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

42 Ant Colony Optimization for Mixed Variable Problems
Mean f(x)
0 5 10 15 20 25 30
Mean f(x)
0 10 20 30 40 50
Ackley−ordered discrete variables
Native mixed approach
Continuous relaxation approach
Rand search
2 10
Number of intervals
1
10 2
10 3
Rastrigin−ordered discrete variables
Native mixed approach
Continuous relaxation approach
Rand search
2 10
Number of intervals
1
10 2
10 3
Mean f(x)
0 5 10 15 20 25 30
Mean f(x)
0 10 20 30 40 50
Ackley−categorical variables
Native mixed approach
Continuous relaxation approach
Rand search
2 10
number of intervals
1
10 2
Rastrigin−categorical variables
Native mixed approach
Continuous relaxation approach
Rand search
2 10
number of intervals
1
10 2
Figure 4.4: The mean value evaluation of ACOMV-o and ACOMV-c on
6 dimensional benchmark functions after 10000 evaluations, with intervals
t ∈ {2, 5, 10, 20, ..., 90, 100, 200, ..., 900, 1000}
.
4.5.1 Parameter Tuning of ACOMV
A crucial aspect of mixed-variable algorithms’ parameter configuration is
generalization. Given a set of artificial mixed-variable benchmark functions
as training instances, our goal is to find high-performing algorithm parameters
that perform well on unseen problems that are not available when deciding
on the algorithm parameters [13]. Therefore, we avoid over-tuning by
applying Iterated F-Race to artificial mixed-variable benchmark functions
rather than the engineering problems , which ACOMV are tested and compared
in Section 4.6. For the generalization of parameters, the instances of
training set are designed across six mixed-variable benchmark functions with
mixed dimensions(2, 4, 6, 8, 10, 12, 14) [61], involving two setups of benchmark
functions,(i) with ordered discrete variables, and (ii) with categorical
variables. We use 300 random instances and 5000 budget of experimental
evaluations in the automatic tuning procedure. The parameters obtained
are in Table 4.2. it is used for performance evaluation of ACOMV later ,
and also for real world engineering optimization problems in Section 4.6.
10 3
10 3