  The decomposition-based method has been recognized as a major approach for
multi-objective optimization. It decomposes a multi-objective optimization
problem into several single-objective optimization subproblems, each of which
is usually defined as a scalarizing function using a weight vector. Due to the
characteristics of the contour line of a particular scalarizing function, the
performance of the decomposition-based method strongly depends on the Pareto
front's shape by merely using a single scalarizing function, especially when
facing a large number of objectives. To improve the flexibility of the
decomposition-based method, this paper develops an adversarial decomposition
method that leverages the complementary characteristics of two different
scalarizing functions within a single paradigm. More specifically, we maintain
two co-evolving populations simultaneously by using different scalarizing
functions. In order to avoid allocating redundant computational resources to
the same region of the Pareto front, we stably match these two co-evolving
populations into one-one solution pairs according to their working regions of
the Pareto front. Then, each solution pair can at most contribute one mating
parent during the mating selection process. Comparing with nine
state-of-the-art many-objective optimizers, we have witnessed the competitive
performance of our proposed algorithm on 130 many-objective test instances with
various characteristics and Pareto front's shapes.
