Cost Partitioning Sample Clauses

Cost Partitioning. ‌ Using multiple abstraction heuristics can lead to solving more complex problems, but to preserve optimality, we need to distribute the cost of an operator among the abstractions. One way of doing this, Saturated Cost Partitioning (SCP), is presented by ▇▇▇▇▇ and ▇▇▇▇▇▇▇ [128]. SCP has shown benefits and often better results to simpler cost partitioning methods, being proven that it dominates these simpler methods [130]. Given an ordered set of heuristics, in our case PDBs, SCP relies on only using those costs which each heuristic uses to create an abstract plan. The remaining costs are left free to be used by any subsequent heuristic. However, considering the limited time budget, this approach is time-consuming compared to other cost partitioning methods [116]. Greedy 0/1 cost partition, zeroes any cost for subsequent heuristics if the previous heuristic has any variables affected by that operator. Both SCP and 0/1 allow heuristics values to be added admissibly. SCP dominates 0/1 cost partitioning (given a set of patterns and enough time, SCP would produce better heuristic values), but it is much more computationally expensive than 0/1 cost partitioning. ▇▇▇▇▇▇ et al., [43] shows that, in order to find good complementary patterns, it is beneficial to try as many pattern collections as possible. As such, we implemented 0/1 cost partitioning in all of our work. We evaluated this using the canonical cost partitioning method [56] as well whenever we added a new PDB, but this resulted in a very pronounced slow down which increased the number of PDBs that were already selected. This was the reason we adopted a hybrid combination approach, where 0/1 cost partition is used on-the-fly to generate new pattern collections, and, only after all interesting pattern collections have been selected, we run v1 v2 v3 v4 v5 v6 v7 v8 Table 3.1 An example set of pattern (database) variable selection, forming a 0/1 GA bitstring (or a solution of the bin packing problem). the canonical combination method, slightly extending to take into account that each pattern has its own 0/1 cost partition.