Document Type
Post-Print
Publication Date
12-2006
Abstract
The optimal partition for linear programming is induced by any strictly complementary solution, and this partition is important because it characterizes the optimal set. However, constructing a strictly complementary solution in the presence of degeneracy was not practical until interior point algorithms became viable alternatives to the simplex algorithm. We develop analogs of the optimal partition for linear programming in the case of multiple objectives and show that these new partitions provide insight into the optimal set (both pareto optimality and lexicographic ordering are considered). Techniques to produce these optimal partitions are provided, and examples from the design of radiotherapy plans show that these new partitions are useful.
Identifier
10.1007/s11081-006-0352-2
Publisher
Kluwer Academic Publishers
Repository Citation
Holder, A. (2006). Partitioning multiple objective optimal solutions with applications in radiotherapy design. Optimization and Engineering, 7(4), 501-526. doi:10.1007/s11081-006-0352-2
Publication Information
Optimization and Engineering