ISSN: 1693-6930
TELKOMNIKA Vol. 14, No. 3A, September 2016 : 282 – 287
283 MOP in power systems. This paper, as a further development of [3-5], is a good and useful
reference for those interested in learning about the development of MOPSO and its applications in smart grid.
2 This paper not only well summarizes general procedure of MOPSO, but also well categorizes MOPSO variants into the following types: parameter adjustable MOPSO, guide selection of
MOPSO, operator embedded MOPSO, and archive adjustable MOPSO. These general procedure and variants of MOPSO is a good reference for the design of MOPSO oriented to
MOP emerging in smart grid.
3 This paper deals with applications of MOPSO in smart grid in detail, including Multi-objective optimal operation problems of DG and microgrid, and gives suggestive comments on
MOPSO. These applications and comments of MOPSO are very helpful for those who try to solve Multi-objective optimal operation problems in smart grid.
2. Principles of MOPSO
MOPSO is based on particle swarm optimization PSO which was invented as a new heuristic optimizer by Eberhart and Kennedy in 1995 [6-7]. PSO has following features including
three advantages and one disadvantage: It can find global optimum by imitating bird swarm flying behavior under the guidance of
personal flying experience pbest and population flying experience gbest. It has better convergence performance than other evolutionary algorithms like genetic
algorithm. It is effective for nonlinear and non-differentiable objective functions which traditional
optimization method is very difficult to deal with. It can not find Pareto optimal solutions because it shares the same gbest during optimization
process. In order to find Pareto front efficiently, the mechanism of guide selection and diversity
preservation needs to be redesigned in MOPSO. In MOPSO, each particle in a population P
t
in the tth iteration has its own population flying experience gbest, and the gbest is chosen
according to a certain rule from external archive A
t
which stores non-dominated or Pareto optimal solutions. New external archive A
t+1
needs to be updated at each iteration based on current external archive A
t
and current population P
t
. Though different variants of MOPSO algorithm have been proposed, the general procedure of MOPSO can be briefly summarized
below: Step 1: t=0
Step 2: 1 Initialize population P
t
: For i=1 to population scale
{Initialize the ith particle position
t i
x
and velocity
t i
v
} End 2 Initialize external archive A
t
={}; Step 3: Evaluate P
t
according to Multi-objective function
t i
f x
Step 4: A
t+1
=UpdateArchiveP
t
, A
t
Step 5: P
t+1
=UpdatePopulationP
t
, A
t+1
1
t i
pbest =FindPersonelBest
1 t
i
pbest
,
t i
x
2
t i
gbest =FindGlobalBestA
t+1
,
t i
x
3 For i=1 to population scale {
1 1 1
2 2 t
t t
t t
t i
i i
i i
i
v v
c r pbest x
c r gbest x
1 1
t t
t i
i i
x x
v
} End 4 P
t+1
=DiversityPreservationP
t+1
Step 6: t=t+1 and goto step 3 if a termination criterion is not met. where
is inertia weight, c
1
and c
2
are learning factors, r
1
and r
2
are random numbers between 0 and 1. The introduction of A
t
is the biggest difference between MOPSO and PSO. Compared with traditional optimization methods and other evolutional computation algorithms,
MOPSO has some distinctive advantages such as the following: It has only two fundamental updating rules and has fewer parameters to be adjusted.
It is easy to implement and program with basic mathematical and logic operations.
TELKOMNIKA ISSN: 1693-6930
Applications of MOPSO Algorithms in Smart Grid: a Comprehensive Survey Bo Yang 284
It requires less computation time. It can conveniently balance the global exploration and local exploitation ability.
3. MOPSO Improvement for Better Performance
