Study Of Preference-based Multi-objective Evolutionary Algorithm And Related Indicator With Decomposition

In order to solve the Multi-objective Optimization Problems(MOPs) in real life, where those problems are sometimes with multi-objectives and need to be solved simultaneously, meanwhile, these problems are used to be non-linear and high-complicated, but Multi-objective Evolutionary Algorithms(MOEAs) can deal with them easily, thus the research of MOEAs has become the hotspots of Artificial Intelligence. The optimal solutions in the process of optimization are referred to as the Pareto Solutions(PS). The researchers found that in the process of optimization, with the increase of the number of dimensions of the MOPs, the number of PS will also increase exponentially, thus increasing the degree of difficulty of random search, so that the decision maker(DM) are hard to select the preferred solutions among the optimal solutions. Consequently, the preference based MOEAs are becoming the hotspot in the research of MOEAs. By the approach of provided reference points by DM, the MOEAs can filter the optimal solutions and expel those solutions which the DM has no interest in, and obtain the preferred solutions for the DM. The region composed with the preferred solutions is defined as region of interest(ROI). Thus, how to efficiently express the preference information will affect the performance of the algorithm and satisfaction of decision makers.The innovations proposed in this paper are as follows: Firstly, we do research on the theory of MOEAs and preference-based MOEAs systematically, then come up with some essential issues when design MOEAs. Secondly, the locations of the reference points given by the DM sometimes seriously impact the performance of the algorithms, so that this paper proposes a preference-based and decomposition-based MOEA(MOEA/D-PRE) to solve this problem. The MOEA/D-PRE mainly uses the weighted iteration method to obtain a set of uniform weight vectors to map the ROI. MOEA/D-PRE can neglect the consideration of the effect of the locations of reference points and can enhance selection pressure of the algorithm which will be beneficial to the convergence of the algorithm. The experimental results of MOEA/D-PRE shows that MOEA/D-PRE has better performance in most of test instances compared with the state-of-art algorithms: G-NSGA-II and R-NSGA-II. Finally, this paper presents an improved metric based on a hyper-plane(PMDA) to evaluate the preference-based MOEAs. By means of the decomposition of reference point to construct a hyper-plane, apply the distances and angles between the solutions and hyper-plane to evaluate the performance of the preference-based algorithms. Compared with other preference-based metrics such as HV and IGD-CF, PMDA can not only evaluate the convergence but also evaluate the distribution of the solutions obtained by MOEAs. To some extent, therefore, PMDA can better evaluate the performance of the algorithm comprehensively.