DiversiTree: A New Method to Efficiently Compute Diverse Sets of Near-Optimal Solutions to Mixed-Integer Optimization Problems

While most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often be more useful. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigate parameterized node selection rules that explicitly consider diversity. Our results indicate that our approach significantly increases diversity of the final solution set. When compared with two existing methods, our method runs with similar runtime as regular node selection methods and gives a diversity improvement of up to 140%. In contrast, popular node selection rules such as best-first search gives an improvement in diversity of no more than 40%. Further, we find that our method is most effective when diversity in node selection is continuously emphasized after reaching a minimal depth in the tree and when the solution set has grown sufficiently large. Our method can be easily incorporated into integer programming solvers and has the potential to significantly increase diversity of solution sets.

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Version 2, University of Tennessee, Knoxville and Business School, Data Science Program Worcester Polytechnic Institute, May 2022.

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