3 MODEL-BASED INVERSE
PROPAGATION
As mentioned in section.2.2, it is difficult to decide
optimal input values by exhaustive search in the qual-
itative and quantitative hybrid simulation. Therefore,
we propose the method to obtain optimal input values
for the target outputs quickly.
3.1 Problem on Inverse Propagation
In order to decide the optimal input for the target out-
put, our approach is to use original simulation models
defined by users. On the model, propagation of ef-
fects between a source node and a destination node is
defined as a rule. So, it is possible to decide the value
of source node from the value of destination node by
using the rule inversely. We define the inverse propa-
gation as shown in Fig.3.
M
H
dH
40
10
x
z
V1, V2 are decided at random
(Condition:C1V1+C2V2 = z)
State value is decided as the
corresponding pair of V1or V2
y
M
H
dH
20
0
M1 C
1
M2 C
2
y
x
0
30
V
1
V
2
State value is decided
as the corresponding
pair of range
Qualitative value is decided at
random in the corresponding
pair of range
Source node
Destination node
Weights from magnitude
Correlation at random
C
1
>C
2
C
1
+C
2
= 1
Source
node
Destination
node
Inverse propagation
Figure 3: Inverse propagation between qualitative and quan-
titative nodes on a model.
• Inverse propagation from a quantitative node to a
qualitative node
The state value of the qualitative node (source
node) is decided as the corresponding pair of
range made by landmarks in which the value of
quantitative node (destination node) exists.
• Inverse propagation from a qualitative node to a
quantitative node
In the corresponding pair of range with the state
value of the qualitative node (destination node),
a unique value of the quantitative node (source
node) is decided by generating random numbers.
• Inverse propagation from a node to multiple nodes
On the basis of magnitude correlation about con-
necting arcs to the destination node, weighting co-
efficient value about each arc is decided at ran-
dom. Moreover, a random number about each arc
is generated so that sum of the products about the
random numbers multiplied by the weighting co-
eeficients is corresponding to the value of destina-
tion node. Finally, the value of each source node
is decided, by inverse propagation of each arc’s
random number in the above-mentioned manner.
A set of values about input nodes that will gener-
ate the target output can be obtained by deciding the
value of source nodes repeatedly. The set of values
about input nodes is considered as candidates of the
optimal values of input nodes, so we repeat the in-
verse simulation to get probability distribution on in-
put values. The sets of values got at high possibility
are defined as the optimal inputs.
However, if a source node has more than two des-
tination nodes, called “branch node”, there is a possi-
bility that the value of source node from one of desti-
nation nodes is different from the value of other ones
as shown in Fig.4. It contradicts the rules of propaga-
tion about normal direction that the value of each des-
tination node is decided from the same source node.
It is possible to adjust the different values to the aver-
age, but that is not an appropriate way for executing
inverse propagation correctly.
7
10
Output
Input
Values of destination
nodes are decided
from identical node
y
1
x
y
2
y
1
= f(x)
y
2
= g(x)
Contradiction!
Contradiction!
Figure 4: Contradiction about inverse propagation at a
branch node.
In case of the contradiction, our approach is to ad-
just the values by executing the inverse propagation
of effect between qualitative and quantitative nodes
again. The factors of the contradiction can be prop-
agated from the cause-effect relation between quali-
tative and quantitative nodes, because values of the
qualitative nodes are decided as a random number in
the corresponding pair of range to the value of qual-
itative node. Therefore, if the contradiction has oc-
curred at a branch node, we re-execute inverse prop-
agation from the nearest qualitative node connecting
to a quantitative node. Re-execution of propagation
from the qualitative node is repeated and stopped in
case of getting the corresponding values at branch
node. If the contradiction can not be solved in the
pre-defined number of times, all the inverse propaga-
tion is considered to be unavailable and canceled.
INVERSE SIMULATION FOR RECOMMENDATION OF BUSINESS SCENARIO WITH QUALITATIVE AND
QUANTITATIVE HYBRID MODEL
335