Counting solutions of knapsack constraints
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Basis reduction and the complexity of branch-and-bound
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Minimal Equivalent Binary Knapsack Inequalities
INFORMS Journal on Computing
Column basis reduction and decomposable knapsack problems
Discrete Optimization
Counting-based search: branching heuristics for constraint satisfaction problems
Journal of Artificial Intelligence Research
On the structure of reduced kernel lattice bases
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
On the resolution of the system of fuzzy Diophantine equations
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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In this article, we consider a class of 0-1 programs that, although innocent looking, is a challenge for existing solution methods. Solving even small instances from this class is extremely difficult for conventional branch-and-bound or branch-and-cut algorithms. We also experimented with basis reduction algorithms and with dynamic programming without much success. The article then examines the performance of two other methods: a group relaxation for 0,1 programs, and a sorting based procedure following an idea of Wolsey. Although the results with these two methods are somewhat better than with the other four when it comes to checking feasibility, we offer this class of small 0,1 programs as a challenge to the research community.