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de Castro and Timmis [5] developed a modified version of aiNet to solve multi-
modal optimization problems, called opt-aiNet. The AIN-based metaheuristics
for optimization are receiving increasing attention in recent research. The Copt-
aiNet algorithm[7,8] is an improved version of opt-aiNet to solve combinatorial
optimization problems. Artificial Immune Network for Dynamic Optimization
[9] (dopt-aiNet) is applied to optimize time-varied functions . Another algo-
rithm, Concentration-based Artificial Immune Network (cob-aiNet) devoted to
real-parameter optimization [10,11,12]. Given its complexity, only a small part
of the immune mechanism model has been used in the studies mentioned above.
The immune network is a regulated network of cells and molecules which
maintain interactions between not only an antibody and an antigen, but also
antibodies themselves. Regulatory mechanisms play a crucial role in maintain-
ing the immune network in a given dynamic steady state. Therefore, in this work,
we propose a novel AIN model-Endocrine-Immune Network (EINET) for opti-
mization, which combining artificial endocrine system (AES) with the immune
network. Specifically, two characteristics of hormone in the artificial endocrine
system, hormonal regulation mechanisms and highly effective enzymatic reac-
tion, are taken advantage of to achieve a faster convergence and better diversity
for immune network algorithm, respectively. The main difference between this
model and current models is that the elimination and mutation probability in the
process of hormonal regulation is according to the hormone updating function.
Based on the framework of EINET, we present EINET-TSP algorithm, which
is applied to solve Traveling Salesman Problem, a classical NP-complete prob-
lem in discrete or combinatorial optimization, and result in high-performance
solution. Furthermore, some comparative experiments are conducted for demon-
strating the effectiveness and high-performance of the proposed EINET for op-
timization.
The remainder of the paper is organized as follows. In Section 2, the new
Endocrine-Immune Network for optimization is described in details and the
framework of the model is given. The design of EINET-TSP algorithm, which is
applied to solve traveling salesman problem, is provided in Section 3. In Section
4, Experimental results are presented and discussed. This paper is concluded in
Section 5.
2 Endocrine-Immune Network for Optimization
In this section the framework of a novel AIN model, Endocrine-Immune Network
(EINET) for Optimization, is outlined. Inspired from the hormonal mechanisms
in AES, two specific operators, Hormonal Regulation and Enzymatic Reaction,
are given in EINET.
2.1 Description of Endocrine-Immune Network
The immune network hypothesizes that antibody not only capable of recognizing
antigens but also each other, which forms a regulated network. In Endocrine-
Immune Network, the objective problem which needs to be solved is regarded
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