Swarm Intelligence

1 Introduction

Optimization is everywhere, from engineering applications to computer science and from

finance to decision making. Optimization is an important paradigm itself with a wide

range of applications. In almost all applications in engineering and industry, we are

always trying to optimize something, whether to minimize the cost and energy con-

sumption, or to maximize the profit, output, performance, and efficiency [1].

Mathematical optimization is the study of such planning and design problems using

mathematical tools [2]. It is possible to write most optimization problems in the generic

form as follows:

min

x∈<

n

f

i

(x), (i = 1, 2, ....M) (1.1)

Subject to h

j

(x) = 0, (j = 1, 2, ...J) (1.2)

g

k

(x) ≤ 0, (k = 1, 2, ..., K) (1.3)

Where M is the number