Non-dominated Sorting Based Multi/Many-Objective Optimization: Two Decades of Research and Application.

The date Vector Evaluated Genetic Algorithms (VEGA)(Schaffer 1985) was proposed is the birthdate of Evolutionary Multi-objective Optimization (EMO), despite a few earlier suggestions on the importance of handling multiple objectives within an evolutionary algorithm. Since then, the classical trend of combining all objectives into one fitness function started to fade. The history of this relatively new field can be viewed from several different perspectives. Here, we are more concerned about the role non-dominated sorting played throughout this history. The concept of nondomination is related to the concept of “Pareto Optimality” first proposed by the Italian economist “Vilfredo Pareto”, hence the naming.“Pareto Optimality” is simply a state of resource allocation among multiple criteria, where it is impossible to reallocate resources so as to make one criterion better without degrading one or more other criteria. In this context, a non-dominated solution is a solution that is not possible to be outperformed in all criteria simultaneously. Unlike “Pareto Optimality”,“Non-domination” can be relative to a set of supplied solutions. A set of solutions are non-dominated with respect to each other if none of them outperforms any of the others in all criteria simultaneously, even if none of them is actually Pareto optimal. Figure 1 shows how the two terms are related yet slightly different.