The problem data is organized and passed to the solver in an instance of the class TspInstance<V,E>. Note the use of generics. Here V is the type of the objects that will correspond to vertices and E is the type of the objects that will correspond to edges. The point of generics is that our code will not really depend on what the types of our nodes and edges are. Lets take a quick look at the highlights of the public interface to this class. | Code Block |
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public UndirectedGraph<V, E> getGraph() {
...
}
public Function<E, Integer> getEdgeWeights() {
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}
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The UndirectedGraph<V,E> returned by getGraph() is from the JUNG library. You can view the complete documentation here (this page might be more helpful), but some important highlights are Name | Return Type | Arguments | Description |
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addVertex | boolean | V vertex | Adds vertex to this graph. Fails if vertex is null or already in the graph. | addEdge | boolean | E e, V v1, V v2 | Adds edge e to this graph such that it connects vertex v1 to v2. | findEdge | E | V v1, V v2 | Returns an edge that connects this vertex to vvertex v1 and vertex v2. Returns null if either v2 is not connected to v1 or either v1 or v2 are not present in this graph. | getIncidentEdges | Collection<E> | V vertex | Returns the collection of edges in this graph which are connected to vertex. | getVertices | Collection<V> | | Returns a view of all vertices in this graph. | getEdges | Collection<E> | | Returns a view of all edges in this graph. |
The Function<E,Integer> will give the cost of any edge for our optimization. The interface is quite simple: Name | Return Type | Arguments | Description |
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apply | Integer | E edge | Returns the result of applying this function to edge. |
Solver InterfaceOpen the file src/solver/TspIpSolver.java by double clicking it from the Project Explorer. This is the file we will be primarily editing. It should contain the following (after the imports):
Toggle TspIpSolver.java | Cloak |
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| visible | true |
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| id | TspIpSolverStart |
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For now, nothing in this class does much. Below, we summarize how all the parts should work. The enum Option is a collection of flags that can be passed in to the solver indicating what special techniques the solver should use. We now briefly summarize what each option indicates: Option Name | Description |
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lazy | Add a LazyConstraintCallback to check potential integer solutions to ensure that the cutset constraints are satisfied. Without this option, there is no guarantee that cutset constraints are checked. | userCut | Add a UserCutCallback to check fractional solutions to ensure that the cutset constraints are satisfied. | randomizedUserCut | A variant of userCut where only a random subset of the cutset constraints are checked. If flagged, userCut should not be flagged | christofidesApprox | Use Christofides Algorithm to give an initial solution to CPLEX. | christofidesHeuristic | Use a variant of Christofides Algorithm to generate integer solutions from fractional solutions. | twoOpt | Use the Two-Opt local search heuristic to improve solutions generated by christofidesApprox, christofidesHeuristic, or incumbent, if any are selected. | incumbent | Collect integer solutions found by CPLEX to have Two-Opt applied. Requires that twoOpt is flagged. |
Next, the constructors for class TspIpSolver: Arguments | Description |
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TspInstance<V,E> tspInstance, EnumSet<Option> options | Creates an instance of the solver according to options | TspInstance<V,E> tspInstance | Creates an instance of the solver with the default options {lazy, userCut, christofidesApprox, christofidesHeuristic} |
Finally, the methods of the class should behave as follows: Name | Return Type | Arguments | Description |
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solve | void | | Runs CPLEX to solve the TSP with problem data given by TspInstance. Do not call more than once. | getEdgesInOpt | ImmutableSet<E> | | Returns the subset of the edges of the TspInstance that are in the optimal solution. Do not call until solve() has finished. Behavior is undefined otherwise. | getOptVal | double | | Returns the value of the optimal solution. Do not call until solve() has finished. Behavior is undefined otherwise. |
Now that we understand the problem, we can begin implementing a solution! |