iterative improvement algorithm with example N-Queens Problem

1. Iterative Improvement Algorithms
Lecture-24
Hema Kashyap
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2. Introduction
• In many optimization problems, path is
irrelevant, the goal state itself is solution. Eg.
TSP, N-Queens Problem
• In such cases , one can use iterative
improvement algorithms
• Keeping a single current state, try to improve
it.
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3. • For the most practical approach in which
• All the information needed for a solution are
contained in the state description itself
• The path of reaching a solution is not
important
• Advantage: memory save by keeping track of
only the current state
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4. • When path is irrevant and goal state itself is the
solution
• Then state space = a set of goal states
– find one that satises constraints (e.g., no two classes at
same time)
– or, nd optimal one (e.g., highest possible value, least
possible cost)
• In such cases, can use iterative improvement
algorithms; keep a single current" state, try to
improve it
– Constant space
– Suitable for online as well as oine search
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5. Example: N-Queens Problem
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6. Example TSP Problem
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7. Classes of Itreative improvement
algorithms
• Hill Climbing (gradient decent)
• Local Beam Search
• Simulated Annealing
• Genetic Algorithm
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