Dynamic Multi-objective Optimization Problems (DMOPs) refer to optimization problems that objective functions will change with time. Solving DMOPs implies that the Pareto Optimal Set (POS) at different moments can be accurately found, and this is a very difficult job due to the dynamics of the optimization problems. The POS that have been obtained in the past can help us to find the POS of the next time more quickly and accurately. Therefore, in this paper we present a Support Vector Machine (SVM) based Dynamic Multi-Objective Evolutionary optimization Algorithm, called SVM-DMOEA. The algorithm uses the POS that has been obtained to train a SVM and then take the trained SVM to classify the solutions of the dynamic optimization problem at the next moment, and thus it is able to generate an initial population which consists of different individuals recognized by the trained SVM. The initial populuation can be fed into any population based optimization algorithm, e.g., the Nondominated Sorting Genetic Algorithm II (NSGA-II), to get the POS at that moment. The experimental results show the validity of our proposed approach.
One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is the optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing the "experiences" to construct a prediction model via statistical machine learning approaches. However most of the existing methods ignore the non-independent and identically distributed nature of data used to construct the prediction model. In this paper, we propose an algorithmic framework, called Tr-DMOEA, which integrates transfer learning and population-based evolutionary algorithm for solving the DMOPs. This approach takes the transfer learning method as a tool to help reuse the past experience for speeding up the evolutionary process, and at the same time, any population based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this, we incorporate the proposed approach into the development of three well-known algorithms, nondominated sorting genetic algorithm II (NSGA-II), multiobjective particle swarm optimization (MOPSO), and the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA), and then employ twelve benchmark functions to test these algorithms as well as compare with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed method through exploiting machine learning technology.