Improved ant colony optimization algorithms for continuous ... - CoDE

4.2 ACOMV Heuristics for Mixed-Variable Optimization Problems 33
Figure 4.1: The structure of the solution archive of ACOMV. The solutions
in the archive are sorted according to their quality, i.e., the value of the
objective function f(si)), hence, the position of a solution in the archive
always corresponds to its rank.
4.2.3 Probabilistic Solution Construction for Ordered
Discrete Variables
If ordered discrete variables are defined, a component of the continuous
relaxation approach, ACOMV-o, is used. The natural ordering of the values
for these variables may have little to do with their actual numerical values
(and they may even not have numerical values, e.g., x ∈ {small, big, huge}).
Hence, instead of operating on the actual values of the ordered discrete
variables, ACOMV-o operates on their indexes. The values of the indexes
for the new solutions are generated as real numbers, as it is the case for the
continuous variables. However, before the objective function is evaluated,
the continuous values are rounded to the nearest valid index, and the value
at that index is then used for the objective function evaluation. At the
algorithm level, ordered discrete variables are transformed into continuous
variables for probabilistically constructing solution.