A linearization method for mixed 0–1 polynomial programs

This paper proposes a concise method for solving mixed 0–1 polynomial programming problems to obtain a global optimal solution. Given a mixed 0–1 polynomial term z=ctx1x2⋯xny, where View the MathML source are 0–1 integer variables, y is a continuous variable, and ct is either a positive or a negative coefficient; we can transform z into a set of auxiliary constraints. Based on this transformation, the original mixed 0–1 polynomial program can then be solved directly by the branch-and-bound method. In addition, the proposed model for solving a mixed 0–1 polynomial problem is expressed in a much more compact way, and also uses fewer additional 0–1 variables and auxiliary constraints than the previous methods, such as those proposed by Glover, Oral–Kettani, and Li. The analytical superiority of this concise method in terms of the number of iterations and execution times can be seen, through a computational experiment conduced on a set of generated mixed 0–1 polynomial problems.