This paper proposes a new framework for the design of evolutionary multi-objective optimization (EMO) algorithms. The main characteristic feature of the proposed framework is that the optimization result of an EMO algorithm is not the final population but a subset of the examined solutions during its execution. As a post-processing procedure, a pre-specified number of solutions are selected from an unbounded external archive where all the examined solutions are stored. In the proposed framework, the final population does not have to be a good solution set. The point of the algorithm design is to examine a wide variety of solutions over the entire Pareto front and to select well-distributed solutions from the archive. In this paper, first we explain difficulties in the design of EMO algorithms in the existing two frameworks: non-elitist and elitist. Next we propose the new framework of EMO algorithms. Then we demonstrate advantages of the proposed framework over the existing ones through computational experiments. Finally we suggest some interesting and promising future research topics.