1. Subject Name: Operation Research Subject Code: 10CS661 Prepared By:Mrs
Subject Name: Operation Research Subject Code: 10CS661 Prepared By:Mrs.Annapoorani Department:CSE

2. UNIT 8-MetaHeuristics
1.The Nature of Metaheuristics 2.Simulated Annealing 3.Tabu Search 4.Genetic Algorithms

3. Heuristics
Heuristics are rules to search to find optimal or near-optimal solutions. Examples are FIFO, LIFO, earliest due date first, largest processing time first, shortest distance first, etc.
Heuristics can be constructive (build a solution piece by piece) or improvement (take a solution and alter it to find a better solution).

4. Many constructive heuristics are greedy or myopic, that is, they take the best thing next without regard for the rest of the solution.
Example: A constructive heuristic for TSP is to take the nearest city next. An improvement heuristic for TSP is to take a tour and swap the order of two cities.

5. 1. Meta-Heuristics
An iterative generation process which guides a subordinate heuristic by combining intelligently different concepts derived from classical heuristics, artificial intelligence, biological evolution, natural and physical sciences for exploring and exploiting the search spaces using learning strategies to structure information in order to find efficiently near-optimal solutions.

6. 1.1 Advantages of Meta-Heuristics
Very flexible
Often global optimizers
Often robust to problem size, problem instance and random variables
May be only practical alternative

7. 1.2 Disadvantages of Meta-Heuristics
Often need problem specific information / techniques
Optimality (convergence) may not be guaranteed
Lack of theoretic basis
Different searches may yield different solutions to the same problem (stochastic)
Stopping criteria
Multiple search parameters

8. 1.3 Hill climbing

9. 1.4 Simulated Annealing
Local Search
Solution space
Cost function ?

10. 2. Simulated Annealing What
Exploits an analogy between the annealing process and the search for the optimum in a more general system.

11. 2.1Annealing Process Annealing Process
Raising the temperature up to a very high level (melting temperature, for example), the atoms have a higher energy state and a high possibility to re-arrange the crystalline structure.
Cooling down slowly, the atoms have a lower and lower energy state and a smaller and smaller possibility to re-arrange the crystalline structure.

12. 2.2 Simulated Annealing Algorithm
Initialize:
initial solution x ,
highest temperature Th,
and coolest temperature Tl
T= Th
When the temperature is higher than Tl
While not in equilibrium
Search for the new solution X’
Accept or reject X’ according to Metropolis Criterion
End
Decrease the temperature T

13. 2.3 Example of Simulated Annealing
Traveling Salesman Problem (TSP)
Given 6 cities and the traveling cost between any two cities
A salesman need to start from city 1 and travel all other cities then back to city 1
Minimize the total traveling cost

14. Contd… Solution representation Search mechanism Cost function
An integer list, i.e., (1,4,2,3,6,5)
Search mechanism
Swap any two integers (except for the first one)
(1,4,2,3,6,5)  (1,4,3,2,6,5)
Cost function

15. What 3.Tabu Search Neighborhood search + memory Neighborhood search
Record the search history – the “tabu list”
Forbid cycling search
Main idea of tabu

16. 3.1 Algorithm of Tabu Search
Choose an initial solution X
Find a subset of N(x) the neighbors of X which are not in the tabu list.
Find the best one (x’) in set N(x).
If F(x’) > F(x) then set x=x’.
Modify the tabu list.
If a stopping condition is met then stop, else go to the second step.

17. 3.2 Effective Tabu Search Effective Modeling Aspiration criteria
Neighborhood structure
Objective function (fitness or cost)
Example:
Graph coloring problem:
Find the minimum number of colors needed such that no two connected nodes share the same color.
Aspiration criteria
The criteria for overruling the tabu constraints and differentiating the preference of among the neighbors

18. Contd… Effective Computing
“Move” may be easier to be stored and computed than a completed solution
move: the process of constructing of x’ from x
Computing and storing the fitness difference may be easier than that of the fitness function.

19. Contd… Effective Memory Use Variable tabu list size
For a constant size tabu list
Too long: deteriorate the search results
Too short: cannot effectively prevent from cycling
Intensification of the search
Decrease the tabu list size
Diversification of the search
Increase the tabu list size
Penalize the frequent move or unsatisfied constraints

20. 3.3 Eample of Tabu Search A hybrid approach for graph coloring problem
Given an undirected graph G=(V,E)
V={v1,v2,…,vn}
E={eij}
Determine a partition of V in a minimum number of color classes C1,C2,…,Ck such that for each edge eij, vi and vj are not in the same color class.
NP-hard

21. 4. Genetic Algorithm
Reproduction (Selection)
Crossover
Mutation

22. Example 1
Maximize f(x) = x2 where x  I and 0  x  31

23. Coding of a solution : A five-bit integer, e.g. 01101
Fitness function : F(x) = f(x) = x2
Initial population : (Randomly generated)

24. Reproduction
Roulette Wheel

25. Reproduction

26. Crossover

27. The probability of mutation Pm = 0.001 20 bits * 0.001 = 0.02 bits

29. Genetic Algorithm (5/5) p1 = 01110, p2 = 01110 p3 = 11100, p4 = 00010
begin
t 0
initialize Pt
evaluate Pt
while (not terminated) do
t  t+1
select Pt from Pt-1
crossover and mutation Pt
end
p1 = 01110, p2 = 01110
p3 = 11100, p4 = 00010
f1 = = 3, f2 = = 3
f3 = = 3, f4 = = 1
s1 = = 0.3, s2 = = 0.3
s3 = = 0.3, s4 = = 0.1
s4 = = 0.3
p1 = , p2 =
p3 = , p4 =
c1 = , c2 =
c3 = , c4 =
c1 = 01101, c2 = 01110
c3 = 11010, c4 = 11111
c1 = 01100, c2 = 01100
c3 = 11110, c4 = 11110 29

30. Initialization
Loop
Each ant applies a state transition rule to
incrementally build a solution and applies a
local updating rule to the pheromone
Until each of all ants has built a complete solution
A global pheromone updating rule is applied
Until End_Condition