Convergence Analysis of a Multiobjective Artificial Immune System Algorithm

This paper presents a mathematical proof of convergence of a multiobjective artificial immune system algorithm (based on clonal selection theory). An specific algorithm (previously reported in the specialized literature) is adopted as a basis for the mathematical model presented herein. The proof is based on the use of Markov chains.

[1]  Raúl Monroy,et al.  Towards a Model for an Immune System , 2002, MICAI.

[2]  Jonathan Timmis,et al.  Artificial immune systems - a new computational intelligence paradigm , 2002 .

[3]  Fernando José Von Zuben,et al.  Learning and optimization using the clonal selection principle , 2002, IEEE Trans. Evol. Comput..

[4]  Carlos A. Coello Coello,et al.  Multiobjective Optimization Using Ideas from the Clonal Selection Principle , 2003, GECCO.

[5]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[6]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[7]  D. Dasgupta,et al.  A formal model of an artificial immune system. , 2000, Bio Systems.

[8]  Carlos A. Coello Coello,et al.  MICAI 2002: Advances in Artificial Intelligence , 2002, Lecture Notes in Computer Science.

[9]  O. Hernondex-lerma,et al.  Adaptive Markov Control Processes , 1989 .

[10]  D. Dasgupta Artificial Immune Systems and Their Applications , 1998, Springer Berlin Heidelberg.

[11]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[12]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

[13]  Marius Iosifescu,et al.  Finite Markov Processes and Their Applications , 1981 .

[14]  Prabhat Hajela,et al.  Immune network modelling in design optimization , 1999 .

[15]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.