  Domain-specific heuristics are an essential technique for solving
combinatorial problems efficiently. Current approaches to integrate
domain-specific heuristics with Answer Set Programming (ASP) are unsatisfactory
when dealing with heuristics that are specified non-monotonically on the basis
of partial assignments. Such heuristics frequently occur in practice, for
example, when picking an item that has not yet been placed in bin packing.
Therefore, we present novel syntax and semantics for declarative specifications
of domain-specific heuristics in ASP. Our approach supports heuristic
statements that depend on the partial assignment maintained during solving,
which has not been possible before. We provide an implementation in ALPHA that
makes ALPHA the first lazy-grounding ASP system to support declaratively
specified domain-specific heuristics. Two practical example domains are used to
demonstrate the benefits of our proposal. Additionally, we use our approach to
implement informed} search with A*, which is tackled within ASP for the first
time. A* is applied to two further search problems. The experiments confirm
that combining lazy-grounding ASP solving and our novel heuristics can be vital
for solving industrial-size problems.
