .. varCount -1] $ repeat ([],[]))) (zip [0..] clauseLines)+ let varLook = ((A.listArray (0,varCount -1) (M.elems clauseMap)) A.!)+ let claLook = ((A.listArray (0,clauseCount -1) clauseLines) A.!)+ return $ satproblem clauseCount varCount varLook claLook (M.fromList $ zip [0 .. varCount -1] $ repeat False)+ where+ mySplit target xs = mySplit' [] xs+ where + mySplit' [] [] =[]+ mySplit' ns [] = [reverse ns]+ mySplit' ns (x:xs) | x == target = (reverse ns) : mySplit' [] xs+ | otherwise = mySplit' (x:ns) xs+ processClause cs = let (as,bs) = partition (>0) cs in (map ((+) (-1)) as,map ((+) (-1)) $ map abs bs)+ f m (clauseIndex,(ords,negs)) = let addNeg m' x = M.adjust (\(as,bs)->(as,clauseIndex:bs)) x m'+ addOrd m' x = M.adjust (\(as,bs)->(clauseIndex:as,bs)) x m'+ in foldl addNeg (foldl addOrd m ords) negs ++{- | Save routine for SATProblem, outputs back into SATLIB cnf format. The code @(loadCNFFile f) >>= (saveAsCNF f)@ should +have no effect upon the file. All information such as variable settings and the truth values of clauses is lost.+To save extra information use standard prelude write file function with show. I will try to improve on that +at some point. -}++saveAsCNF :: FilePath->SATProblem->IO ()+saveAsCNF fName s = writeFile fName $ fixedHeader++problemHeader++concatMap prepareClause [0.. (numClauses s)-1]+ where+ fixedHeader = concat ["c\n","c SAT instance in DIMACS CNF input format.\n","c\n"]+ problemHeader = concat ["p cnf ",show . numVariables $ s," ",show . numClauses $ s,"\n"]+ prepareClause c = let (as,bs) = clauseLookUp s c+ (as',bs') = (map (\a->(a,a+1)) as,map (\a->(a,-(a+1))) bs)+ cs = map snd (sortBy (\a b->compare (fst a) (fst b)) $ as' ++ bs')+ in (init . init . concat $ [show k++" " | k<-cs ++ [0]]) ++ "\n"+ ++
+ FileFormat/TSPLIB.hs view
@@ -0,0 +1,104 @@+module FileFormat.TSPLIB(+ loadTSPFile+ )where++-- only supports a subset of the TSPLIB format+-- not using real parsing libraries. This is probably a mistake.+-- also, still not using ByteString, also a misake.++import CombinatorialOptimisation.TSP+++-- load save of TSPLIB -- can only resave explicit data, could be cripling for big+-- data sets+++-- for those files where the co-ordinates of nodes are given+euclidianDistance :: (Float,Float)->(Float,Float)->Float+euclidianDistance (a,b) (c,d) = sqrt ((a-c)*(a-c)+(b-d)*(b-d))++geoDistance :: (Float,Float)->(Float,Float)->Float+geoDistance (x1,y1) (x2,y2) = encodeFloat (floor dij) 0+ where+ q1 = cos (lon1 - lon2)+ q2 = cos (lat1 - lat2)+ q3 = cos (lat1 + lat2)+ lon1 = degConvert y1+ lon2 = degConvert y2+ lat1 = degConvert x1+ lat2 = degConvert x2+ + dij = 6378.388 * (acos( 0.5*((1.0+q1)*q2 - ((1.0-q1)*q3) )) ) + 1.0++ degConvert m = let deg = encodeFloat (floor m) 0+ miN = m - deg+ in 3.141592 * (deg + (5.0 * miN/3.0))/180.0+{-+readSpecification :: String->([(String,String)],String)+readSpecification s | name -> print?+ | type -> TSP or ATSP only+ | comment -> throw or print+ | dimension Int+ | capacity, not interested+ | edge-weight-type -> Lots+ | edge-weight-format+ | edge-data-format+ | node-coord-type+ | display-data-type+ | eof: end do not expect++-}++data Specification = IGNORE String | USEFUL String String | ENDSPEC String | FAIL String deriving Show++isUsefulSpec (USEFUL _ _) = True+isUsefulSpec _ = False++readSpecificationLine :: String->Specification+readSpecificationLine s + | likeString "NAME" s = IGNORE s+ | likeString "TYPE" s = USEFUL "Type" (trim s)+ | likeString "NODE_COORD_SECTION" s = ENDSPEC "NODE COORD"+ | likeString "EDGE_WEIGHT_SECTION" s = ENDSPEC "EDGE WEIGHT"+ | likeString "COMMENT" s = IGNORE s+ | likeString "DIMENSION" s = USEFUL "Dimension" (trim s)+ | likeString "DISPLAY_DATA_TYPE" s = IGNORE s+ | likeString "EDGE_WEIGHT_TYPE" s = USEFUL "EdgeWeightType" (trim s)+ | otherwise = FAIL $ "unrecognised field in specification : "++s+ where+ likeString q s = take (length q) s == q+ trim s = let s' = (dropWhile (==' ')) . (drop 1) . (dropWhile (/=':')) $ s + in reverse . (dropWhile (==' ')) . reverse $ s'++readSpecification :: [String]->([Specification],[String])+readSpecification [] = ([FAIL "seem to have run out of data, without ending the specification phase"],[]) +readSpecification (s:ss) = let p = readSpecificationLine s+ (rs,es) = readSpecification ss+ in case p of + ENDSPEC k -> ([USEFUL "DATA PART TYPE" k],ss)+ IGNORE _ -> (p:rs,es)+ FAIL _ -> (p:rs,es)+ USEFUL _ _ -> (p:rs,es)+ +loadTSPFile :: String->IO () -- TSPProblem+loadTSPFile fName = do rawContents<-readFile fName+ let (spec,remainder) = readSpecification $ lines rawContents+ mapM_ print spec+ print ""+ mapM_ print $ filter isUsefulSpec spec++{- +readEdgeWeightSection++FULL_MATRIX ++readEdgeWeightSection :: Num a=>String->Int->String->IO (Int->Int->Float)+readEdgeWeightSection ty dim inputData + = do ++readNodeCoordSection :: Num a=>String->Int->String->IO (Int->Int->Float)+readNodeCoordSection dim inputData + = do + ++-}
+ FileFormat/TSPLIB.hs~ view
@@ -0,0 +1,105 @@+module FileFormat.TSPLIB(+ loadTSPFile+ )where++-- only supports a subset of the TSPLIB format+-- not using real parsing libraries. This is probably a mistake.+-- also, still not using ByteString, also a misake.++import CombinatorialOptimisation.TSP+++-- load save of TSPLIB -- can only resave explicit data, could be cripling for big+-- data sets+++-- for those files where the co-ordinates of nodes are given+euclidianDistance :: (Float,Float)->(Float,Float)->Float+euclidianDistance (a,b) (c,d) = sqrt ((a-c)*(a-c)+(b-d)*(b-d))++geoDistance :: (Float,Float)->(Float,Float)->Float+geoDistance (x1,y1) (x2,y2) = encodeFloat (floor dij) 0+ where+ q1 = cos (lon1 - lon2)+ q2 = cos (lat1 - lat2)+ q3 = cos (lat1 + lat2)+ lon1 = degConvert y1+ lon2 = degConvert y2+ lat1 = degConvert x1+ lat2 = degConvert x2+ + dij = 6378.388 * (acos( 0.5*((1.0+q1)*q2 - ((1.0-q1)*q3) )) ) + 1.0++ degConvert m = let deg = encodeFloat (floor m) 0+ miN = m - deg+ in 3.141592 * (deg + (5.0 * miN/3.0))/180.0+{-+readSpecification :: String->([(String,String)],String)+readSpecification s | name -> print?+ | type -> TSP or ATSP only+ | comment -> throw or print+ | dimension Int+ | capacity, not interested+ | edge-weight-type -> Lots+ | edge-weight-format+ | edge-data-format+ | node-coord-type+ | display-data-type+ | eof: end do not expect++-}++data Specification = IGNORE String | USEFUL String String | ENDSPEC String | FAIL String deriving Show++isUsefulSpec (USEFUL _ _) = True+isUsefulSpec _ = False++readSpecificationLine :: String->Specification+readSpecificationLine s + | likeString "NAME" s = IGNORE s+ | likeString "TYPE" s = USEFUL "Type" (trim s)+ | likeString "NODE_COORD_SECTION" s = ENDSPEC "NODE COORD"+ | likeString "EDGE_WEIGHT_SECTION" s = ENDSPEC "EDGE WEIGHT"+ | likeString "COMMENT" s = IGNORE s+ | likeString "DIMENSION" s = USEFUL "Dimension" (trim s)+ | likeString "DISPLAY_DATA_TYPE" s = IGNORE s+ | likeString "EDGE_WEIGHT_TYPE" s = USEFUL "EdgeWeightType" (trim s)+ | otherwise = FAIL $ "unrecognised field in specification : "++s+ where+ likeString q s = take (length q) s == q+ trim s = let s' = (dropWhile (==' ')) . (drop 1) . (dropWhile (/=':')) $ s + in reverse . (dropWhile (==' ')) . reverse $ s'++readSpecification :: [String]->([Specification],[String])+readSpecification [] = ([FAIL "seem to have run out of data, without ending the specification phase"],[]) +readSpecification (s:ss) = let p = readSpecificationLine s+ (rs,es) = readSpecification ss+ in case p of + ENDSPEC k -> ([USEFUL "DATA PART TYPE" k],ss)+ IGNORE _ -> (p:rs,es)+ FAIL _ -> (p:rs,es)+ USEFUL _ _ -> (p:rs,es)+ ++loadTSPFile :: String->IO () -- TSPProblem+loadTSPFile fName = do rawContents<-readFile fName+ let (spec,remainder) = readSpecification $ lines rawContents+ mapM_ print spec+ print ""+ mapM_ print $ filter isUsefulSpec spec++{- +readEdgeWeightSection++FULL_MATRIX ++readEdgeWeightSection :: Num a=>String->Int->String->IO (Int->Int->Float)+readEdgeWeightSection ty dim inputData + = do ++readNodeCoordSection :: Num a=>String->Int->String->IO (Int->Int->Float)+readNodeCoordSection dim inputData + = do + ++-}
+ LICENSE view
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+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main=defaultMain
+ Test.hs~ view
@@ -0,0 +1,62 @@+import CombinatorialOptimisation.SAT +import CombinatorialOptimisation.TSP+import FileFormat.SATLIB+import FileFormat.TSPLIB++import System.Random+import qualified Data.Map as M++{- +main :: IO()+main = do s<-loadCNFFile "./CBS_k3_n100_m403_b10_0.cnf"+ print s+ saveAsCNF "test.cnf" s++-}++{- +-- checking basic Symmetric TSP code and mutator algorithms+main :: IO()+main = do gen<-newStdGen+ let meep = makeSymmetricTSPMap (2,5) 5 gen+ -- print meep+ let meep' = randomiseRoute gen meep+ print meep'+ print $ routeElementToIndex meep'+ print $ indexToRouteElement meep'+ print ""+ let meep'' = exchangeCities 1 1 meep'+ print meep''+ print $ routeElementToIndex meep''+ print $ indexToRouteElement meep''+ putStrLn $ showEdgeWeights meep''++-}++{- +-- checking stability of arrays, rather than map+main :: IO()+main = do gen<-newStdGen+ let (meep,meep') = makeASymmetricTSPMap (2,5) 50 gen+ putStrLn $ showEdgeWeights meep+ putStrLn ""+ putStrLn $ showEdgeWeights meep'+ putStrLn $ show $ showEdgeWeights meep == showEdgeWeights meep'+-}++-- checking stability of arrays, rather than map+main :: IO()+main = do let gen = mkStdGen 5+ let gen' = mkStdGen 10+ let meep = makeEuclideanTSPMap ExplicitMatrix (2,8) (2,8) 100 gen+ let meep' = makeEuclideanTSPMap TriangularMatrix (2,8) (2,8) 100 gen+ let meep'' = makeEuclideanTSPMap Recomputation (2,8) (2,8) 100 gen+ putStrLn $ showEdgeWeights meep+ putStrLn ""+ putStrLn $ showEdgeWeights meep'+ putStrLn $ show $ (showEdgeWeights meep == showEdgeWeights meep') && (showEdgeWeights meep == showEdgeWeights meep'')++{- +-- checking loading TSPs+main :: IO()+main = do loadTSPFile "../exampleProblems/ali535.tsp" -}
+ build.sh~ view
@@ -0,0 +1,3 @@+runghc Setup configure+runghc Setup build+runghc Setup hscolour
+ combinatorial-problems.cabal view
