Haijuan Zhang

Multi-objective problems in real world are often contradictory and even change over time. As we know, how to find the changing Pareto front quickly and accurately is challenging during the process of solving dynamic multi-objective optimization problems (DMOPs). In addition, most solutions obey different distributions in decision space and the performance of NSGA-III when dealing with DMOPs should be further improved. In this paper, centroid distance is proposed and combined into NSGA-III with transfer learning together for DMOPs, called TC_NSGAIII. Centroid distance-based strategy is regarded as a prediction method to prevent some inappropriate individuals through measuring the distance of the population centroid and reference points. After the distance strategy, transfer learning is used for generating an initial population using the past experience. To verify the effectiveness of our proposed algorithm, NSGAIII, Tr_NSGAIII (NSGA-III combining with transfer learning only), Ce_NSGAIII (NSGA-III combining with centroid distance only), and TC_NSGAIII are compared. Seven state-of-the-art algorithms have been used for comparison on CEC 2015 benchmarks. Besides, transfer learning and centroid distance are regarded as a dynamic strategy, which is incorporated into three static algorithms, and the performance improvement is measured. What’s more, twelve benchmark functions from CEC 2015 and eight sets of parameters in each function are used in our experiments. The experimental results show that the performance of algorithms can be greatly improved through the proposed approach.

Most real-world problems that have two or three objectives are dynamic, and the environment of the problems may change as time goes on. For the purpose of solving dynamic multi-objective problems better, two proposed strategies (second-order difference strategy and random strategy) were incorporated with NSGA-III, namely SDNSGA-III. When the environment changes in SDNSGA-III, the second-order difference strategy and random strategy are first used to improve the individuals in the next generation population, then NSGA-III is employed to optimize the individuals to obtain optimal solutions. Our experiments were conducted with two primary objectives. The first was to test the values of the metrics mean inverted generational distance (MIGD), mean generational distance (MGD), and mean hyper volume (MHV) on the test functions (Fun1 to Fun6) via the proposed algorithm and the four state-of-the-art algorithms. The second aim was to compare the metrics’ value of NSGA-III with single strategy and SDNSGA-III, proving the efficiency of the two strategies in SDNSGA-III. The comparative data obtained from the experiments demonstrate that SDNSGA-III has good convergence and diversity compared with four other evolutionary algorithms. What is more, the efficiency of second-order difference strategy and random strategy was also analyzed in this paper.