Multi-Objective Optimization Problems with Arena Principle and NSGA-II

Existing test problems for multi-objective optimization are mainly criticized for high computational complexity. In this study, we introduce a new non- dominated sorting algorithm based on Pareto optimal solutions which alleviates the problem of high computational complexity in NSGA-II. We use the Arena Principle in NSGA-II to retain the non-dominated solutions found during the evolutionary process. The main goal of this work is to keep the fast convergence exhibited by Arena Principle in global optimization when extending this heuristic to multi-objective optimization. The algorithm’s computational complexity is O(rmN). We adopt two standard test functions and simulation results show that the Arena Principle is able to find more useful and better spread of solutions.