Advances in Artificial Intelligence Theory - MICAI - Mexican ...

Genetic Algorithms for Dynamic Variable Ordering in Constraint Satisfaction Problems 41
Mean
checks
120000
100000
80000
60000
40000
20000
✸
+
✸
+ ✸
+
✸
+
✸
+
+
✸
0 + ✸
0.22 0.24 0.26 0.28 0.3 0.32 0.34
160000
140000
120000
100000
✸
80000
+
60000
✸
40000 ✸ + ✸
20000 ✸
✸
+ + +
+
0 ✸+
0.22 0.24 0.26 0.28 0.3 0.32 0.34
p 2
(a) p 1 =0.75, step =1
300000
p 2
(b) p 1 =0.75, step =2
300000
Mean
checks
250000
200000
150000
+ ✸
100000
+ ✸
100000
50000 +
✸
+ ✸
+ ✸
50000
+ ✸
✸
0
0
+
0.18 0.2 0.22 0.24 0.26 0.28
p 2
250000
200000
150000
✸
+
✸+
✸+
✸+
✸+
0.18 0.2 0.22 0.24 0.26 0.28
p 2
Ka ✸
Bz +
Rho
(c) p 1 =1.0, step =1
GA best
GA avr
Ka ✸
Bz +
Rho
(d) p 1 =1.0, step =2
GA best
GA avr
Figure 3. Results on problems 〈20, 10〉 with uniform p 2.
instantiate at each invocation. When we set step = 2 results can be observed
in Figure 2 ((b) and (d)). We found for these cases and even when step had a
higher value, single heuristics outperform our strategy.
The connection we deduced from these results is that indeed assigning a value
to the most-left variable produces changes in the domains of the uninstantiated
variables including that one selected by the parameter step. Consequently, those
changes affect the domains of this variable, and so its selection is no longer the
best one.
We now present results for instances with 20 variables. In this case, 20 different
instances were randomly generated and tested with the FC algorithm and
for each different value of p 2 . The average number of consistency checks is reported
in the figures. For the GA, the figures report the average of the average