diff --git a/Control/Search/Local.hs b/Control/Search/Local.hs new file mode 100644 --- /dev/null +++ b/Control/Search/Local.hs @@ -0,0 +1,149 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Control.Search.Local +-- Copyright : (c) Richard Senington & David Duke 2010 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- Stability : provisional +-- Portability : portable +-- +-- This is the unification, and it is not expected that a user will have to directly import any other files, they are +-- all exposed through this one. It then defines some basic search strategies of its own. +----------------------------------------------------------------------------- + +module Control.Search.Local ( + -- Strategies + firstImprov, + minImprov, + maxImprov, + randomImprov, + randomWalk, + simpleTabu, + minFirstTabu, + maxFirstTabu, + stochasticTabu, + saTemp, + simulatedAnnealingA, + simulatedAnnealingB, + + -- Navigators + firstChoice, + manualNavigator, + -- Transformations + improvement, + nShuffle, + nSort, + nReverse, + tabu, + thresholdWorsening, + varyingThresholdWorsening, + multiLevelApply, + sImprovement, + + -- The internal tree, and accessor functions + LSTree(LSTree), + treeNodeName, + treeNodeChildren, + mkTree, + + -- Neighbourhoods and problem specific stuff + exchange, + basicExchange, + priceSolution, + NumericallyPriced +)where + +import Control.Search.Local.Tree +import Control.Search.Local.Transformation +import Control.Search.Local.Navigator +import Control.Search.Local.Neighbourhood +import System.Random + +-- | First improvement, relies upon the solutions forming an ordering. + +firstImprov :: Ord nme=>LSTree nme->[nme] +firstImprov = firstChoice . improvement + +{- | Minimal improvement, will take the worst solution, that still improves upon the current + solution. It is slightly more cautious, and is likely to create longer paths in most problems. -} + +minImprov :: Ord nme=>LSTree nme->[nme] +minImprov = firstImprov . nSort + +-- | Maximal improvement, always takes the best neighbour, and stops when there are no more improvements + +maxImprov :: Ord nme=>LSTree nme->[nme] +maxImprov = firstImprov . nReverse . nSort + +-- | Random improvement, only accepts improvements, but is less predictable as to which it will take. + +randomImprov :: (RandomGen g,Ord nme)=>g->LSTree nme->[nme] +randomImprov g = firstImprov . (nShuffle g) + +{- | The simplest strategy. The randomisation may not be needed, it depends how + structured the tree is originally. Using the basicExchange function it will + be very ordered, so this is useful. -} + +randomWalk :: RandomGen g=>g->LSTree nme->[nme] +randomWalk g = firstChoice . (nShuffle g) + +{- | The simplest Tabu search, simply disallows backtracking, should do slightly better than a random walk, + but that is about it. -} + +simpleTabu :: Eq nme=>Int->LSTree nme->[nme] +simpleTabu l = firstChoice . (tabu l []) + +{- | This will always choose the lowest ordered element of the +neighbourhood, unless it has been seen recently. +The choice of the minFirstTabu or maxFirstTabu, depends upon the +problem, and how it has been encoded, does the user wish for +high ordered, or low ordered solutions. In most cases the +other becomes pointless. -} + +minFirstTabu :: Ord nme=>Int->LSTree nme->[nme] +minFirstTabu l = (simpleTabu l) . nSort + +maxFirstTabu :: Ord nme=>Int->LSTree nme->[nme] +maxFirstTabu l = (simpleTabu l) . nReverse . nSort + +{- | Injection of a random element into TABU, less useful than it +sounds in this case, as this is very similar to simpleTabu. +In practice, real TABU systems use a process of choices. +If improvement is possible (subject to the TABU list) you +accept the first (in whatever order, that is where randomness comes in) +improvement you find. Otherwise you take another element and continue. +This has not yet been represented. -} + +stochasticTabu :: (Eq nme,RandomGen g)=>Int->g->LSTree nme->[nme] +stochasticTabu l g =(simpleTabu l) . (nShuffle g ) + +{- | A helper function for creating a falling temperature list. Used by +Simulated Annealing. Really just to make it slightly easier to see +what it is doing. -} + +saTemp :: Num a=>a->a->[a] +saTemp p iTemp = iterate (*p) iTemp + +{- | There are two variants on simulated annealing represented here. The first is simpler, +it assumes that the temperature represents a threshold for a limited worsening filter. +This is applied, and the system is then navigated randomly. -} + +simulatedAnnealingA :: (NumericallyPriced nme a,RandomGen