A Fast Method of Constructing the Non-dominated Set: Arena´s Principle

The objectives in multiobjective optimization problem (MOP) conflict with each others in usually, and no single solution can optimize all the objectives at the same time. An important task in multiobjective optimization is to identify the set of Pareto-optimal solutions. The Pareto front is the set of all the optimal tradeoffs in the objective space. constructing a non-dominated set is an important process in the multiobjective evolutionary algorithm (MOEAs). In this paper we introduce a fast method for constructing the non-dominated set, called the arena´s principle (AP). The method with O(mnn ) computational complexity is presented. Experimental results have demonstrated that the computational complexity of the arena´s principle is better than the fast non-dominated sorting approach in NSGA-II.