The document describes the Polar Bear Optimization Algorithm (PBO), a nature-inspired metaheuristic optimization technique. PBO mimics the hunting behavior of polar bears in three main steps: (1) global search simulates polar bears drifting on icebergs to find food, (2) local search encircling and capturing prey is modeled as movement along a modified trifolium leaf equation, and (3) dynamic population introduces diversity by simulating life and death in the population based on a threshold. The algorithm is applied to optimize the IEEE 3-Unit Test System in a case study.

1. POLAR BEAR
OPTIMIZATION ALGORITHM

2. CONTENTS
• Optimization and its spirit
• Optimization Problem
• Power System Economics and Optimization
• Optimization Algorithms
• Heuristics and Meta-Heuristics
• Taxonomy of Optimization Algorithms
• Key Points from Taxonomy
• Polar Bear Optimization Algorithm (PBO)
• PBO Steps
• Case Study
• Questions?

3. OPTIMIZATION AND ITS SPIRIT
• Optimization is achieving the best with the available resources while satisfying the
constraints
• We optimize in our daily lives. Nature seems to have optimized almost everything
• It is not an exaggeration; indeed everything can be optimized.
• It is simply a question of knowing what is the best, what the issues are, and how we can
achieve it
• This is the most important thing in optimization; we need to know what we want to improve
to the extreme.
• Extreme can be a maximum or minimum, depending on the identified objective.
• We call it an objective function because it must depend on some variables in order to
optimize.
• The objective function should be a function of optimization variables

4. OPTIMIZATION PROBLEM
• Optimization problems can be classified based on the
type of constraints, nature of design variables,
physical structure of the problem, nature of the
equations involved, deterministic nature of the
variables, permissible value of the design variables,
separability of the functions and number of objective
functions

5. OPTIMIZATION PROBLEM

6. POWER SYSTEM ECONOMICS
AND OPTIMIZATION
• Economics is driving force in all ventures; power
industry is no exception
• Optimization also plays a pivotal role in power system
economic problems
• Power system economic problems include
• Economic dispatch
• Unit Commitment
• Dynamic Economic Dispatch

7. OPTIMIZATION ALGORITHMS
• Generally, optimization algorithms can be divided in two basic
classes:
• Deterministic algorithms
• Probabilistic algorithms
• In each iteration of deterministic algorithms there exists at most
one way to proceed if infeasible process terminates
• Deterministic algorithms do not contain instructions that use
random numbers in order to decide what to do or how to modify
data.
• Probabilistic approach results in multiple solutions with a varying
degree of correctness and fitness. They can employ random or
stochastic functions.

8. HEURISTIC AND META-
HEURISTIC
• Heuristics are part of optimization algorithms that:
• Use the information currently gathered by the algorithm to help to decide
which solution candidate should be tested next or how the next
individual can be produced.
• Are usually problem class dependent.
• Define the processing order of the solution candidates in deterministic
algorithms
• Are used to select elements of the search space that are to be
considered in further computations in probabilistic algorithm
• A meta-heuristic is a method for solving very general classes
of problems.
• It combines objective functions or heuristics in an abstract and hopefully
efficient way, usually without utilizing deeper insight into their structure, i.
e., by treating them as black-box-procedures.

9. TAXONOMY OF
OPTIMIZATION
ALGORITHMS

10. KEY POINTS FROM TAXONOMY
• Inspiration (Evolution, Nature, Natural phenomenon)
• An important class of probabilistic Monte Carlo meta-
heuristics is Evolutionary Computation. It encompasses
all algorithms that are based on a set of multiple solution
candidates (called population) which are iteratively
refined.
• Each algorithm in this class has two distinct phases local
search and global search.

11. POLAR BEAR
OPTIMIZATION
ALGORITHM (PBO)
• Nature inspired meta heuristic
optimization algorithm
• Inspired from hunting mechanism of Polar
Bears in arctic region
• Novel evolutionary computational
technique that combines three distinct
features (local, global and dynamic
population)
• Least number of control parameters

12. POLAR BEAR
OPTIMIZATION
ALGORITHM (PBO)
• Some significant features of Polar Bears life
in arctic region are listed below:
• Deadliest predators in the harsh arctic region
• Thick white fur helps them to hide in plain sight
and prevents them from freezing
• Prime food source is seals but they also eat fish
or other arctic animals
• A normal adult polar bear consumes 60kg of seal
• They can travel large distances by drifting on ice
floats
• Once in sight they can swiftly encircle their prey
through ice or water and kill it with their fangs and
paws

13. PBO STEPS
• PBO algorithm transforms this behavior into following
sequence of steps
• Initializing population
• Global Search
• Local Search
• Dynamic Population

14. POPULATION INITIALIZATION
• Unique structure of population initialization
• Initialized at 70-75% of maximum limit
• Random population initialization using normal
distribution within limits
• Variety can be introduced by using different initializing
schemes
• A bear is represented as

15. GLOBAL
SEARCH
• In case of unavailability
of food in local vicinity
Polar Bears tend to
float on ice bergs to a
more feasible location.
• Mathematical model
mimics this drifting
behavior of Polar Bears

16. GLOBAL
SEARCH
• ( 𝑥𝑗
𝑡
)𝑖
= ( 𝑥𝑗
𝑡−1
)𝑖
+𝑠𝑖𝑔𝑛 ω α + γ
• Where ( 𝑥𝑗
𝑡
)𝑖
is movement of i-th polar bear
having j coordinates in t-th iteration towards
the optimum, α is random number in range
(0,1), ω is distance between the present
bear and optimum bear and γ is random
number in the range (0,ω).The distance is
dealt in Euclidian metrics and is given as
• 𝑑(( 𝑥) 𝑖
, 𝑥) 𝑗
= 𝑘=0
𝑛−1
( 𝑥 𝑘
𝑖 − (𝑥 𝑘)(𝑗))2

17. LOCAL SEARCH
• When prey is available in local vicinity bears
encirlce stab it with their fangs.
• Bears have thick fur and large paws that allow
them to approach their prey swiftly through ice
and water alike.
• Movement of each individual was visualized
as a movement along modified excerpt from
the trifolium leaf equation starting from the
current position of the polar bear.
• The radius of the view of a polar bear can be
represented by two parameters: a ∈ (0, 0.3)
which regulates the distance in which polar
bear can see
the seal, and φ0 ∈ (0, π/2) the angle of the
tumbling around the victim.

18. LOCAL SEARCH
• These parameters are used to
define vision radius as
• 𝑟 = 4 acos 𝛷𝑜 𝑠𝑖𝑛(𝛷𝑜)
• The radius is used to compute movement in local
search space for each coordinate
•
𝑥0
𝑛𝑒𝑤
= 𝑥0
𝑎𝑐𝑡𝑢𝑎𝑙
± 𝑟𝑐𝑜𝑠(𝛷1)
𝑥1
𝑛𝑒𝑤
= 𝑥1
𝑎𝑐𝑡𝑢𝑎𝑙
± [𝑟𝑠𝑖𝑛 𝛷1 + 𝑟𝑐𝑜𝑠 𝛷2 ]
𝑥2
𝑛𝑒𝑤
= 𝑥2
𝑎𝑐𝑡𝑢𝑎𝑙
± [𝑟𝑠𝑖𝑛 𝛷1 + 𝑟𝑠𝑖𝑛 𝛷2 + 𝑟𝑐𝑜𝑠 𝛷3 ]
…
𝑥 𝑛−2
𝑛𝑒𝑤
= 𝑥 𝑛−2
𝑎𝑐𝑡𝑢𝑎𝑙
± [ 𝑘=1
𝑛−2
𝑟𝑠𝑖𝑛 𝛷 𝑘 + 𝑟𝑐𝑜𝑠 𝛷 𝑛−1 ]
𝑥 𝑛−1
𝑛𝑒𝑤
= 𝑥 𝑛−1
𝑎𝑐𝑡𝑢𝑎𝑙
± [ 𝑘=1
𝑛−2
𝑟𝑠𝑖𝑛 𝛷 𝑘 + 𝑟𝑠𝑖𝑛 𝛷 𝑛−1 ]

19. DYNAMIC POPULATION
• Mimics the natural phenomenon of life and death in
harsh artic weather
• Introduces diversity and dynamism in population
• Reduces unnecessary calculations
• To implement this strategy a new constant k is
introduced having value in range (0,1)
•
𝐷𝑒𝑎𝑡ℎ 𝑖𝑓 𝑘 < 0.25
𝑅𝑒𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑓 𝑘 > 0.75

20. DYNAMIC POPULATION
• The individuals are destroyed depending on k until
population in above 50% whereas the reproduced
individual is given as:
• ( 𝑥 𝑗
𝑡
) 𝑟𝑒𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑
=
𝑥 𝑗
𝑡(𝑏𝑒𝑠𝑡)
+ 𝑥 𝑗
𝑡(𝑖)
2
• Where 𝑥𝑗
𝑡(𝑏𝑒𝑠𝑡)
the best solution is up to current
iteration and 𝑥𝑗
𝑡(𝑖)
is chosen randomly from among top
10% of best individuals up to current iteration

21. CASE STUDY
• IEEE 3-Unit Test System

22. ANY
QUESTION
S?

23. THANKS