g)=>a->a->g->LSTree nme->[nme] +simulatedAnnealingA p iTemp g = firstChoice . (varyingThresholdWorsening (saTemp p iTemp)) . (nShuffle g) + +{- | +The second takes the approach that SA tends to be (based upon a level of randomisation) +a random walk at high temperatures, and an iterative improver at low temperatures. +It generates a list of single level transformations based upon this idea, and then +applies them one at a time. -} + +simulatedAnnealingB :: (Ord nme,RandomGen g,Num a,Random a,Ord a)=>a->a->g->LSTree nme->[nme] +simulatedAnnealingB p iTemp g = let (g' , g'' ) = split g + xs = zip (saTemp p iTemp) (randoms g') + gFuncs = [if x < y then id else sImprovement | (x, y ) <- xs ] + in firstChoice . (multiLevelApply gFuncs) . (nShuffle g'') + + + + diff --git a/Control/Search/Local/Example.hs b/Control/Search/Local/Example.hs new file mode 100644 --- /dev/null +++ b/Control/Search/Local/Example.hs @@ -0,0 +1,148 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Control.Search.Local.Example +-- Copyright : (c) Richard Senington & David Duke 2010 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- Stability : provisional +-- Portability : portable +-- +-- An example of the system running, on some randomly generated TSP (Traveling Sales Person) problems. +-- The focus of the code is on generation of TSPs and representation of them. +----------------------------------------------------------------------------- + +module Control.Search.Local.Example ( + main +) where + +import Control.Search.Local +import System.Random +import qualified Data.Map as M + +-- | The data types defined are TSPMaps, the problems, and TSPTours, the solutions. + +data TSPMap = TSPMap { tspNumCities :: Int, + tspLinkPricer :: Int->Int->Float} + +data TSPTour = TSPTour { tspPath :: [Int], + tspCost :: Float} + +{- | Slightly out of date with the TSPTour data type, but this is the function +that combines a sequence with a map, and gives a price. It is very slow, +as it loops over an entire solution list every time it is called. -} + +priceTour :: TSPMap->[Int]->Float +priceTour (TSPMap _ f) xs = let priceTour' (_:[]) = 0 + priceTour' (s:(ks@(k:_))) = f s k + (priceTour' ks) + in priceTour' xs + +-- | makeTour is a helper function for taking a sequence of ints and returning a TSPTour data type, capturing the path and the price. + +makeTour :: TSPMap->[Int]->TSPTour +makeTour m p = TSPTour p (priceTour m p) + +{- | The TSPTour is then made member of a number of classes that are needed for interaction with the library, + Eq, Ord, Show (for display to the user) and NumericallyPriced. -} + +instance Eq TSPTour where + (==) a b = (tspPath a) == (tspPath b) + +instance Ord TSPTour where + compare a b = compare (tspCost a) (tspCost b) + +instance NumericallyPriced TSPTour Float where + priceSolution t = tspCost t + +instance Show TSPTour where + show (TSPTour p c) = "Tour : "++ (show p) ++" with cost "++(show c) + +{- | This is a wrapper, to allow a user of this example to create a specialised TSP neighbourhood, complete with pricing + from a basic neighbourhood function from the Neighbourhood file. -} + +tourNeighbourhood :: ([Int]->[[Int]])->TSPMap->TSPTour->[TSPTour] +tourNeighbourhood basicNeighbourhood m t + = let n = basicNeighbourhood $ tspPath t + f = makeTour m + in map f n + +-- | Make an Asymmetric TSP example problem + +makeASymmetricTSPMap :: RandomGen g=>Float->Int->g->TSPMap +makeASymmetricTSPMap distanceUpperLimit numCities g + = let cities = [0 ..(numCities-1)] + cityCoords = [(a,b) | a<-cities,b<-cities,a/=b] + matrix = M.fromList $ zip cityCoords (randomRs (1,distanceUpperLimit) g) + in TSPMap numCities (\x y->M.findWithDefault 0 (x,y) matrix) + +-- | Make a Symmetric TSP example problem + +makeSymmetricTSPMap :: RandomGen g=>Float->Int->g->TSPMap +makeSymmetricTSPMap distanceUpperLimit 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 (1,distanceUpperLimit) g)) + in TSPMap numCities (\x y->M.findWithDefault 0 (x,y) matrix) + +-- | So that we can convince ourselves the maps have the properties suggested by the names. + +displayTSPMap :: TSPMap->IO() +displayTSPMap (TSPMap n f) = + do let cities = [0 ..