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<h2>Introduction</h2>

<p>Artificial <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une algorithms are inspired by the principles and processes of biological <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une systems. This article shows how to develop a simple C# <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une algorithm which models clonal selection, affinity maturation, and antibody interaction. </p>

<h2>Background </h2>

<p>Our <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une
system protects us from pathogenic organisms including bacteria,
viruses, and toxins. It provides a number of levels of defense, with
the skin being the first barrier to infection. Once pathogens have
entered the body, they are handled with the innate <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une system, and then by the acquired <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une response system (see Fig 1.). The innate <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une
system provides protection that is always present. It uses roaming
scavenger cells (phagocytes) to ingest abnormal cells, thus clearing
the system.</p>

<p><img src="codeproject_crispin2.aspx_files/immune1.gif" width="600" height="242"></p>

<div class="caption">Fig 1. Levels of defense in the <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une system</div>

<p>The acquired <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une system provides protection that arises from an <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une response. Substances capable of starting a specific <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une response are called antigens. Nearly all pathogens are antigens. Antibodies are used by the <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une
system to identify and neutralise antigens (foreign bodies), and are
produced from a kind of white blood cell called a B-cell.</p>

<p>Clonal selection models the production of antibodies which bind to
specific antigens. The binding process of receptors is often likened to
a key-lock mechanism. The probability of forming a bond (i.e., match
strength) is referred to as affinity. Clonal selection establishes the
idea that only those antibodies that recognise the antigens are
selected for cloning and mutation. Cloned antibodies mutate in inverse
proportion to how well they match the antigen so that better matching
antigens are mutated less and weakly matching antibodies are mutated
much more. This process is called affinity maturation, and improves the
likelihood of antibodies forming a bond. Immune models also have to
take into account the activity resulting from interactions between
antibodies.</p>

<h2>Optimisation by Immune Algorithm</h2>

<p>From a computer science perspective, modeling the behaviour of the acquired <span class="__mozilla-findbar-search" style="padding: 0pt; background-color: yellow; color: black; display: inline; font-size: inherit;">imm</span>une
system can provide potential new ways of solving problems. The function
optimisation problem involves finding the best solution (either the
peak or trough) to a function bounded by constraints. </p>

<p>In the example code, a test function has been used and is plotted in
Fig. 2. This test function uses the sine function to produce the hilly
plot, and so finding the highest peak is a challenge. The equation is
given by:</p>

<p>Fitness = (15*x*y*(1-x)*(1-y)*sin(9*pi*x)*sin(9*pi*y))<sup>2</sup></p>

<p>This is the function used by Barry Lapthorn in his article entitled 鈥