Multi-objective Optimal Combination Queries

Multi-objective optimization problem finds out optimal objects w.r.t. several objectives rather than a single objective. We propose a new problem called a multi-objective optimal combination problem (MOC problem) which finds out object combinations w.r.t. multiple objectives. A combination dominates another combination if it is not worse than anther one in all attributes and better than another one in one attribute at least. The combinations, which cannot be dominated by any other combinations, are optimal. We propose an efficient algorithm to find out optimal combinations by reducing the search space with a lower bound reduction method and an upper bound reduction method based on the R-tree index. We implemented the proposed algorithm and conducted experiments on synthetic data sets.