Existing studies on dynamic multi-objective optimization focus on problems with time-dependent objective functions, while the ones with a changing number of objectives have rarely been considered in the literature. Instead of changing the shape or position of the Pareto-optimal front/set when having time-dependent objective functions, increasing or decreasing the number of objectives usually leads to the expansion or contraction of the dimension of the Pareto-optimal front/set manifold. Unfortunately, most existing dynamic handling techniques can hardly be adapted to this type of dynamics. In this paper, we report our attempt toward tackling the dynamic multi-objective optimization problems with a changing number of objectives. We implement a new two-archive evolutionary algorithm which maintains two co-evolving populations simultaneously. In particular, these two populations are complementary to each other: one concerns more about the convergence while the other concerns more about the diversity. The compositions of these two populations are adaptively reconstructed once the environment changes. In addition, these two populations interact with each other via a mating selection mechanism. Comprehensive experiments are conducted on various benchmark problems with a time-dependent number of objectives. Empirical results fully demonstrate the effectiveness of our proposed algorithm.
تحميل البحث