A presentation covering important Optimization heuristics.

1. A presentation on
Optimization Heuristics
by
Kausal Malladi
(Student, IIIT Bangalore)

2. Agenda
● Definition of a Heuristic
● Optimization heuristics
– Genetic Algorithms
– Hill Climbing
– Tabu Search
– Simulated Annealing
– Swarm Intelligence
● With example applications

3. Heuristic
● Experience based techniques for problem
solving, learning and discovery. [Adopted from
Wikipedia]
● Different types
Rule of thumb
–
– Common sense
– Educated Guess
● Meta-heuristics: Parameters that influence
employing a heuristic

4. Optimization Heuristics
● Always difficult to solve NP-Hard and NP-
Complete computational problems
● Even with different optimization techniques,
actual running time is never guaranteed
● We employ some rules / results based on
experiments to state that a near-optimal
solution can be obtained
● No proof as to why and how we get
solution

5. Genetic Algorithms
● A heuristic that mimics natural evolution
● A population of Candidate Solutions
evolved towards better solutions
● Generations
● Requires
– Genetic Representation of solution domain
– Fitness function to evaluate solution
● Applications: Game Theory

6. Local Search
● To solve hard Optimization problems
● Search Space : Domain of function to be
optimized
● Finding a solution among number of
candidate solutions, maximizing a criterion
● Sub-families:
– Hill Climbing
– Tabu Search
– Simulated Annealing

7. Hill Climbing
● Iterative algorithm, starts with arbitrary
solution
● Looks for better solutions incrementally
● Repeats until no further improvements
● Good for finding a local optimum
● Doesn't guarantee global optimum
● Simple, popular
● Works well, generally

8. Hill Climbing
● Popular example – TSP
– Travelling Salesman Problem
● Known NP-Hard problem
● Initial solution may not be optimal
● Shorter route is more likely to be obtained
● Widely used in Artificial Intelligence
● Significant results in real-time systems
● Any-time algorithm
● Pitfall: Plateau

9. Tabu Search
● Iteratively proceeds from one potential
solution S to an improved one S' in the
neighbourhood of S
● Overcomes few pitfalls of other Local
Search techniques (Example: Plateau)
● Visited solutions marked “tabu”
● Search progresses using Memory
Structures
● Often a benchmark heuristic!

10. Tabu Search
● Memory structures
– Describe
● Visited solutions
● User provided sets of rules
– Categories
● Short term
● Intermediate term
● Long term
● Form tabu list

11. Tabu Search
● Issues
– Only effective in discrete search spaces
● Workaround: A similarity measure
– High dimensional search space
● Workaround: Create a tabu list consisting
of attributes of a solution
● Can be more effective solution, has
problems too
● Aspiration criteria introduced
– Override solution's tabu state

12. Tabu Search
● Common example – TSP
– Travelling Salesman Problem
● Tabu Search finds a satisficing solution
● Starts with an initial solution that can be
found randomly or using some algorithm
● Order in which two cities are visited, is
swapped
● Total travelling distance is the metric
● A acceptable solution added to tabu list if
in neighbourhood of accepted solution

13. Simulated Annealing
● Inspiration: Annealing in Metallurgy
● Probabilistic meta-heuristic
● Approximates global optimum in a large
search space
● Gives acceptably good solution if not the
best
● Slow decrease in probability of accepting
worse solutions

14. Simulated Annealing
● Example – TSP
– Travelling Salesman Problem
● Metric under consideration is Mileage
● Metropolis Algorithm
● Pairwise changing order of visit to cities
– Solutions that don't lower mileage also
accepted
●
e-∆D/T > R(0,1)
– ∆D is the change of distance implied
● If T is large, many bad choices are made

15. Swarm Intelligence
● A collective behavior of self-organized
systems which are decentralized [Adopted from
Wikipedia]
● Can't predict how the systems behave
even without a centralized control
● Widely employed in Artificial Intelligence
● Example
– Ant Colony Optimization
● Natural ants ≈ Simulation agents
● Pheromones ≈ Recording position, quality

16. References
●
http://www.iaeng.org/publication/WCE2007/WCE2007_pp61-64.pdf
(Game Theory using Genetic Algorithms)
●
http://mathworld.wolfram.com/SimulatedAnnealing.html
(Simulated Annealing)
● http://artificialintelligence-notes.blogspot.in/2010/07/hill-climbing-procedure.htm
(Hill Climbing in Artificial Intelligence)

17. Thank you!