Quality assessment of Multi-objective Optimization algorithms has been a major concern in the scientific field during the last decades. The entropy metric is introduced and highlighted in computing the diversity of Multi-objective Optimization Algorithms. In this paper, the definition of the entropy metric and the approach of diversity measurement based on entropy are presented. This measurement is adopted to not only Multi-objective Evolutionary Algorithm but also Multi-objective Immune Algorithm. Besides, the key techniques of entropy metric, such as the appropriate principle of grid method, the reasonable parameter selection and the simplification of density function, are discussed and analyzed. Moreover, experimental results prove the validity and efficiency of the entropy metric. The computational effort of entropy increases at a linear rate with the number of points in the solution set, which is indeed superior to other quality indicators. Compared with Generational Distance, it is proved that the entropy metric have the capability of describing the diversity performance on a quantitative basis. Therefore, the entropy criterion can serve as a high-efficient diversity criterion of Multi-objective optimization algorithms.

Artificial Immune System (AIS) is a hotspot in the area of Computational Intelligence. While the Multi-Objective Optimization (MOP) problem is one of the most widely applied NP-Complete problems. During the past decade more than ten kinds of Multi-Objective optimization algorithms based on AIS were proposed and showed outstanding abilities in solving this kind of problem. The paper presents a general framework of Multi-Objective Immune Algorithms, which summarizes a uniform outline of this kind of algorithms and gives a description of its principles, mainly used operators and processing methods. Then we implement the proposed framework and build four typical immune algorithms on it: CLONALG, MISA, NNIA and CMOIA. The experiment results showed the framework is very suitable to develop the various multi-objective optimization immune algorithms.