Combinatorial Problems Clause Samples

Combinatorial Problems. ‌ As we discussed in the previous chapter, the initial results of ▇▇▇▇▇▇▇▇▇ and ▇▇▇▇▇▇▇▇▇ [21] in sliding-tile puzzles, where the concept of a pattern is a selection of tiles, quickly carried over to a number of other combinatorial search domains, leading to solving optimally random instances of the Rubik’s cube, with non-pattern labels being removed [84]. For solving most combinatorial problems, such as the 15-puzzle, all the domain projections (i.e. the patterns used for the domain abstraction) were constructed manually by the developers. However, once the approach was seen to perform well in combinatorial optimisation, it was then implemented in the field of AI Planning by ▇▇▇▇▇▇▇▇ [29], and extended to work in a domain-independent approach, without needing to extend the modelling capabilities of PDDL. This then led to research focusing on automated creation of PDBs, and how a heuristic can be best created to solve as many planning tasks across different domains. Introducing PDBs to solve planning tasks has led to another research question: should you create one or many PDBs to solve one task. In the rest of this chapter, we will go over our work in investigating how generating many smaller PDBs can be combined, by using different solutions to the bin-packing problem, and show that combining it with one greedily-constructed best pattern will result into state-of-the-art results.