  For general multi-objective optimization problems, we propose a novel
performance metric called domination measure to measure the quality of a
solution, which can be intuitively interpreted as the size of the portion of
the solution space that dominates that solution. As a result, we reformulate
the original multi-objective problem into a stochastic single-objective one and
propose a model-based approach to solve it. We show that an ideal version
algorithm of the proposed approach converges to a set representation of the
global optima of the reformulated problem. We also investigate the numerical
performance of an implementable version algorithm by comparing it with numerous
existing multi-objective optimization methods on popular benchmark test
functions. The numerical results show that the proposed approach is effective
in generating a finite and uniformly spread approximation of the Pareto optimal
set of the original multi-objective problem, and is competitive to the tested
existing methods.
