Search Algorithms with Examples by Hsinchun Chen & Reza Ebrahimi
This comprehensive guide delves into various search algorithms such as Depth First Search, Breadth First Search, Hill Climbing, A*, Genetic Algorithms, and Reinforcement Learning. The content includes examples, explanations, and visuals to help understand the principles and applications of these algorithms in different scenarios. Whether you are a beginner or an experienced practitioner in the field, this resource offers valuable insights into deterministic and stochastic search strategies for pathfinding and optimization problems.
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Search Algorithms with Examples Hsinchun Chen & Reza Ebrahimi February, 2020 Acknowledgement: Chapter 4, Exploring Alternatives, AI, Winston 1
Search Algorithms: Deterministic I. Find a path: heuristic (e.g., estimated remaining distance, e.r.d.) 1. Depth First Search (DFS): Stack (LIFO) 2. Hill Climbing: DFS + heuristic (e.r.d.) 3. Breadth First Search (BFS): Queue (FIFO) 4. Beam Search: BFS + search only the best (e.r.d.) w nodes at each level (pruning) 5. Best First Search: follows the best path based on heuristic (e.r.d.) only II. Find an optimal path: actual distance 6. British Museum Search: exhaustive DFS or BFS, add all distances 7. Brand and Bound (BNB): follows the optimal path based on actual accumulated distance 8. Dynamic Programming: BNB + removing longer paths reaching the same node (pruning) 9. A*: follows the optimal path based on actual distance + heuristic (e.g., e.r.d.) 2
Search Algorithms: Stochastic (Global Optimum) III. Genetic Algorithms: modeled as evolution/natural selection with genes Random initialization (G0, stochastic) with bit strings (genes, e.g., m bits) & initial population (pop- size, Vi) & evaluate fitness (fitness function, F(Vi)) Reproduction based on fitness & roulette wheel selection (of Vi; random) based on individual fitness (F(Vi)) Recombination with crossover (Pc, e.g., 0.3-0.9; exploitation ) and mutation (Pm, e.g., 0.01-0.03; exploration ) Evolve over many generations until convergence IV. Reinforcement Learning: modeled as Markov Decision Process (MDP) with agents S: a set of environment and agent states A: a set of actions of the agent (e.g., agent s action selection as policy map ) P(S |S, A): the probability of transition from state S to S under action A R(S |S, A): the immediate reward after transition from state S to S under action A Stochastic (random) rules that describe what the agent observes (O). An RL agent (A) interacts with its environment in discrete time steps to receive an observation (O) with a specific reward (R). RF aims to collect as much reward as possible through the process of exploration (e.g., e-greedy method; e at random) and exploitation (1 e). 3
A Simple Example: Traveling from S to G (Chapter 4, AI, Exploring Alternatives) 4 4 A B C 3 6.7 10.4 Actual Distance S G 5 5 8.9 6.9 Estimated Remaining Distance (e.r.d.) 4 D F E 3 2 4 Rules: 1) Search direct neighbors 2) No cycle/repeat 3) Stop when goal reached 4
I. Find a Path: (1) Depth First Search (DFS) & (2) Hill Climbing DFS: Stack (LIFO); search depth first Hill Climbing: DFS + e.r.d. (check only unfinished paths at the same level) S S A D 8.9 10.4 A D B D 10.4 6.9 A E C E X B F 3 6.7 F D X G Stop! Stop! G 5
I. Find a Path: (3) Breadth First Search (BFS) & (4) Beam Search BFS: Queue (FIFO); search level by level (by breadth) S Beam Search: BFS + best (e.r.d.) w (e.g., 2) nodes S 10.4 8.9 A D A D 6.9 A E A E B 10.4 D B D 8.9 6.7 X X E B C E 6.9 C E 6.7 B F B F 3 X X X G G A C C E B F D F Stop! Stop! 6
I. Find a Path: (5) Best First Search Search the best path based on heuristic only (e.g., e.r.d.) Check all unfinished paths at all levels S 10.4 8.9 A D 10.4 6.9 A E F 6.7 3 B Stop! G 7
II. Find an Optimal Path: (6) British Museum Search (BMS) BMS Steps: 1. Perform exhaustive BFS or DFS to find all paths 2. Add all actual distances for all paths 3. Pick the shortest path S 4 3 A D 4 5 2 5 A E B D 4 5 4 2 4 5 E B C E B F 3 4 4 5 4 5 2 4 4 G A C C E B F D F . . . 8
II. Find an Optimal Path: (7) Branch and Bound (BNB) & (8) Dynamic Programming Dynamic Programming: BNB + removing longer paths reaching the same node BNB: actual accumulated distances S 3 4 S 4 3 (4) (3) A D (4) (3) 4 A D 2 5 5 4 2 5 5 (6) (8) (9) (7) A E B D (6) (8) (9) (7) A E B D 4 5 4 4 2 4 5 5 5 X X 4 (10) (13) (10) E (11) B (12) C E (10) (11) B F (11) (12) C E (11) B F 3 4 4 5 2 4 4 X 3 X X X (13) G (15) (15) (14) A C (16) (15) F B (14) (13) D F G Stop! Stop! Stop: All unfinished paths >= Finished path 9
II. Find an Optimal Path: (9) A* (A Star) A*: Actual Distance + e.r.d. (needs to be under-estimate) S 4 3 (12.9) A D (13.4) 5 2 (19.4) (12.9) 4 A E 5 (17.7) B F (13) G Stop: when a finished path is found Stop! 10