(n-1)] + let cityCoords = [(a,b) | a<-cities,b<-cities,a/=b] + mapM_ (print.show) (zip cityCoords $ map (\(x,y)->f x y) cityCoords) + +{- | +The manual solve example, give it a tree transformation you wish to see +used, and a map, with an initial solution sequence. E.g. + +import System.Random +g <- getStdGen +let p = makeSymmetricTSPMap 10 10 g +manualSolve improvement p [0..9] + +(this will work on the GHCI command prompt) -} + +manualSolve :: (LSTree TSPTour->LSTree TSPTour)->TSPMap->[Int]->IO() +manualSolve trans tspmap iPath = + do let tourN = tourNeighbourhood basicExchange tspmap + let tree = mkTree tourN (makeTour tspmap iPath) + (manualNavigator :: LSTree TSPTour->IO()) (trans tree) + +{- | +And this is closer to useful code, though still printing out, not returning +a list. The termination condition of this process is just to run until +it hits 50, or the list ends. More sophisticated post navigation +behaviour is also possible. + +Example usage. + +import System.Random +g <- getStdGen +let p = makeSymmetricTSPMap 10 10 g +justResultsSequence minImprov p [0..9] +justResultsSequence (simulatedAnnealingA 0.8 40 g) p [0..9] -} + +justResultsSequence :: (LSTree TSPTour->[TSPTour])->TSPMap->[Int]->IO() +justResultsSequence trans tspmap iPath = + do let tourN = tourNeighbourhood basicExchange tspmap + let tree = mkTree tourN (makeTour tspmap iPath) + mapM_ print $ take 50 $ trans tree + +{- | Finally a main function, to allow users to just run it and see what it does -} + +main = do g <- getStdGen + let tspmap = makeSymmetricTSPMap 10 10 g + let tourN = tourNeighbourhood basicExchange tspmap + let iPath = [0..9] + let tree = mkTree tourN (makeTour tspmap iPath) + mapM_ print $ take 50 $ minImprov tree -- so you can see it just running + (manualNavigator :: LSTree TSPTour->IO()) ((improvement . nSort) tree) -- so you can step through the process and see what the rest of the space looks like + + + + + + + diff --git a/Control/Search/Local/Navigator.hs b/Control/Search/Local/Navigator.hs new file mode 100644 --- /dev/null +++ b/Control/Search/Local/Navigator.hs @@ -0,0 +1,48 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Control.Search.Local.Navigator +-- Copyright : (c) Richard Senington & David Duke 2010 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- Stability : provisional +-- Portability : portable +-- +-- The two ways to navigate a tree. The paper reduced all the different local search strategies to transformations +-- composed with a first choice system, so that is the navigator that is expected to be used. However we also +-- provide a manual inspection navigator, that allows for human interaction, by typing the number of the node +-- you wish to move to. +----------------------------------------------------------------------------- + +module Control.Search.Local.Navigator ( + firstChoice, + manualNavigator +)where + +import Control.Search.Local.Tree +import Control.Search.Local.Transformation +import Control.Search.Local.Neighbourhood + +firstChoice :: LSTree a->[a] +firstChoice t | (null.treeNodeChildren) t = [treeNodeName t] + | otherwise = treeNodeName t : (firstChoice (head (treeNodeChildren t))) + +-- | Types left out of the next two parts because of compilation problems with type inference if included. + +manualNavigator t = + do displayLSSpace t + putStr ": " + x<-getLine + if x=="q" then return () + else do let i = (read x)::Int + manualNavigator (treeNodeChildren t !! i) + +displayLSSpace t = + do let nme = treeNodeName t + putStrLn $ "Current Location : "++(show nme) + putStrLn $ " Current Price : " -- ++(show $ priceSolution nme) + putStrLn $ " Neighbourhood" + mapM_ putStrLn $ map (\(x,y)->" "++(show x)++" "++(show.treeNodeName $ y)++" "++(show.priceSolution.treeNodeName $ y)) (zip [0..] $ treeNodeChildren t) + + + diff --git a/Control/Search/Local/Neighbourhood.hs b/Control/Search/Local/Neighbourhood.hs new file mode 100644 --- /dev/null +++ b/Control/Search/Local/Neighbourhood.hs @@ -0,0 +1,66 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Control.Search.Local.Neighbourhood +-- Copyright : (c) Richard Senington & David Duke 2010 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- Stability : provisional +-- Portability : portable +-- +-- Simple Neighbourhood functions for the representation of problems to the library. +-- All neighbourhood functions must ultimately be of the form a->[a]. +-- +-- This module also contains some additional code for the modeling of problems and the +-- link between the model and the library. +----------------------------------------------------------------------------- + +module Control.Search.Local.Neighbourhood ( + exchange, + basicExchange, + priceSolution, + NumericallyPriced +) where + +import Data.List + +-- | following helper function pinched from http://www.polyomino.f2s.com/david/haskell/combinatorics.html + +combinationsOf 0 _ = [[]] +combinationsOf _ [] = [] +combinationsOf k (x:xs) = map (x:) (combinationsOf (k-1) xs) ++ combinationsOf k xs + +{- | my code again from here on + +The first type of neighbourhood is based upon combination exchange in a sequence of elements. This is appropriate for something like TSP, where +order matters, but would be less useful for SAT. + +It takes 2 numbers as parameters, one of which is the number of exchanges to perform, the other the maximum distance within the list. +For example exchange 2 2, would change up to 2 elements in each neighbourhood, either adjacent or separated by 1 other element. -} + +exchange :: Eq a=>Int->Int->[a]->[[a]] +exchange _ 0 inlist = [inlist] +exchange exchanges dist inlist = nub (map (implement inlist) variants) + where + len = (length inlist -1) + opts = [(x,x+y) | x<-[0..len],y<-[1..dist],x+y<= len] + variants = combinationsOf exchanges opts + implement :: [a]->[(Int,Int)]->[a] + implement i [] = i + implement i ((x,y):xs) = implement (begin++[x2]++middle++[x1]++rest') xs + where + (begin,x1:rest) = splitAt x i + (middle,x2:rest') = splitAt (y-x-1) rest + +-- | We provide the most basic exchange system for testing + +basicExchange :: Eq a=>[a]->[[a]] +basicExchange = exchange 1 1 + +{- | +Some transformations (and the manual inspector of the search process) need to be able to extract a numeric price from +a solution. To use these, the solution representation data type must be a part of the following class, please see +the example code. -} + +class (Ord b,Num b)=>NumericallyPriced a b | a->b where + priceSolution :: a->b diff --git a/Control/Search/Local/Transformation.hs b/Control/Search/Local/Transformation.hs new file mode 100644 --- /dev/null +++ b/Control/Search/Local/Transformation.hs @@ -0,0 +1,134 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Control.Search.Local.Transformation +-- Copyright : (c) Richard Senington & David Duke 2010 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- Stability : provisional +-- Portability : portable +-- +-- Transformations for capturing characteristics of algorithms. +----------------------------------------------------------------------------- + +module Control.Search.Local.Transformation ( + improvement, + nShuffle, + nSort, + nReverse, + tabu, + thresholdWorsening, + varyingThresholdWorsening, + multiLevelApply, + sImprovement +) where + +-- | Transformations for the trees, to capture specific characteristics of different local search algorithms. + +import Control.Search.Local.Tree +import Control.Search.Local.Neighbourhood +import Data.List +import System.Random + +{- | A basic recursive filter. This will check every neighbourhood, and remove those +neighbours that do not improve upon their parent solution. -} + +improvement :: Ord nme=>LSTree nme -> LSTree nme +improvement = multiLevelApply (repeat sImprovement) + +{- | A single level improvement transformation, that will remove from the top neighbourhood +of the tree those solutions that do not improve upon the parent solution. It is +used by both the recursive improvement transformation, and one of the +attempts to encode Simulated Annealing. -} + +sImprovement :: Ord nme=>LSTree nme -> LSTree nme +sImprovement t = let ns' = filter ([b]->[a]->[a] +shuffle rs xs = map snd (sortBy (\(a,_) (b,_)->compare a b) $ zip rs xs) + +{- | Another helper, to generate a specific number of random values from a + generator, and return them with the updated generator. -} + +makeLimitedRands :: (Random a,RandomGen g)=>g->Int->([a],g) +makeLimitedRands g l = foldl f ([],g) [1..l] + where + f (a,b) _ = let (c,b') = random b + in (c:a,b') + +-- | Recursive neighbourhood shuffling transformation, all neighbourhoods will become randomised. + +nShuffle :: RandomGen g=>g->LSTree nme -> LSTree nme +nShuffle g t = LSTree (treeNodeName t) ns' + where + ns = treeNodeChildren t + (rs,g') = makeLimitedRands g $ length ns + ns' = map (nShuffle g') (shuffle (rs :: [Int]) ns) + +{- | Recursive neighbourhood ordering transformation. Could be reimplemented in +the future in a similar way to improvement, with a single level +transformation, this would allow odd combinations in lists to be used in +other multi-apply configurations. -} + +nSort :: Ord nme=>LSTree nme -> LSTree nme +nSort t = let ns = sort (treeNodeChildren t) + in LSTree (treeNodeName t) ns + +{- | Reversal, recursive again. To be used in combination with sorting to + place in ascending or descending order, depending on what