didppy.CAASDy

class didppy.CAASDy(model, f_operator=Ellipsis, primal_bound=None, time_limit=None, get_all_solutions=False, quiet=False, initial_registry_capacity=1000000)

Cost-Algebraic A* Solver for DyPDL (CAASDy).

This performs cost-algebraic A* using the dual bound as the heuristic function.

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.

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 on the optimal cost (upper/lower bound for minimization/maximization).

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

  • get_all_solutions (bool, default: False) – Return a new solution even if it is not improving when search_next() is called.

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

  • initial_registry_capacity (int, default: 1000000) – Initial size of the data structure storing all generated states.

Raises:

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

  • OverflowError – If initial_registry_capacity is negative.

  • PanicException – If time_limit is negative.

References

Ryo Kuroiwa and J. Christopher Beck. “Domain-Independent Dynamic Programming: Generic State Space Search for Combinatorial Optimization,” Proceedings of the 33rd International Conference on Automated Planning and Scheduling (ICAPS), pp. 236-244, 2023.

Stephen Edelkamp, Shahid Jabbar, Alberto Lluch Lafuente. “Cost-Algebraic Heuristic Search,” Proceedings of the 20th National Conference on Artificial Intelligence (AAAI), pp. 1362-1367, 2005.

Peter E. Hart, Nills J. Nilsson, Bertram Raphael. “A Formal Basis for the Heuristic Determination of Minimum Cost Paths”, IEEE Transactions of Systems Science and Cybernetics, vol. SSC-4(2), pp. 100-107, 1968.

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.CAASDy(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.CAASDy(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.CAASDy(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.CAASDy(model, quiet=True)
>>> solution, terminated = solver.search_next()
>>> solution.cost
1
>>> terminated
True