Acceleration of parametric Multi-objective Optimization by an initialization technique for Multi-Objective Evolutionary Algorithms

Most real world problems can be formulated as multi-objective optimization problems (MOPs) because they have various competing objectives. Engine calibration, which is the tuning process of controller parameters in automotive engine development, is such a problem. In the engine calibration, a set of MOPs depending on plural operating conditions such as engine speed have to be optimized one at a time. In this paper, such a problem composed by MOPs parameterized by condition variables as subproblems is called parametric MOP (PMOP). We can solve the PMOP by applying multi-objective evolutionary algorithms (MOEAs) to each MOP separately. However, the calculation cost of PMOP becomes quite expensive in real world applications. To accelerate the evolutionary multi-objective optimization of PMOPs, we propose an initialization method of MOEAs for PMOPs. This method uses an interpolation of plural Pareto approximation populations of different conditions obtained in the past for an initial population of succeeding MOPs. The effectiveness of the proposed method is demonstrated through a numerical experiment.