Immune
Optimization Algorithm based on
-MHC Regulation Min Hu Sydney Institute of Language and Commerce Shanghai University Shanghai 200072, China E-mail:
[email protected]
Gengfeng Wu School of Computer Engineering and Science Shanghai University Shanghai200072, China E-mail: gfwu(staff.shu.edu.cn
Abstract-The protein Major Histocompatibility Complex
(MIHC) plays an important role in immune systems, the benefit
of the MIIC polymorphism in immune response is due to its critical influence on the selection and evolution of the antibody. This paper presents an Immune Optimization Algorithm based on the MHC regulation function (IOAMHC) in immune responses. The work presented here build upon previous evolutionary algorithm and clonal selection principle for optimization. In the IOAMHC, the MHC is used to guide the evolution of the antibody, so as to accelerate optimization. The experiment results on the Traveling Salesman Problem (TSP) show that the IOAMHC has much higher convergence speed and better optimization results than that of classical optimization algorithms. The performance of the IOAMHC parameters has also been discussed in this paper. I. iNRODUCTION
Artificial immune system was designed to solve optimization problem in recent years. Particularly, the three learning mechanisms are primarily used in immune optimization algorithm. These include the immune network theory[l], the clonal section principals[21 and gene evolution[3]. In vertebrate immune system, the protein Major Histocompatibility Complex (MHC) plays a critical role[4] besides Ag-Ab binding. Toma et al[5 proposed an adaptive optimization inspired by the immune network theory and MHC peptide presentation, but yet, the features of MHC can not be recognized and used. This paper presents a new Immune Optimization Algorithm based on the MHC regulation function (IOAMHC) in immune responses. In the IOAMHC, the optimization problem is a metaphor for antigen, the feasible solution of the problem is a metaphor for antibody, and the segment of the solution is a metaphor for the MHC. The MHC guides and regulates the binding of antigen and antibody effectively and quickly, this makes the good solution searching more rapid. We analyzed the performances of the IOAMHC on Traveling Salesman Problem (TSP).
0-7803-9422-4/05/$20.00 ©2005 IEEE
II. MHC REGULATION
The immune system serves as body's defense system, monitoring the internal environment for foreign antigens indicative of the presence of pathogens. Antigen presenting cells have the role of gathering antigens and presenting them to the immune system as processed peptides in the context of a cell surface protein assembly known as the MHC. There are two classes of molecules on cell surfaces. The MHC class I molecules exist on all cells and hold and present foreign antigens to T lymphocytes if the cell is infected by a virus or other microbe. The MHC class II molecules are the billboards of the immune system. P.C. Doherty & R.M.Zinkernagel6] illustrated that T cells must recognize antigen as a complex with MHC molecules. Obviously, the MHC plays a critical role in cellular immune responses. The MHC is highly polymorphic. There are a large number of genetic variants (alleles) at each genetic locus. For example, in humans there are more than 200 alleles described at some MHC loci. The allelic variation of MHC molecules is functionally reflected in the selection of peptides which can bind, each allelic product has a unique set of peptides which can bind with high affinity. It means that the polymorphism of MHC not only enhances polymorphism of antibody, but also helps antibody bind antigen in immune response. III. IOAMHC DEFINITIONS
Based upon the MHC regulation principle, combining the ideas from clonal selection principle and gene evolution, we design a new immune optimization algorithm IOAMHC. The follows are the basic definitions of the IOAMHC and TSP are taken as an example to introduce these definitions.
A. Optimization Problem - Antigen The optimization problem is assimilated to antigen in the
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immune system. For TSP, the antigen is: the traveling defined as: salesman must visit every city in his territory only once and then return to the starting city. A tour with smallest cost is MHCj={MHCjl,MHCj2,MHCj3 ........MHCjL} (7) expected to be given, i.e. the total distance among all the For the n-City TSP, each MHC is the vector of the two cities should be shortest. cities. Those solution segments from same city are called alleles, (1,2),(1,3),(1,4),(1,5) is a group of alleles. B. Feasible Solution -Antibody
Optimization Problem is seeking the best or relatively E. Competition among the Solution Segments solution from many feasible solutions in terms of a certain - Competition among MHCAlleles object, so the feasible solution is assimilated to antibody in the immune system. The different alleles produce the different affinitvy to same Suppose an antibody (feasible solution) xi,it is a vector antigen. The higher the affinity of MHC is, the higher the intensity of MHC is, vice versa. We use the competition which is composed of M variables. It is defined as below: among MHC alleles to simulate the competition among the solution segments. XI {X,1, Xi2, X3 .........X,M}(l) Suppose the former intensity of MHCj is For TSP, each antibody is one of visiting routers. The Fitness_MHCOLD . the current set of the solutions is with fitness corresponding set of the antibodies is represented as follows: X=fxj,X2, ...x} F={fl,f2,....f,},then, the new intensity of MHCj is determined by the following expressions: X= {X,X2,X3 ........ XJ} (2) Fitness_MHC"j=Fitress_MHCOLD.*AFitness_MHCj
C. Optimization Object -Ag-Ab Affinity Optimization problem can be described as follows: min f(x) or max f(x)
Here,
*rj1 /'r,
Z a! AFitness MHICJ -=l n
(3)
g(x).O
-xED
i=l
Then, x is a feasible solution, f(x) is optimization object and g(x) is constraints, where D represents the whole search space. So we select optimization object or its transformation as antigen-antibody (Ag-Ab) affinity. The Ag-Ab affinity can be described as fimction Fitness.
Fitness(x)=J(x)
"
t(
otherwise
f _fjfmm
(4)
J
fmax-fm
mean
f-
-f
fm.= max(fi,f2,f3 .......f)
In the case of the n-City TSP, Ag-Ab affinity is represented as: Fitness6
(8)
fmr; =min(fl,f2 Af3..f.... f)
n-i
=Fi d'skxi,k,xi,k+l) + disRxins,xi,l) (5)
n
Where dist(m,n) is the distance from city No. m to city No. n.
D. Solution Segment - MiHC Antibody must recognize antigen and MHC molecules at the same time, so we consider the segment of the feasible solution as the MHC molecules, so as to ensure the solution is feasible. The set of MHC is called MHS, defined as follows:
MHS={MHC1,MHC2MHC3,..., MHCm} (6) Each MHCj molecule composed of L variables (L
