The OPL optimization programming language
The OPL optimization programming language
Mixed logical-linear programming
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Logic, Optimization, and Constraint Programming
INFORMS Journal on Computing
A scheme for unifying optimization and constraint satisfaction methods
The Knowledge Engineering Review
Integrated Methods for Optimization (International Series in Operations Research & Management Science)
A Branch and Bound Clustering Algorithm
IEEE Transactions on Computers
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A branch and bound strategy is proposed for solving the clusterwise regression problem, extending Brusco's repetitive branch and bound algorithm (RBBA). The resulting strategy relies upon iterative heuristic optimization, new ways of observation sequencing, and branch and bound optimization of a limited number of ending subsets. These three key features lead to significantly faster optimization of the complete set and the strategy has more general applications than only for clusterwise regression. Additionally, an efficient implementation of incremental calculations within the branch and bound search algorithm eliminates most of the redundant ones. Experiments using both real and synthetic data compare the various features of the proposed optimization algorithm and contrasts them against a benchmark mixed logical-quadratic programming formulation optimized by CPLEX. The results indicate that all components of the proposed algorithm provide significant improvements in processing times, and, when combined, generally provide the best performance, significantly outperforming CPLEX.