packages feed

local-search (empty) → 0.0.1

raw patch · 9 files changed

+1294/−0 lines, 9 filesdep +basedep +containersdep +randomsetup-changed

Dependencies added: base, containers, random

Files

+ Control/Search/Local.hs view
@@ -0,0 +1,149 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Control.Search.Local+-- Copyright   :  (c) Richard Senington & David Duke 2010+-- License     :  GPL-style+-- +-- Maintainer  :  Richard Senington <sc06r2s@leeds.ac.uk>+-- 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'')++++
+ Control/Search/Local/Example.hs view
@@ -0,0 +1,148 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Control.Search.Local.Example+-- Copyright   :  (c) Richard Senington & David Duke 2010+-- License     :  GPL-style+-- +-- Maintainer  :  Richard Senington <sc06r2s@leeds.ac.uk>+-- 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++++++ +
+ Control/Search/Local/Navigator.hs view
@@ -0,0 +1,48 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Control.Search.Local.Navigator+-- Copyright   :  (c) Richard Senington & David Duke 2010+-- License     :  GPL-style+-- +-- Maintainer  :  Richard Senington <sc06r2s@leeds.ac.uk>+-- 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)         +                         ++
+ Control/Search/Local/Neighbourhood.hs view
@@ -0,0 +1,66 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Control.Search.Local.Neighbourhood+-- Copyright   :  (c) Richard Senington & David Duke 2010+-- License     :  GPL-style+-- +-- Maintainer  :  Richard Senington <sc06r2s@leeds.ac.uk>+-- 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
+ Control/Search/Local/Transformation.hs view
@@ -0,0 +1,134 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Control.Search.Local.Transformation+-- Copyright   :  (c) Richard Senington & David Duke 2010+-- License     :  GPL-style+-- +-- Maintainer  :  Richard Senington <sc06r2s@leeds.ac.uk>+-- 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 (<t) (treeNodeChildren t)+                 in LSTree (treeNodeName t) ns'++{- | A helper function for shuffling lists, based upon a +   randomised sequence of numbers (expected). -}++shuffle :: (Ord b)=>[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<thresh)   $ treeNodeChildren t+     ns' = map (thresholdWorsening thresh) ns  ++{- | An adaptation of the above. We now have a list of thresholds, constructed in +some way (user defined) and then applied each to a different level of the tree.+Used in one of the Simulated Annealing experiments. -}++varyingThresholdWorsening :: NumericallyPriced nme a=>[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 - tP<thresh)   $ treeNodeChildren t+     ns' = map (varyingThresholdWorsening thresh') ns    ++{- | Takes a list of single level transformations, and applies them each to a different level+of a tree. These are also generated in a user defined way, and this function is used +in the other Simulated Annealing experiment. -}++multiLevelApply :: [LSTree nme->LSTree nme]->LSTree nme->LSTree nme+multiLevelApply (x:xs) t = let ns = map (multiLevelApply xs) (treeNodeChildren $ x t)+                           in LSTree (treeNodeName t) ns++++
+ Control/Search/Local/Tree.hs view
@@ -0,0 +1,40 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Control.Search.Local.Tree+-- Copyright   :  (c) Richard Senington & David Duke 2010+-- License     :  GPL-style+-- +-- Maintainer  :  Richard Senington <sc06r2s@leeds.ac.uk>+-- 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)++
+ LICENSE view
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+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main=defaultMain
+ local-search.cabal view
@@ -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