MIP: Theory and Practice - Closing the Gap
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
Exploring relaxation induced neighborhoods to improve MIP solutions
Mathematical Programming: Series A and B
An Evolutionary Algorithm for Polishing Mixed Integer Programming Solutions
INFORMS Journal on Computing
Optimizing over the first chvàtal closure
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Energy efficient spatial TDMA scheduling in wireless networks
Computers and Operations Research
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
Towards automated structure-based NMR resonance assignment
RECOMB'10 Proceedings of the 14th Annual international conference on Research in Computational Molecular Biology
Upper bounds on the number of solutions of binary integer programs
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
How to select a small set of diverse solutions to mixed integer programming problems
Operations Research Letters
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As mixed integer programming (MIP) problems become easier to solve in pratice, they are used in a growing number of applications where producing a unique optimal solution is often not enough to answer the underlying business problem. Examples include problems where some optimization criteria or some constraints are difficult to model, or where multiple solutions are wanted for quick solution repair in case of data changes. In this paper, we address the problem of effectively generating multiple solutions for the same model, concentrating on optimal and near-optimal solutions. We first define the problem formally, study its complexity, and present three different algorithms to solve it. The main algorithm we introduce, the one-tree algorithm, is a modification of the standard branch-and-bound algorithm. Our second algorithm is based on MIP heuristics. The third algorithm generalizes a previous approach that generates solutions sequentially. We then show with extensive computational experiments that the one-tree algorithm significantly outperforms previously known algorithms in terms of the speed to generate multiple solutions, while providing an acceptable level of diversity in the solutions produced.