24 Questions
What is the primary inspiration behind genetic algorithms in the family of local search algorithms?
Evolutionary biology
What is the key characteristic that allows local search algorithms to operate with very little memory?
They move only to neighbors of the current node
What type of problems are local search algorithms particularly well-suited for solving?
Pure optimization problems
What is the primary objective of the Hill Climbing technique in optimization problems?
To maximize some condition until a goal state is reached
What is the criterion for selecting a new operator in the Hill Climbing algorithm?
The new operator is selected and applied if it is better than the current state
What is the primary difference between local search algorithms and systematic algorithms?
Local search algorithms operate using a single current node, whereas systematic algorithms keep multiple paths in memory
What is the purpose of evaluating the initial state in the Hill Climbing algorithm?
To check if it is the goal state
What is the analogy behind the name 'Hill Climbing' in the context of optimization problems?
Starting with a sub-optimal solution and repeatedly improving it until reaching the optimal state is compared to walking up a hill and reaching the top
What is the main limitation of an algorithm that applies a random walk by moving a successor?
It may complete but not efficiently
What is the inspiration behind the name 'Simulated Annealing' in algorithm design?
The process of hardening a metal or glass to a high temperature then cooling gradually to reach a low-energy crystalline state
How does the Simulated Annealing algorithm decide whether to follow a new random move?
If the new move improves the state, it follows the same path; otherwise, it moves downhill with a probability of less than 1
What is the purpose of the 'BEST-SO-FAR' variable in the Simulated Annealing algorithm?
To keep track of the current best state
What determines the termination of the Simulated Annealing algorithm?
Either a solution is found or there are no new operators left to be applied in the current state
What is the role of the 'annealing schedule' in the Simulated Annealing algorithm?
To initialize the temperature 'T'
How does the Simulated Annealing algorithm evaluate the new state?
By computing ΔE = (value of current) - (value of new state)
What happens when the new state is a goal state in the Simulated Annealing algorithm?
The algorithm returns the new state and quits
What is the condition for A* algorithm to be complete?
Branching factor is finite and cost at every action is fixed.
What is the time complexity of A* search algorithm?
O(b^d), where b is the branching factor and d is the depth of the search tree.
What is the space complexity of A* search algorithm?
O(b^d), where b is the branching factor and d is the depth of the search tree.
What is the purpose of a heuristic function in A* search algorithm?
To estimate the cost of an optimal path between a pair of states in a single agent path-finding problem.
What is the characteristic of a good heuristic function?
Its efficiency.
What is the relationship between the amount of information about a problem and the processing time?
More information about the problem leads to more processing time.
What is the goal of an 8-puzzle problem?
To slide the tiles of the current/start state and place it in an order followed in the goal state.
What are the possible moves in an 8-puzzle problem?
Left, right, up, or down.
Study Notes
Local Search Algorithms
- Inspired by statistical physics (simulated annealing) and evolutionary biology (genetic algorithms)
- Operate using a single current node, moving only to neighbors of that node
- Use very little memory, usually a constant amount
- Can find reasonable solutions in large or infinite state spaces
- Useful for solving pure optimization problems and finding the best state according to an objective function
Hill Climbing
- A technique to solve optimization problems, starting with a sub-optimal solution and improving it repeatedly
- Steps:
- Evaluate the initial state, if it's the goal state, return and quit
- Loop until a solution is found or there are no new operators left
- Select and apply a new operator, evaluate the new state
- If it's the goal state, quit, if it's better than the current state, make it the new current state
Simulated Annealing
- An algorithm that combines efficiency and completeness
- Inspired by the process of annealing in mechanical terms
- Steps:
- Evaluate the initial state, if it's the goal state, return and quit
- Initialize BEST-SO-FAR to the current state and T according to the annealing schedule
- Loop until a solution is found or there are no new operators left
- Select an operator, apply it to produce a new state, and evaluate it
- If the new state is a goal state, return it and quit, if it's better than the current state, make it the current state
A* Search Algorithm
- Complete as long as the branching factor is finite and the cost at every action is fixed
- Time complexity: O(b^d), where b is the branching factor
- Space complexity: O(b^d)
- Optimal: A* search algorithm is optimal
Heuristic Functions
- Estimates the cost of an optimal path between a pair of states in a single agent path-finding problem
- Helps in solving problems, but no guarantee it will never lead in the wrong direction
- A good heuristic function is determined by its efficiency
- More information about the problem means more processing time
- Heuristic functions can be used to solve toy problems like 8-puzzle, 8-queen, and tic-tac-toe more efficiently
This quiz covers local search algorithms, including simulated annealing and genetic algorithms, and their applications in problem-solving.
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