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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.

Assumption interface

Chuffed has FlatZinc hooks to the internal assumption handling. By adding an assume(array [int] of var bool) annotation to a solve item, the specified Booleans will be treated as assumptions. This annotation can be used when chuffed's solver specific definitions are included (i.e., by adding include "chuffed.mzn"; to your MiniZinc model).

If the resulting problem is unsatisfiable (or the optimum is found), the solver will print a valid -- though not necessarily minimal -- nogood in terms of assumptions (and, for optimization instances, an objective bound).

Integration with CP Profiler

The CP Profiler, integrated into the MiniZincIDE, 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, Chuffed includes profiler connection code. This has been included as a git subtree in thirdparty/cp-profiler-integration. To pull the newest version of the integration code, use the following command in the repository root.

git subtree pull --prefix thirdparty/cp-profiler-integration master --squash


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). To automatically format the Chuffed source code, the clang-format executable must be available.

CMake & Co

To initialize the CMake build environment, using build as the build directory, use the following command:

cmake -B build -S .

To then build the fzn-chuffed executable run:

cmake --build build

To install fzn-chuffed run the following command:

cmake --build build --target install

The installation directory can be chosen by appending -DCMAKE_INSTALL_PREFIX=$LOCATION with the chosen location to the initial CMake command.

To build the C++ examples:

cmake --build build --target examples

To format the Chuffed source files

cmake --build build --target format


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 z >= 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.