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Fig. 7.1. 2-Opt exchange tour
7.3
Discrete Set Handling and Its Application
7.3.1
Introduction and Principle
In its canonical form, DE is only capable of handling continuous variables. However,
extending it for optimization of integer variables is rather easy. Only a couple of sim-
ple modifications are required. First, for evaluation of the cost-function, integer values
should be used. Despite this, the DE algorithm itself may still work internally with
continuous floating-point values. Thus,
f cost ( y i ) i = 1 ,.., n param
where :
y i = x i
for continuous variables
(7.3)
INT ( x i )
for integer variables
x i
X
INT() is a function for converting a real value to an integer value by truncation.
Truncation is performed here only for purposes of cost function value evaluation. Trun-
cated values are not assigned elsewhere. Thus, EA works with a population of continu-
ous variables regardless of the corresponding object variable type. This is essential for
maintaining the diversity of the population and the robustness of the algorithm.
Secondly, in case of integer variables, the population should be initialized as follows:
i , j = r i , j x ( High )
+ 1 + x ( Low )
j
P (0) = x (0)
x ( Low )
j
j
(7.4)
i = 1 ,..., n pop ,
j = 1 ,..., n param
Additionally, the boundary constraint handling for integer variables should be per-
formed as follows:
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