Jip J. Dekker
35a3110598
git-subtree-dir: software/chuffed git-subtree-split: 2ed0c01558d2a5c49c1ce57e048d32c17adf92d3
75 lines
4.5 KiB
Plaintext
75 lines
4.5 KiB
Plaintext
Chuffed - A lazy clause solver
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Geoffrey Chu, Peter J. Stuckey, Andreas Schutt, Thorsten Ehlers, Graeme Gange, Kathryn Francis
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Data61, CSIRO, Australia
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Department of Computing and Information Systems
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University of Melbourne, Australia
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Chuffed is a state of the art lazy clause solver designed from the ground up
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with lazy clause generation in mind. Lazy clause generation is a hybrid
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approach to constraint solving that combines features of finite domain
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propagation and Boolean satisfiability. Finite domain propagation is
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instrumented to record the reasons for each propagation step. This creates an
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implication graph like that built by a SAT solver, which may be used to create
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efficient nogoods that record the reasons for failure. These nogoods can be
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propagated efficiently using SAT unit propagation technology. The resulting
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hybrid system combines some of the advantages of finite domain constraint
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programming (high level model and programmable search) with some of the
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advantages of SAT solvers (reduced search by nogood creation, and effective
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autonomous search using variable activities).
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The FD components of Chuffed are very tightly integrated with a SAT solver. For
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"small" variables (|D| <= 1000), SAT variables representing [x = v] or [x >= v]
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are eagerly created at the start of the problem. Channelling constraints are
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natively enforced by the variable objects in order to keep the FD solver and
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the SAT solver's view of the domains fully consistent at all times. For "large"
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variables (|D| > 1000), the SAT variables are lazily generated as needed. Every
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propagator in Chuffed has been instrumented so that all propagation can be
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explained by some combination of the literals in the SAT solver. An explanation
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is of the form a_1 /\ ... /\ a_n -> d, where a_i represent domain restrictions
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which are currently true, and d represents the domain change that is implied.
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e.g. Suppose z >= x + y, and we have x >= 3, y >= 2. Then the propagator would
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propagate x >= 5 with explanation clause x >= 3 /\ y >= 2 -> z >= 5.
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The explanations for each propagation form an implication graph. This allows us
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to do three very important things. Firstly, we can derive a nogood to explain
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each failure. Such nogoods often allow us to avoid a very large amount of
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redundant work, thus producing search trees which are orders of magnitude
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smaller. Secondly, nogoods allow us to make informed choices about
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non-chronological back-jumping. When no literal from a decision level appears
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in the nogood, it is indicative of the fact that the decision made at that
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level was completely irrelevant to the search. Thus by back-jumping over such
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decisions, we retrospectively avoid making such bad decisions, and hopefully
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make good decisions instead which drive the search towards failure. Thirdly, by
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analysing the conflict, we can actively gain some information about what good
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decision choices are. The Variable State Independent Decaying Sum (VSIDS)
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heuristic is an extremely effective search heuristic for SAT problems, and is
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also extremely good for a range of CP problems. Each variables has an
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associated activity, which is increased whenever the variable is involved in
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the conflict. Variables with the highest activity is chosen as the decision
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variable at each node. The activities are decayed to reflect the fact that the
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set of important variables changes with time.
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Although Chuffed implements lazy clause generation, which is cutting edge and
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rather complex, the FD parts of Chuffed are relatively simple. In fact, it is
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quite minimalistic. Chuffed only supports 3 different propagator priorities.
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Chuffed implements a number of global propagators (alldiff, inverse,
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minimum, table, regular, mdd, cumulative, disjunctive, circuit, difference).
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It also only supports two kinds of integer variables. Small integer variables
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for which the domain is represented by a byte string.
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And large integer variables for which the domain is represented only by its
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upper and lower bound (no holes allowed). All boolean variables and boolean
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constraints are handled by the builtin SAT solver.
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Great pains have been taken to make everything as simple and efficient as
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possible. The solver, when run with lazy clause generation disabled, is
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somewhat comparable in speed with older versions of Gecode. The overhead from
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lazy clause generation ranges from negligible to perhaps around 100%. The
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search reduction, however, can reach orders of magnitude on appropriate
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problems. Thus lazy clause generation is an extremely important and useful
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technology. The theory behind lazy clause generation is described in much
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greater detail in various papers.
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