Globally Optimal Clusterwise Regression By Column Generation Enhanced with Heuristics,Sequencing and Ending Subset Optimization

A column generation based approach is proposed for solving the cluster-wise regression problem. The proposed strategy relies firstly on several efficient heuristic strategies to insert columns into the restricted master problem. If these heuristics fail to identify an improving column, an exhaustive search is performed starting with incrementally larger ending subsets, all the while iteratively performing heuristic optimization to ensure a proper balance of exact and heuristic optimization. Additionally, observations are sequenced by their dual variables and by their inclusion in joint pair branching rules. The proposed strategy is shown to outperform the best known alternative (BBHSE) when the number of clusters is greater than three. Additionally, the current work further demonstrates and expands the successful use of the new paradigm of using incrementally larger ending subsets to strengthen the lower bounds of a branch and bound search as pioneered by Brusco's Repetitive Branch and Bound Algorithm (RBBA).