Chuffed, a lazy clause generation solver
Geoffrey Chu, Peter J. Stuckey, Andreas Schutt, Thorsten Ehlers, Graeme Gange, Kathryn Francis
Data61, CSIRO, Australia
Department of Computing and Information Systems University of Melbourne, Australia
The easiest way to use Chuffed is as a backend to the MiniZinc constraint modelling language. Compiling Chuffed using the
instructions below will create the
fzn-chuffed executable that can interpret
MiniZinc's FlatZinc solver language.
You can also use Chuffed directly from C++. Take a look at the files in the
examples folder to get started.
Chuffed can be compiled on Windows, macOS and Linux.
You need a recent C++ compiler that supports C++11 (e.g. Microsoft Visual Studio 2013, gcc 4.8, clang), as well as the CMake build tool (at least version 3.1).
CMake & Co
To build the
mkdir build cd build cmake .. cmake --build .
To build the C++ examples:
mkdir build cd build cmake .. cmake --build . --target examples
Integration with CP Profiler
The CP Profiler tool can be used with Chuffed to visualise the search trees and analyse the nogoods that Chuffed explores when solving a problem. In order to enable profiling support, you need to fetch the profiler connection code as a submodule by executing the following command in the root directory of your local copy of the Chuffed git repository:
git submodule update --init
After that, you can run
cmake and compile
fzn-chuffed as described above.
Chuffed is a state of the art lazy clause solver designed from the ground up with lazy clause generation in mind. Lazy clause generation is a hybrid approach to constraint solving that combines features of finite domain propagation and Boolean satisfiability. Finite domain propagation is instrumented to record the reasons for each propagation step. This creates an implication graph like that built by a SAT solver, which may be used to create efficient nogoods that record the reasons for failure. These nogoods can be propagated efficiently using SAT unit propagation technology. The resulting hybrid system combines some of the advantages of finite domain constraint programming (high level model and programmable search) with some of the advantages of SAT solvers (reduced search by nogood creation, and effective autonomous search using variable activities).
The FD components of Chuffed are very tightly integrated with a SAT solver. For "small" variables (|D| <= 1000), SAT variables representing [x = v] or [x >= v] are eagerly created at the start of the problem. Channelling constraints are natively enforced by the variable objects in order to keep the FD solver and the SAT solver's view of the domains fully consistent at all times. For "large" variables (|D| > 1000), the SAT variables are lazily generated as needed. Every propagator in Chuffed has been instrumented so that all propagation can be explained by some combination of the literals in the SAT solver. An explanation is of the form a_1 /\ ... /\ a_n -> d, where a_i represent domain restrictions which are currently true, and d represents the domain change that is implied. e.g. Suppose z >= x + y, and we have x >= 3, y >= 2. Then the propagator would propagate x >= 5 with explanation clause x >= 3 /\ y >= 2 -> z >= 5.
The explanations for each propagation form an implication graph. This allows us to do three very important things. Firstly, we can derive a nogood to explain each failure. Such nogoods often allow us to avoid a very large amount of redundant work, thus producing search trees which are orders of magnitude smaller. Secondly, nogoods allow us to make informed choices about non-chronological back-jumping. When no literal from a decision level appears in the nogood, it is indicative of the fact that the decision made at that level was completely irrelevant to the search. Thus by back-jumping over such decisions, we retrospectively avoid making such bad decisions, and hopefully make good decisions instead which drive the search towards failure. Thirdly, by analysing the conflict, we can actively gain some information about what good decision choices are. The Variable State Independent Decaying Sum (VSIDS) heuristic is an extremely effective search heuristic for SAT problems, and is also extremely good for a range of CP problems. Each variables has an associated activity, which is increased whenever the variable is involved in the conflict. Variables with the highest activity is chosen as the decision variable at each node. The activities are decayed to reflect the fact that the set of important variables changes with time.
Although Chuffed implements lazy clause generation, which is cutting edge and rather complex, the FD parts of Chuffed are relatively simple. In fact, it is quite minimalistic. Chuffed only supports 3 different propagator priorities. Chuffed implements a number of global propagators (alldiff, inverse, minimum, table, regular, mdd, cumulative, disjunctive, circuit, difference). It also only supports two kinds of integer variables. Small integer variables for which the domain is represented by a byte string. And large integer variables for which the domain is represented only by its upper and lower bound (no holes allowed). All boolean variables and boolean constraints are handled by the builtin SAT solver.
Great pains have been taken to make everything as simple and efficient as possible. The solver, when run with lazy clause generation disabled, is somewhat comparable in speed with older versions of Gecode. The overhead from lazy clause generation ranges from negligible to perhaps around 100%. The search reduction, however, can reach orders of magnitude on appropriate problems. Thus lazy clause generation is an extremely important and useful technology. The theory behind lazy clause generation is described in much greater detail in various papers.