  This paper presents a piecewise convexification method for solving non-convex
multi-objective optimization problems with box constraints. Based on the ideas
of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global
optimization and the interval subdivision, a series of convex relaxation
sub-multiobjective problems for this non-convex multi-objective optimization
problem are firstly obtained, and these sub-problems constitute a piecewise
convexification problem of the original problem on the whole box. We then
construct the (approximate, weakly) efficient solution set of this piecewise
convexification problem, and use these sets to approximate the globally
(weakly) efficient solution set of the original problem. Furthermore, we
propose a piecewise convexification algorithm and show that this algorithm can
also obtain approximate globally efficient solutions by calculating a finite
subset of the efficient solution set of the multi-objective convex sub-problems
only. Finally, its performance is demonstrated with various test instances.