@@ -0,0 +1,38 @@+Name: combinatorial-problems+Version: 0.0.1+Synopsis: A number of data structures to represent and allow the manipulation of standard combinatorial problems, used as test problems in computer science.+Description: In computer science there are a number of standard test problems that are used for testing algorithms, + especially those related to Artificial Intelligence and Operations Research. Online there are a number + of repositories for collections of known interesting problems, for example the TSPLIB at + <http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/> and the SATLIB at + <http://www.satlib.org/>. + .+ This library seeks to provide implementations of data structures to store these problems, along with + functions for manipulating the problems and routines to load problem files from various sources. + .+ At present it only supports TSP and SAT\/SATLIB (TSPLIB coming soon), however it is hoped that the loading routines + can be expanded and the range of problems expanded to cover problems like scheduling and timetabling.+ The internal data structures make heavy use of the @Data.Map@ library and @Data.Array@. It is not currently+ using unboxed values. The library does not use the @bytestring@ library for loading and saving data either, + which will probably need to be changed later.++Stability: experimental+Category: Optimisation+Author: Richard Senington+License: GPL+license-file: LICENSE+Copyright: Copyright (c) 2011 Richard Senington+Homepage: http://www.comp.leeds.ac.uk/sc06r2s/Projects/HaskellLocalSearch+Maintainer: sc06r2s@leeds.ac.uk+Build-Type: Simple+Cabal-Version: >= 1.2++library+ Exposed-Modules: FileFormat.SATLIB+ CombinatorialOptimisation.SAT+ CombinatorialOptimisation.TSP+ Build-Depends: base >= 2.0 && <=5, + random >= 1.0.0.1,+ containers >= 0.2.0.1,+ array >= 0.2.0.0+ extensions:
+ combinatorial-problems.cabal~ view
@@ -0,0 +1,38 @@+Name: combinatorial-problems+Version: 0.0.1+Synopsis: A number of data structures to represent and allow the manipulation of standard combinatorial problems, used as test problems in computer science.+Description: In computer science there are a number of standard test problems that are used for testing algorithms, + especially those related to Artificial Intelligence and Operations Research. Online there are a number + of repositories for collections of known interesting problems, for example the TSPLIB at + <http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/> and the SATLIB at + <http://www.satlib.org/>. + .+ This library seeks to provide implementations of data structures to store these problems, along with + functions for manipulating the problems and routines to load problem files from various sources. + .+ At present it only supports TSP and SAT\/SATLIB (TSPLIB coming soon), however it is hoped that the loading routines + can be expanded and the range of problems expanded to cover problems like scheduling and timetabling.+ The internal data structures make heavy use of the @Data.Map@ library and @Data.Array@. It is not currently+ using unboxed values. The library does not use the @bytestring@ library for loading and saving data either, + which will probably need to be changed later.++Stability: experimental+Category: Optimisation+Author: Richard Senington+License: GPL+license-file: LICENSE+Copyright: Copyright (c) 2011 Richard Senington+Homepage: http://www.comp.leeds.ac.uk/sc06r2s/Projects/HaskellLocalSearch+Maintainer: sc06r2s@leeds.ac.uk+Build-Type: Simple+Cabal-Version: >= 1.2++library+ Exposed-Modules: FileFormat.SATLIB+ CombinatorialOptimisation.SAT+ CombinatorialOptimisation.TSP+ Build-Depends: base >= 2.0 && <=5, + random >= 1.0.0.1,+ containers >= 0.2.0.1,+ array >= 0.2.0.0+ extensions:
+ new file~ view