combinatorial-problems-0.0.2: A number of data structures to represent and allow the manipulation of standard combinatorial problems, used as test problems in computer science.

Portability portable provisional Richard Senington

CombinatorialOptimisation.TSP

Description

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.

Synopsis

# Documentation

data TSPProblem Source

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.

Constructors

 TSPProblem FieldscurrentPrice :: Float routeMap :: Map Int (Int, Int) edgePrices :: Int -> Int -> Float numCities :: Int routeElementToIndex :: Map Int Int indexToRouteElement :: Map Int Int

Instances

 Show TSPProblem

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.

Constructors

 ExplicitMatrix TriangularMatrix Recomputation

Instances

 Eq InternalStorage Show InternalStorage

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.

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.

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.

A brute force recalculation of the current length of the path. Use sparingly.

randomiseRoute :: RandomGen g => g -> TSPProblem -> TSPProblemSource

Shuffles a simple list of cities and then passes off the work to setRoute.

setRoute :: [Int] -> TSPProblem -> TSPProblemSource

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.

makeASymmetricTSPMap :: RandomGen g => (Float, Float) -> Int -> g -> TSPProblemSource

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.

makeSymmetricTSPMap :: RandomGen g => InternalStorage -> (Float, Float) -> Int -> g -> TSPProblemSource

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.

makeEuclideanTSPMap :: RandomGen g => InternalStorage -> (Float, Float) -> (Float, Float) -> Int -> g -> TSPProblemSource

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.