you want. -} + +nReverse :: LSTree nme -> LSTree nme +nReverse t = LSTree (treeNodeName t) (reverse $ treeNodeChildren t) + +{- | A simple (very simple) TABU system. Based upon a limited Queue, and +direct node comparison (not the way it is usually used in the OR +community). Acts as a recursive filter based upon memory. -} + +tabu :: Eq nme=>Int->[nme]->LSTree nme->LSTree nme +tabu queueSize q t = LSTree nme ns'' + where + nme = treeNodeName t + q' = take queueSize $ nme:q + ns' = filter (\n->not $ elem (treeNodeName n) q') (treeNodeChildren t) + ns'' = map (tabu queueSize q') ns' + +{- | Takes advantage of numerically priced solutions, rather than just ordering, +to allow through solutions that are worse than the current solution, but +only to a limited extent. Would require some understanding of the maximum +and minimum differences likely in a solution set. -} + +thresholdWorsening :: NumericallyPriced nme a=>a->LSTree nme->LSTree nme +thresholdWorsening thresh t = LSTree nme ns' + where + nme = treeNodeName t + tP = priceSolution nme + ns = filter (\n->(priceSolution.treeNodeName) n - tP[a]->LSTree nme->LSTree nme +varyingThresholdWorsening (thresh:thresh') t = LSTree nme ns' + where + nme = treeNodeName t + tP = priceSolution nme + ns = filter (\n->(priceSolution.treeNodeName) n - tPLSTree nme]->LSTree nme->LSTree nme +multiLevelApply (x:xs) t = let ns = map (multiLevelApply xs) (treeNodeChildren $ x t) + in LSTree (treeNodeName t) ns + + + + diff --git a/Control/Search/Local/Tree.hs b/Control/Search/Local/Tree.hs new file mode 100644 --- /dev/null +++ b/Control/Search/Local/Tree.hs @@ -0,0 +1,40 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Control.Search.Local.Tree +-- Copyright : (c) Richard Senington & David Duke 2010 +-- License : GPL-style +-- +-- Maintainer : Richard Senington +-- Stability : provisional +-- Portability : portable +-- +-- The internal data structure of the library. +----------------------------------------------------------------------------- + +module Control.Search.Local.Tree( + LSTree(LSTree),treeNodeName,treeNodeChildren,mkTree +)where + +{- | A rose tree, but not currently using an optimised data structure, just this little + home built one. The accessor functions should be easy enough to understand. -} + +data LSTree nme = LSTree {treeNodeName :: nme, + treeNodeChildren :: [LSTree nme]} + +{- | The construction function, as seen in the paper. Takes a neighbourhood function, that + is, a function that takes a solution and perterbs it in some way, giving a selection of + new solutions. It then requires a seed, and gives back an initial tree. -} + +mkTree :: (a->[a])->a->LSTree a +mkTree f seed = LSTree seed $ map (mkTree f) (f seed) + +{- | Making a tree part of Ord and Eq, for ease of comparison later. + Note that how the order is determined depends upon the implementation given for a solution. -} + +instance (Ord nme)=>Ord (LSTree nme) where + compare t1 t2 = compare (treeNodeName t1) (treeNodeName t2) + +instance (Eq nme)=>Eq (LSTree nme) where + (==) t1 t2 = (treeNodeName t1) == (treeNodeName t2) + + 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/local-search.cabal b/local-search.cabal new file mode 100644 --- /dev/null +++ b/local-search.cabal @@ -0,0 +1,33 @@ +Name: local-search +Version: 0.0.1 +Synopsis: AA first attempt at generalised local search within Haskell, for applications in combinatorial optimisation. +Description: This library represents a first attempt at creating a generalised library for + local (non-exhaustive) search in Haskell. It is based on work presented to + IFL2010, a draft of which is currently available on the homepage. The library + models local search space using a rose tree, with child nodes forming the + neighbourhood of any solution. The tree can then be transformed by various + combinators to implement different searching strategies; the result is then + "navigated" to yield a sequence of solutions. +Stability: experimental +Category: Control, Optimisation, Local Search +Author: Richard Senington & David Duke +License: GPL +license-file: LICENSE +Copyright: Copyright (c) 2010 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: Control.Search.Local, + Control.Search.Local.Example + Control.Search.Local.Navigator + Control.Search.Local.Neighbourhood + Control.Search.Local.Transformation + Control.Search.Local.Tree + Build-Depends: base >= 2.0 && <=5, + random >= 1.0.0.1, + containers >= 0.2.0.1 + extensions: MultiParamTypeClasses, + FunctionalDependencies