TreesearchLib is a framework for modeling optimization problems that are to be solved by constructive heuristics. It includes a number of algorithms: exhaustive depth-first and breadth-first search, limited discrepancy search, the PILOT method, beam search, monotonic beam search, rake search, and Monte Carlo tree search.
$ dotnet add package TreesearchLibTreesearchLib is a C# framework for modeling optimization problems as search trees and a collection of algorithms to identify good solutions for those problems. It includes exhaustive algorithms, as well as heuristics.
Modeling optimization problems is performed by implementing a problem state class. This class maintains the decisions that have been taken, as well as the next choices, i.e., branches in the search tree. It is possible to compute bounds, which algorithms may use to discard parts of the tree.
class MyProblem : IState<MyProblem, Minimize> {
bool IsTerminal { get; }
TQuality Bound { get; }
TQuality? Quality { get; }
IEnumerable<TState> GetBranches();
}
You can use a default bound, e.g. a low enough value for Minimize, or a high enough value for Maximize, if you don't have a specific bound. Of course stronger bounds make the application of exhaustive algorithms more efficient. You should return a quality value, at least for a terminal state, but also if a quality can be estimated for non-terminal states. Finally, GetBranches() returns all descendet states, sorted in a way that the first branch returned is likely the best one. Depth-first search has a bias to descend into the first branch first, also limited discrepancy search assumes the first branch is the one that incurs no cost to follow, while the second and third branch already cost 1 or 2 "discrepancies". Beam search and monotonic beam search allow to define a separate rank function.
When you implement a Bound and use it for sorting (e.g. in beam search), make sure the calculation is cached in the state class. Otherwise, the performance of beam search will be unnecessarily bad.
You can invoke the algorithms in several different ways:
var problem = new MyProblem();
// By using the ISearchControl extension methods
var control = Minimize.Start(problem)
.WithRuntimeLimit(TimeSpan.FromSeconds(10))
.PilotMethod();
// By using the IState extension methods
var result = problem.PilotMethod(runtime: TimeSpan.FromSeconds(10));
Check out the SampleApp to see implementations of the following problems:
These samples should give you an idea on how to use the framework for problem modeling.
You should use the state's extension method Test to check whether your implementation is correct. Not all errors can be detected, but several subtle problems can be discovered, e.g. undo operations that result in a state which outputs a different set of choices than before. The Program.cs in the SampleApp calls this method for all problems. For instance
var hanoi = new TowerOfHanoi(3, 3);
var testResult = hanoi.Test<TowerOfHanoi, (int, int), Minimize>(EqualityComparer<(int, int)>.Default);
Console.WriteLine($"Is TowerOfHanoi implemented correctly: {testResult}");If the result is TestResult.Ok the implementation is likely correct. Otherwise, the enum provides hints on potential problems. If you have a more complex choice type, you need to provide an equality comparer for it.
The algorithms that are included are:
Rake search essentially combines a breadth-first search with a depth-first search. New hybrid algorithms can be implemented, also by making use of the existing algorithms.
Additionally, the rake search and pilot method use a lookahead delegate to complete the solution from the current state. There are several options for lookahead which can be used within these two methods:
The static class LA has several methods to create parameterized lookahead delegates. For instance, the following code creates a lookahead that uses a depth-first search with a filter width of 2 and a backtrack limit of 100:
LA.DFSLookahead<MyProblem, Minimize>(filterWidth: 2, backtrackLimit: 100);This means you consider the first two branches at each depth for expansion, but stop after a total of 100 backtracking operations have been performed. Beware, that if you don't use backtrackLimit, your lookahead may take a very long time, as the number of states is $2^n$ (for filterWidth = 2) with $n$ being the depth.
An overview of selveral parameters that the algorithms support: