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(3) When the objective function value of pbest of the particle is improved
for a certain period, the parameter (
p
) is reduced more than 0.5 so that
the particle may divergence.
7.3.4.
Simple expansion of PSO for optimal operational
planning
In order to reduce the number of state variables, the following simple
expansion of PSO is utilized. Namely, all of the state variables can be
expressed as continuous variables. If the input value for a facility is under
the minimum input value, then the facility is recognized as shutdown.
Otherwise, the facility is recognized as startup and the value is recognized
as the input of the facility. The reduction method can reduce the number of
state variables to half, and drastic improvement of PSO search procedures
can be expected.
7.4. Optimal Operational Planning for Energy Plants
Using PSO
All of state variables have 24 elements and one state in the solution space
can be expressed as an array with number of all facilities multiplied by 24
elements. A flow chart is shown in Fig. 7.1.
The whole algorithm can be expressed as follows:
(1) Step 1: Generation of initial searching points (states): States and
velocities of all facilities are randomly generated. The upper and lower
bounds of facilities are considered.
(2) Step 2: Evaluation of searching points: The current states are input
to facility models and the total operational costs are calculated as the
objective function value. The pbests and gbest are updated based on
the value.
(3) Step 3: Modification of searching points: The current searching points
(facility states) are modified using the state equations. The upper and
lower bounds of facilities are considered when the current states are
modified.
(4) Step 4: Stop criterion: The search procedure can be stopped when
the current iteration number reaches the predetermined maximum
iteration number. Otherwise, go to Step 2. The last gbest is output as a
solution.
