/he International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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from nature immune system to solve complex problems 
(Timmis, 2001). 
The natural immune system consists of immune organs, 
immune cells and immune molecules. Immune organs are 
composed of central immune organs and peripheral immune 
organs. Central immune organs are composed of bone marrow 
and thymus, where lymphocytes and other immune cells 
generate, differentiate and mutate. Peripheral immune organs 
include lymphocytes, spleen, and catarrh tissues, where T-cell 
and B-cell settle and proliferate, and where immune system 
responds to antigen’s stimulation. 
AIS provides new ideas for multi-objective optimization. 
Chung et al (J.S.Chung, 1998) confirmed that immune 
algorithm were superior to other algorithms in solving multi 
objective optimization problems. Then the research on immune 
algorithm has absorbed significant attention in recent years 
(Zhang, 2006). Clonal selection algorithm is an excellent 
immune algorithm in AIS, and has been tested useful in multi 
objective optimization. 
2.1 The clonal selection algorithm 
In 1950s, the clonal selection theory was developed by Burnet 
for the first time (Burnet, 1959). De Castro then proposed a 
clonal selection algorithm (De Castro, 2002) which was based 
on the clonal selection theory. The algorithm is mentioned 
briefly as Figure 1. 
Figure 2. Diagram of the clonal selection algorithm 
Stepl: Produce original population S(Ab), which is a set of 
antibodies. 
Step2: Select n best individuals Sn from original population 
through affinity estimation. 
Step3: Clone these n best individuals, and generate temporary 
population T(Ab). The clone size increases as the increasing of 
the affinity. 
Step4: A mutation operation is used to temporary population 
T(Ab), and a mature mature population T*(Ab) is generated. 
Step5: Select d best individuals from T*(Ab), and a set T* d is 
composed. 
Step6: Replace d worst individuals from original population 
S(Ab) by T* d , and a clonal selection of S(Ab) is completed. 
2.2 Immune algorithm in multi-objective optimization 
2.2.1 The definition of multi-objective optimization 
problem: Multi-objective optimization problem is that find the 
decision variable which satisfies constrains and optimizes the 
objective functions. A typical multi-objective optimization 
problem with n decision variables, m constrains and p 
objectives are described as formula (1). 
minF(x) = [f\(x),f2(x),...,f P (x)] T 
s.t. gj(x)<0,i = \,2,...,m (1) 
X = {x\ g t (x) < 0,i = 1,2which is constrained domain 
is said to the feasible domain of decision variables. 
Pareto optimal solution: the optimal solution is always a set in 
multi-objective optimization problems, so pareto optimal 
solution is an important concept which is described as formula 
(2). 
X is a Pareto optimal solution if and only if there exist no other 
variable X, which satisfies the expression as below when it does 
not contravene the constrains: 
Vie {1,2,...«}:/(X)£/(*•)a3 
2.2.2 Immune algorithm in multi-objective optimization: 
In multi-objective optimization problems, a feasible solution 
could be treated as an antibody, and an object function could be 
treated as an antigen. The affinity between antibody and antigen 
could be described as the value of the object functions for 
feasible solutions (Figure 2). 
f A r A 
Antibody 
Solution 
Antigen 
Object function 
Affinition 
Value of function 
Figure 2. The reference from immune system to multi-objective 
optimization problem 
Immune memory is contained in clonal selection algorithm. It 
makes sure the fast convergence of global optimal solution. The 
clonal proportion conforms to direct ratio with affinity. Then 
through the mutation, it promotes or inhibits the antibodies. It 
shows the self-adjustment ability of immune system. There are 
two forms to calculate the affinity: one reflects the correlation 
between antibodies and antigens (the matching degree between 
solution and objects), and the other one reflects the correlation 
between antibodies and antibodies, which ensures the diversity 
of antibody in immune system (Zhai, 2006).