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A Population Adaptive Based Immune Algorithm for
Solving Multi-objective Optimization Problems
Jun Chen and Mahdi Mahfouf
Dept. of Automatic Control and Systems Engineering, The University of Sheffield
Mappin Street, S1 3JD, Sheffield, United Kingdom
Phone: +44 (0) 114 222 5607; Fax: +44 (0) 114 222 5624
{jun.chen, m.mahfouf}@sheffield.ac.uk
Abstract. The primary objective of this paper is to put forward a general frame-
work under which clear definitions of immune operators and their roles are
provided. To this aim, a novel Population Adaptive Based Immune Algorithm
(PAIA) inspired by Clonal Selection and Immune Network theories for solving
multi-objective optimization problems (MOP) is proposed. The algorithm is
shown to be insensitive to the initial population size; the population and clone
size are adaptive with respect to the search process and the problem at hand. It
is argued that the algorithm can largely reduce the number of evaluation times
and is more consistent with the vertebrate immune system than the previously
proposed algorithms. Preliminary results suggest that the algorithm is a valuable
alternative to already established evolutionary based optimization algorithms,
such as NSGA II, SPEA and VIS.
1 Introduction
Bio-Inspired Computing lies within the realm of Natural Computing, a field of re-
search that is concerned with both the use of biology as inspiration for solving com-
putational problems and the use of the natural world experiences to solve real world
problems. The increasing interest in this field lies in the fact that nowadays we are
having to deal with more and more complex, large, distributed and ill-structured sys-
tems, while on the other hand, one cannot help noticing that the apparently simple
structures and organizations in nature are capable of dealing with the most complex
systems and tasks with ease. Artificial Immune Systems (AIS) is one such recognized
computing paradigm, which has been receiving more attention recently.
Most previous research efforts in the AIS area were mainly concerned with fault
diagnosis [1], computer security [2], and data analysis [3, 4] and only very recently
have a few attempts seen AIS extended to the optimization field, and most of them
being dedicated to solving single objective optimization problems (SOP) [5, 6]. The
reason behind this is that it is relatively easy to create a direct link between real im-
mune system and the aforementioned three application areas, e.g. in applications of
data analysis, clusters to be recognized are easily related to antigens (Ag), and the set
of solutions to distinguish between these clusters is linked to antibodies (Ab) [3].
However, such direct links are vague in the optimization field, especially in the MOP
field. The main difficulty in exploiting immune metaphors for optimization problems
 
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