diff --git a/CombinatorialOptimisation/SAT.hs b/CombinatorialOptimisation/SAT.hs new file mode 100644 --- /dev/null +++ b/CombinatorialOptimisation/SAT.hs @@ -0,0 +1,186 @@ +----------------------------------------------------------------------------- +-- | +-- Module : CombinatorialOptimisation.SAT +-- Copyright : (c) Richard Senington 2011 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- 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') + + diff --git a/CombinatorialOptimisation/SAT.hs~ b/CombinatorialOptimisation/SAT.hs~ new file mode 100644 --- /dev/null +++ b/CombinatorialOptimisation/SAT.hs~ @@ -0,0 +1,186 @@ +----------------------------------------------------------------------------- +-- | +-- Module : CombinatorialOptimisation.SAT +-- Copyright : (c) Richard Senington 2011 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- 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') + + diff --git a/CombinatorialOptimisation/TSP.hs b/CombinatorialOptimisation/TSP.hs new file mode 100644 --- /dev/null +++ b/CombinatorialOptimisation/TSP.hs @@ -0,0 +1,262 @@ +----------------------------------------------------------------------------- +-- | +-- Module : CombinatorialOptimisation.TSP +-- Copyright : (c) Richard Senington 2011 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- 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)) + + + diff --git a/CombinatorialOptimisation/TSP.hs~ b/CombinatorialOptimisation/TSP.hs~ new file mode 100644 --- /dev/null +++ b/CombinatorialOptimisation/TSP.hs~ @@ -0,0 +1,262 @@ +----------------------------------------------------------------------------- +-- | +-- Module : CombinatorialOptimisation.TSP +-- Copyright : (c) Richard Senington 2011 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- 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)) + + + diff --git a/FileFormat/SATLIB.hs b/FileFormat/SATLIB.hs new file mode 100644 --- /dev/null +++ b/FileFormat/SATLIB.hs @@ -0,0 +1,67 @@ +----------------------------------------------------------------------------- +-- | +-- Module : FileFormat.SATLIB +-- Copyright : (c) Richard Senington 2011 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- 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" + + + diff --git a/FileFormat/SATLIB.hs~ b/FileFormat/SATLIB.hs~ new file mode 100644 --- /dev/null +++ b/FileFormat/SATLIB.hs~ @@ -0,0 +1,67 @@ +----------------------------------------------------------------------------- +-- | +-- Module : FileFormat.SATLIB +-- Copyright : (c) Richard Senington 2011 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- 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" + + + diff --git a/FileFormat/TSPLIB.hs b/FileFormat/TSPLIB.hs new file mode 100644 --- /dev/null +++ b/FileFormat/TSPLIB.hs @@ -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 + + +-} diff --git a/FileFormat/TSPLIB.hs~ b/FileFormat/TSPLIB.hs~ new file mode 100644 --- /dev/null +++ b/FileFormat/TSPLIB.hs~ @@ -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 + + +-} 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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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main=defaultMain diff --git a/Test.hs~ b/Test.hs~ new file mode 100644 --- /dev/null +++ b/Test.hs~ @@ -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" -} diff --git a/build.sh~ b/build.sh~ new file mode 100644 --- /dev/null +++ b/build.sh~ @@ -0,0 +1,3 @@ +runghc Setup configure +runghc Setup build +runghc Setup hscolour diff --git a/combinatorial-problems.cabal b/combinatorial-problems.cabal new file mode 100644 --- /dev/null +++ b/combinatorial-problems.cabal @@ -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 + and the SATLIB at + . + . + 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: diff --git a/combinatorial-problems.cabal~ b/combinatorial-problems.cabal~ new file mode 100644 --- /dev/null +++ b/combinatorial-problems.cabal~ @@ -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 + and the SATLIB at + . + . + 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: diff --git a/new file~ b/new file~ new file mode 100644 --- /dev/null +++ b/new file~