1 Chapter 5 Advanced Search

2 l

3 Chapter 5 Contents l Constraint satisfaction problems l Heuristic repair l The eight queens problem l Combinatorial optimization problems l Local search l Exchanging heuristics l Iterated local search

4 Chapter 5 Contents, continued l Simulated annealing l Genetic algorithms l Real time A* l Iterative deepening A* l Parallel search l Bidirectional search l Nondeterministic search l Nonchronological backtracking

5 Constraint Satisfaction Problems l Combinatorial optimization problems involve assigning values to a number of variables. l A constraint satisfaction problem is a combinatorial optimization problem with a set of constraints. It is also called CSP. l Can be solved using search. l With many variables it is essential to use heuristics.

6 Different Approaches l 1. An extremely simplistic approach to solving this kind of problem would be to analyze every possible configuration until one was found that matched the constraints. l 2. Use proper search plus heuristic.

7 Example l ore/queens/ ore/queens/ l simple.html simple.html

8 Backtracking Search l Backtracking is a process where steps are taken towards the final solution and the details are recorded. l If these steps do not lead to a solution some or all of them may have to be retraced and the relevant details discarded. l In theses circumstances it is often necessary to search through a large number of possible situations in search of feasible solutions.

9 Heuristic Repair l A heuristic method for solving constraint satisfaction problems. l Generate a possible solution, and then make small changes to bring it closer to satisfying constraints.

10 The Eight Queens Problem l A constraint satisfaction problem: nPlace eight queens on a chess board so that no two queens are on the same row, column or diagonal. l Can be solved by search, but the search tree is large. l Heuristic repair is very efficient at solving this problem.

11 Heuristic Repair for The Eight Queens Problem l Initial state – one queen is conflicting with another. l We’ll now move that queen to the square with the fewest conflicts.

12 Heuristic Repair for The Eight Queens Problem l Second state – now the queen on the f column is conflicting, so we’ll move it to the square with fewest conflicts.

13 Heuristic Repair for The Eight Queens Problem l Final state – a solution!

14 Local Search l Like heuristic repair, local search methods start from a random state, and make small changes until a goal state is achieved. l Local search methods are known as metaheuristics. l Most local search methods are susceptible to local maxima, like hill-climbing.

15 Tabu search l Tabu search is a metaheuristic that uses a list of state that have already been visited to attempt to avoid repeating paths – even going down hill to search a path seemingly a very bad choice. l Therefore, it might be able to avoid local maxima.

16 Example l 1. In hill-climbing l 2. Dr. Edward de Bono, founder of the Cognitive Research Trust in Cambridge. l When the following two pieces of plastic are given to someone with the instructions that they be arranged in a shape that can easily be described, the pieces always get arranged as shown to give a rectangle.

17

18

19

20

21 l l ch/what_is_tabu_search.asp ch/what_is_tabu_search.asp

22 Exchanging Heuristics l A simple local search method. l Heuristic repair is an example of an exchanging heuristic. l Involves swapping two or more variables at each step until a solution is found. l A k-exchange involves swapping the values of k variables. l Can be used to solve the traveling salesman problem.

23 Iterated Local Search l A local search is applied repeatedly from different starting states. l Attempts to avoid finding local maxima. l Useful in cases where the search space is extremely large, and exhaustive search will not be possible.

24 Ant Colony Optimization - ACO l Foraging ants leave a trail of pheromones so that they can lead other ants to find the food that they have found. l 04/index.html 04/index.html

25 Simulated Annealing l 1. Annealing - To heat and then cool usually for softening and rendering less brittle, gradual cooling being required for some materials (as steel and glass) but not for others (as copper and brass) l 2. Simulated Annealing - Based on metropolis Monte Carlo Simulation. l Aims at obtaining a minimum value for some function of a large number of variables. nThis value is known as the energy of the system.

26 Simulated Annealing (2) l A random start state is selected l A small random change is made. nIf this change lowers the system energy, it is accepted. nIf it increases the energy, it may be accepted, depending on a probability called the Boltzmann acceptance criteria: –e (-dE/T)

27 Simulated Annealing (3) –e (-dE/T) l T is the temperature of the system, and dE is the change in energy. l When the process starts, T is high, meaning increases in energy are relatively likely to happen. l Over successive iterations, T lowers and increases in energy become less likely.

28 Simulated Annealing (4) l Because the energy of the system is allowed to increase, simulated annealing is able to escape from global minima. l Simulated annealing is a widely used local search method for solving problems with very large numbers of variables. l For example: scheduling problems, traveling salesman, placing VLSI (chip) components.

29 Genetic Algorithms l A method based on biological evolution. l Create chromosomes which represent possible solutions to a problem. l The best chromosomes in each generation are bred with each other to produce a new generation. l Much more detail on this later.

30 Iterative Deepening A* l A* is applied iteratively, with incrementally increasing limits on f(n). l Works well if there are only a few possible values for f(n). l The method is complete, and has a low memory requirement, like depth- first search.

31 Parallel Search l Some search methods can be easily split into tasks which can be solved in parallel. l Important concepts to consider are: nTask distribution nLoad balancing nTree ordering

32 Bidirectional Search l Also known as wave search. l Useful when the start and goal are both known. l Starts two parallel searches – one from the root node and the other from the goal node. l Paths are expanded in a breadth-first fashion from both points. l Where the paths first meet, a complete and optimal path has been formed.

33 Nondeterministic Search l Useful when very little is known about the search space. l Combines the depth first and breadth first approaches randomly. l Avoids the problems of both, but does not necessarily have the advantages of either. l New paths are added to the queue in random positions, meaning the method will follow a random route through the tree until a solution is found.

34 Nonchronological backtracking l Depth first search uses chronological backtracking. nDoes not use any additional information to make the backtracking more efficient. l Nonchronological backtracking involves going back to forks in the tree that are more likely to offer a successful solution, rather than simply going back to the next unexplored path.