A strategy is defined by picking the order of node expansion is - PDF document

�✁ ❹ ⑩ ⑨ ❿ ⑥❾ ③❽ ❼ ⑥ ③❽ ❼ ✐ ❹ ❤ ❦ ❺ ✐ ⑩ r ② ③ ④ ⑤⑥⑦ ✉ ➆ ➆ ❺ ♦ ❼ ③❽ ⑥ ❦ ➊ ♦ ❶ ➆ ➒ ➉ ✐ ❺ ⑥⑦ ⑤ ②③④ ① ➏ q ➃ ➆ r q ♦ ➓ ♣ ⑥ ❷ t ❸ ♣ ❼ ③❽ ❾ ⑥ ➐➑➒ r ♣ ➄ ❼ ③❽ ① ➏ ✿❀❁❂ ♦ ③❽ ❼ ❣ ❧ ♠ ➉ ➈ ♠ ♠ ➇ ⑥⑦ ⑤ ②③④ ① ➆ ❦ ➅ ♦ t ➂ ➃ ➄ ♦ ♣ r ❶➆ ❶ ✂ t ✉ ➆ ⑥❾ ➊ ♦ ⑥❾ ➃ ♣ ➆ ❼ ③ ❽ ❧ ❸ ❣ ♥ ➃ rs t ➎ q t ❺ ✐ ✐ ❹ ❺ ❦ ❤ ❹ ❼ ♦ ③❽ ⑥ ❿ ➋ ♦➌ ➃➍ ✾ ❃ ➀ ❂ ✿ ❉ ❉ ❁ ❀ ❀ ❏ ■ ❍ ❈ ● ❋ ❀ ❁ ❉❊ ❂ ➝ ➙ ➛ ➙ ➛➜➝ ➞ ➟ ❴ ❈ ✾ ✿❀❁❂ ❃ ❄❅ ❆❇ ❅ ❄ ❑ ↔ ❀ ❁ ❋ ❲ ❊ ❃ ❄ ◗ P ❨ ❩ P ❳ ❬ ❭ ❈ ▼❳ ❍▲ ◗ ❃ ▼ ◆ ❊ ❖ P ❘ ❁ ❘❙ ❚ ❯ ✿ ❱ ❲ ↕ ❢ ❄❅ ❉ ❘ ◗ P ❖ ❊ ◆ ▼ ❃ ❍▲ ❑ ❂ ❄ ✿ ❉ ❁ ❚ ❀ ❆❇ ❅ ❈ ❉❊ ❂ ❁ ❋ ❀ ● ❈ ❍ ■ ❏ ❀ ❘❙ ❯ ✞ ✡ ❬ ❭ ❩ ➔ ✌ ❡ ✄ P ❡ ✂ ❡ ✌ ☛ ✄ ❳ ❩ ✿ ❁ ❱ ❲ ❁ ▼❳ P ❈ ❋ ❨ ❲ ❊ ❃ ❄ ❀ ◗ r➁ rs ➠ ❱ ❨ ◗ ❀ ❄ ❃ ❊ ❲ ❋ ❁ ❈ P ▼❳ ❁ ❲ ✿ P ❯ ❚ ❘❙ ❘ ◗ P ❖ ❊ ◆ ▼ ❃ ❍▲ ❑ ❂ ❩ ❳ ✿ ❫ ❈ ❅ ❆❇ ❄❅ ❃ ✿❀❁❂ ✾ ☞ �✁ ❫ ✂✌ ❫ ☞ ☞ ♦ ❬ ❴ ✟ ❫ ✍ ❫ ✌ ✁ ✟ ☞ ✂ ✝ ❪ ❬ ❭ ❄ ❉ ❂ ✪✫ ✒ ✓✔ ✕✖ ✗ ✲ ✕✘ ✱ ✰ ✯ ★ ✮ ✩ ✭ ✬ ★✩ ✴ ✧ ✦ ✥ ✤ ✗ ✔ ✚ ✣ ✓✢ ✒ ✜ ✛ ✘ ✚ ✳ ✵ ❉ ❈ ❁ ❀ ❀ ❏ ■ ❍ ❈ ● ❋ ❀ ❁ ✌ ❂ ❉❊ ❅ ✬ ✻ ✫ ✶ ✷✸✹ ✸✺ ✎✏✑ ✌ ✞ ❆❇ ✁ ✼✽ ✾ ✿❀❁❂ ❃ ❄❅ ❉❊ ☛ ✓ ✐ ① ☎ ✇ q✈ r ♦ ✉ t rs q ✁ ♦ ♦♣ ♥ ♠ ⑤⑥⑦ ❧ ❥❦ ✐ ❤ ❣ ❢ ✞ ✄ ☛ ✂ ✌ ❡ ☞ ☛ ②③④ ⑧⑨ ❁ ✐ ⑩ ♦ ⑩ ⑨ t ♦ ✄ r➁ ➀ ⑥❾❿ ③❽ ❼ ☎✆ ❻ ❹ ⑩ ❸ ♦ ⑩ ❶ ♣ ❷ t ✟ ❤ ♣ ✂ ❹ ❺ ✝✞ ❦ ☎ ✄ ✌ ✿ ❚ ❘❙ ❘ ◗ P ❖ ❊ ◆ ▼ ❃ ❍▲ ❑ ❂ ❄ ❉ ✿ ❉ ✟✡ ❁ ❀ ❀ ❏ ✞ ■ ❍ ❈ ● ✟ ❋ ❀ ❯ ❱ ✁ ❨ ✌ ❞ ❝ ✌❜ ✟ ✌❛ ❵ ◗ ❭ ❬ ❳ P ✠ ❩ ◗ ❲ ❋ ❁ ▼❳ P ❈ ❁ ✙ ✂ ❲ ❊ ❃ ✄ ❄ ❀ A strategy is defined by picking the order of node expansion is empty [ ( ( ( ] applied to ( , ) failure ( ( ( , ) ) succeeds [ [ a solution, or failure ])) ])) Special cases: Implementation : Idea : use an evaluation function for each node Expand most desirable unexpanded node Simulated annealing Hill-climbing Heuristics A Best-first search search A greedy search – estimate of “desirability” = insert successors in decreasing order of desirability search ✂➣→

❵ ❄❅ ● ❋ ❀ ❁ ❂ ❉❊ ❈ ❅ ❆❇ ❃ ❍ ✿❀❁❂ ✾ ✌ ☞ ➢ ➡ ☛ ➼ ✌ ❈ ■ ✞ ▼ ❯ ❚ ❘❙ ❘ ◗ P ❖ ❊ ◆ ❃ ❏ ❍▲ ❑ ❂ ❄ ✿ ❉ ❉ ❁ ❀ ❀ ❢ ✄ ❱ ◗ ▼❳ ❁ ❲ ❱ ✿ ❯ ❚ ❘❙ ❘ P ❈ ❖ ❊ ◆ ▼ ❃ ❍▲ ❑ ☎ ❄ ✿ P ❁ ☛ ❭ ✌ ❡ ➥ ✆ ✌ ✌ ✄ ❞ ➻ ❬ ❋ ❳ P ❩ ❨ ◗ ❀ ❄ ❃ ❊ ❲ ✿ ❲ ❉ ❂ ◗ P ❖ ❊ ◆ ▼ ❃ ❍▲ ❑ ❄ ❘❙ ✿ ❉ ❉ ❁ ❀ ❀ ❏ ■ ❍ ❈ ❘ ❚ ❋ ❃ ❭ ❬ ❳ P ❩ ❨ ◗ ❀ ❄ ❊ ❯ ❲ ❋ ❁ ❈ P ▼❳ ❁ ❲ ❱ ✿ ● ❀ ❁ ❨ ✌ ✄ ❞ ➽ ❭ ❬ ❳ P ❩ ◗ ✆ ❀ ❄ ❃ ❊ ❲ ❋ ❁ ❈ P ▼❳ ✌ ➥ ❁ ✌ ❂ ❉❊ ❈ ❅ ❆❇ ❄❅ ❃ ✿❀❁❂ ✾ ☞ ❡ ➢ ➡ ☛ ➼ ✌ ❢ ✞ ✄ ☛ ✌ ❉ ❂ ❁ ❃ ❈ ❍ ■ ❏ ❀ ❀ ❁ ❉ ❉ ✿ ❄ ❂ ❑ ❍▲ ▼ ❋ ◆ ❊ ❖ P ◗ ❘ ❘❙ ❚ ❯ ✿ ❱ ❲ ❁ ▼❳ ● ❀ ❈ ❡ ➡ ☛ ✁ ✟ ☛ ❜ ✟ ✂ ❢ ❡ ✂✌ ➢ ✞ ☎ ✂ ❀ ❡ ✟ ✁ ➤ ➡ ✾ ✿❀❁❂ ❃ ❄❅ ❆❇ ❅ ❈ ❉❊ ❂ P ❁ ❁ ❆❇ ➭ ➯➲➳ ➦ ➵ ➸➺ ➫ ❋ ➨ ✾ ✿❀❁❂ ❃ ❄❅ ❅ ➫ ❈ ❉❊ ❂ ❁ ❀ ❋ ● ❈ ❍ ■ ❏ ❀ ➨ ➾ ➦ ❳ ❄ ❀ ◗ ❨ ❩ P ❭ ❊ ❳ ❞ ✄ ✆ ✌ ✌ ❃ ❬ ✄ ❲ ➥ ❢ ❡ ✌ ☛ ✞ ( heuristic ) Evaluation function Straight−line distance ➧➩➨ Oradea to Bucharest = estimate of cost from to 71 Arad Neamt Bucharest 87 Zerind 151 Craiova 75 E.g., = straight-line distance from to Bucharest Dobreta Iasi ➧➩➨ Eforie Arad 140 92 Fagaras Greedy search expands the node that appears to be closest to goal Sibiu 99 Fagaras Giurgiu 118 Hirsova Vaslui 80 Iasi Rimnicu Vilcea Lugoj Timisoara Mehadia 142 211 111 Neamt Pitesti 97 Lugoj Oradea 70 98 Pitesti 85 Hirsova 146 101 Rimnicu Vilcea Mehadia Urziceni Sibiu 86 75 138 Timisoara Bucharest 120 Urziceni Dobreta 90 Vaslui Craiova Eforie Giurgiu Zerind Arad Arad 366 366 Zerind Sibiu Timisoara 374 253 329

❞ ❃ ❘❙ ❘ ◗ P ❖ ❊ ◆ ▼ ❍▲ ❯ ❑ ❂ ❄ ✿ ❉ ❉ ❁ ❀ ❀ ❚ ✿ ■ ❄ ◗ ❭ ❬ ❳ P ❩ ❨ ◗ ❀ ❃ ❱ ❊ ❲ ❋ ❁ ❈ P ▼❳ ❁ ❲ ❏ ❍ ➚ ✌ ✍ ➪ ☎ ❡ ✌ ✟ ✂ ✄ ➢ ✌ ☎ ✄ ✄ ❘ ❭ ❬ ❳ P ❩ ✄ ✌ ❈ ❄❅ ● ❋ ❀ ❁ ❂ ❉❊ ❈ ❅ ❆❇ ❃ ✆ ✿❀❁❂ ✾ ❢ ✞ ✄ ☛ ✌ ❡ ➥ ❬ ✄ ◗ ❃ ❘❙ ❘ ◗ P ❖ ❊ ◆ ▼ ❍▲ ❯ ❑ ❂ ❄ ✿ ❉ ❉ ❁ ❀ ❀ ❚ ✿ ■ ❄ ◗ ❭ ❬ ❳ P ❩ ❨ ◗ ❀ ❃ ❱ ❊ ❲ ❋ ❁ ❈ P ▼❳ ❁ ❲ ❏ ❍ ☎ ✄ ✄ ☛ ✌ ❡ ