A decomposition-based archiving approach for multi-objective evolutionary optimization

External archive can be used to improve the performance of a multi-objective evolutionary algorithm. Various archiving approaches have been developed but with some drawbacks. These drawbacks such as computation-inefficiency, retreating and shrinking, have not yet been well addressed. In this paper, we propose an efficient decomposition-based archiving approach (DAA) inspired from the decomposition strategy for dealing with multi-objective optimization. In DAA, the whole objective space is uniformly divided into a number of subspaces according to a set of weight vectors. At each generation, only one non-dominated solution lying in a subspace is chosen to be used for updating the external archive in consideration of its diversity. A normalized distance-based method, incorporated with the Pareto dominance, is proposed to decide which subspace a new solution should fall into, and whether this solution should replace existing one in this subspace or not. Empirical results on a diverse set of benchmark test problems show that DAA is more efficient than a number of state-of-the-art archiving methods in terms of the diversity of the obtained non-dominated solutions; and DAA can accelerate the convergence speed of the evolutionary search for most test problems.