Dynamic Multi-objective Optimization and Decision-Making Using Modified NSGA-II: A Case Study on Hydro-thermal Power Scheduling

Most real-world optimization problems involve objectives, constraints, and parameters which constantly change with time. Treating such problems as a stationary optimization problem demand the knowledge of the pattern of change a priori and even then the procedure can be computationally expensive. Although dynamic consideration using evolutionary algorithms has been made for single-objective optimization problems, there has been a lukewarm interest in formulating and solving dynamic multi-objective optimization problems. In this paper, we modify the commonly-used NSGA-II procedure in tracking a new Pareto-optimal front, as soon as there is a change in the problem. Introduction of a few random solutions or a few mutated solutions are investigated in detail. The approaches are tested and compared on a test problem and a real-world optimization of a hydro-thermal power scheduling problem. This systematic study is able to find a minimum frequency of change allowed in a problem for two dynamic EMO procedures to adequately track Pareto-optimal frontiers on-line. Based on these results, this paper also suggests an automatic decision-making procedure for arriving at a dynamic single optimal solution on-line.