The Construction Of Evolutionary Multi-Objective Optimization Test Problems

Multi-objective Optimization Problems (MOPs) originated from design, planning and modeling of complex systems in real-world. Almost every important decision problems in real life need deal with conflicting objectives with various constrains, which has significantly added the complexity of the problems. From early 1960s, MOPs attracted significant attention of researchers in different background.Most of the current research concentrates on improving the efficiency and effectiveness of Multi-objective Optimization Evolutionary Algorithms (MOEAs). However, the important aspect of this area is how to construct the standard test problems and metrics in order to fairly assess the performance of MOEAs. Unfortunately, most of the researchers haven't paid much attention to this issue.After reading a large number of domestic and overseas literatures and books, we analyze and sum up the key operations and features of MOEAs, discuss the construction methods of Multi-objective Optimization Test Problems (MOTPs), and present the construction method of Dynamic Multi-objective Optimization Test Problems (DMOTPs) which is one of the hot topics in current years. The main contents of this paper are described as follows:1. Analyzing the basic idea of various methods of MOEAs in general. A new algorithm was presented for obtaining non-dominated set of a population; the basic framework of MOEAs was designed.2. Illustrating how to construct Two-objective Optimization Test Problems (TOTPs) and scalable MOTPs, proving the exact location of Pareto optimal set and Pareto front of a class of TOTPs theoretically, and then giving some examples.3. Analyzing the types and characteristics of DMOTPs, presenting the method and examples of allowing static MOTPs to be directly transferred to the DMOTPs, and then giving some examples.4. The construction of DMOTPs is a new and difficult research topic. This paper did some elementary work presently. At last, some of the most promising future paths of research in multi-objective optimization area are also addressed.