Exact and heuristic algorithms for the maximum weighted submatrix coverage problem
针对数据挖掘中的最大加权子矩阵覆盖问题，提出了新的整数线性规划模型（包括基于Benders分解的模型）和一种增强局部搜索的贪心随机自适应搜索算法，在真实和合成实例上均优于现有方法。
The maximum weighted submatrix coverage problem is a recently introduced problem with applications in data mining. It is concerned with selecting K submatrices of a given numerical matrix such that the sum of the matrix-entries, which occur in at least one of the selected submatrices, is maximized. In the paper introducing the problem, a problem-specific constraint programming approach was developed and embedded in a large neighborhood-search to obtain a heuristic. A compact integer linear programming formulation was also presented, but deemed inefficient due to its size. In this paper, we introduce new integer linear programming formulations for the problem, one of them is based on Benders decomposition. The obtained Benders decomposition-based formulation has a nice combinatorial structure, i.e., there is no need to solve linear programs to separate Benders cuts. We present preprocessing procedures and valid inequalities for all formulations. We also develop a greedy randomized adaptive search procedure for the problem, which is enhanced with a local search. A computational study using the instances from literature is done to evaluate the effectiveness of our new approaches. Our algorithms manage to find improved primal solutions for ten out of 17 real-world instances, and optimality is proven for two real-world instances. Moreover, for over 700 of 1617 large-scale synthetic instances, our algorithms find improved primal solutions compared to the heuristics from the literature.