didppy.DDLNS

class didppy.DDLNS(model, f_operator=Ellipsis, primal_bound=None, time_limit=None, quiet=False, initial_solution=None, beam_size=1000, keep_probability=0.1, keep_all_layers=False, seed=2023, cabs_initial_beam_size=1, cabs_max_beam_size=None)

Large Neighborhood Search with Decision Diagrams (DD-LNS) solver.

This performs LNS by constructing restricted multi-valued decision diagrams (MDD).

To apply this solver, the cost must be computed in the form of x + state_cost, x * state_cost, didppy.max(x, state_cost), or didppy.min(x, state_cost) where, state_cost is either of IntExpr.state_cost() and FloatExpr.state_cost(), and x is a value independent of state_cost. Otherwise, it cannot compute the cost correctly and may not produce the optimal solution. if x can be negative, please set has_negative_cost to True.

DD-LNS searches layer by layer, where the i th layer contains states that can be reached with i transitions. By default, this solver only keeps states in the current layer to check for duplicates. If keep_all_layers is True, DD-LNS keeps states in all layers to check for duplicates.

Parameters:

  • model (Model) – DyPDL model to solve.

  • f_operator (FOperator, default: FOperator.Plus) – Operator to combine a g-value and the dual bound to compute the f-value. If the cost is computed by +, this should be Plus. If the cost is computed by *, this should be Product. If the cost is computed by max, this should be Max. If the cost is computed by min, this should be Min.

  • primal_bound (int, float, or None, default: None) – Primal bound.

  • time_limit (int, float, or None, default: None) – Time limit.

  • quiet (bool, default: False) – Suppress the log output or not.

  • initial_solution (list of Transition or None, default: None) – Initial feasible solution. If None, CABS is is performed to find an initial feasible solution.

  • beam_size (int, default: 1000) – Beam size.

  • keep_probability (float, default: 0.1) – Probability to keep a non-best state.

  • keep_all_layers (bool, default: False) – Keep all layers of the search graph for duplicate detection in memory.

  • seed (int, default: 2023) – Random seed.

  • cabs_initial_beam_size (int, default: 1) – Initial beam size for CABS to find an initial feasible solution.

  • cabs_max_beam_size (int or None, default: None) – Maximum beam size for CABS to find an initial feasible solution. If None, the beam size is kept increased until a feasible solution is found.

Raises:

  • TypeError – If primal_bound is float and model is int cost.

  • PanicException – If time_limit is negative or CABS raises an exception when finding an initial solution.

References

Xavier Gillard and Pierre Schaus. “Large Neighborhood Search with Decision Diagrams,” Proceedings of the 31st International Joint Conference on Artificial Intelligence (IJCAI), pp. 4754-4760, 2022.

Examples

Example with + operator.

>>> import didppy as dp
>>> model = dp.Model()
>>> x = model.add_int_var(target=1)
>>> model.add_base_case([x == 0])
>>> t = dp.Transition(
...     name="decrement",
...     cost=1 + dp.IntExpr.state_cost(),
...     effects=[(x, x - 1)]
... )
>>> model.add_transition(t)
>>> model.add_dual_bound(x)
>>> solver = dp.DDLNS(model, quiet=True)
>>> solution = solver.search()
>>> print(solution.cost)
1

Example with max operator.

>>> import didppy as dp
>>> model = dp.Model()
>>> x = model.add_int_var(target=2)
>>> model.add_base_case([x == 0])
>>> t = dp.Transition(
...     name="decrement",
...     cost=dp.max(x, dp.IntExpr.state_cost()),
...     effects=[(x, x - 1)]
... )
>>> model.add_transition(t)
>>> model.add_dual_bound(x)
>>> solver = dp.DDLNS(model, f_operator=dp.FOperator.Max, quiet=True)
>>> solution = solver.search()
>>> print(solution.cost)
2

Methods

search()

Search for the optimal solution of a DyPDL model.

search_next()

Search for the next solution of a DyPDL model.
search()

Search for the optimal solution of a DyPDL model.

Returns:

Solution.

Return type:

Solution

Raises:

PanicException – If the model is invalid.

Examples

>>> import didppy as dp
>>> model = dp.Model()
>>> x = model.add_int_var(target=1)
>>> model.add_base_case([x == 0])
>>> t = dp.Transition(
...     name="decrement",
...     cost=1 + dp.IntExpr.state_cost(),
...     effects=[(x, x - 1)]
... )
>>> model.add_transition(t)
>>> model.add_dual_bound(x)
>>> solver = dp.DDLNS(model, quiet=True)
>>> solution = solver.search()
>>> solution.cost
1
search_next()

Search for the next solution of a DyPDL model.

Returns:

  • solution (Solution) – Solution.

  • terminated (bool) – Whether the search is terminated.

Raises:

PanicException – If the model is invalid.

Examples

>>> import didppy as dp
>>> model = dp.Model()
>>> x = model.add_int_var(target=1)
>>> model.add_base_case([x == 0])
>>> t = dp.Transition(
...     name="decrement",
...     cost=1 + dp.IntExpr.state_cost(),
...     effects=[(x, x - 1)]
... )
>>> model.add_transition(t)
>>> model.add_dual_bound(x)
>>> solver = dp.DDLNS(model, quiet=True)
>>> solution, terminated = solver.search_next()
>>> solution.cost
1
>>> terminated
True