Equivalent Formulations of Nonlinear Integer Problems for Efficient Optimization
改进了Glover的线性化技术,将0-1二次整数问题的等价表示所需新增线性约束从4n减少到2n,同时保持新增连续变量数为n但约束其符号,提升了优化效率。
The linearization technique of Glover, which seems to be the most efficient one appearing in the literature, requires the addition of n new continuous variables (unconstrained in sign) and 4n new linear constraints to equivalently represent a 0-1 “quadratic” integer problem with n variables. This paper shows that it is still possible to improve such a procedure. In fact, the number of new continuous variables can be kept at n (but constrained in sign) while further reducing the number of new linear constraints from 4n to 2n.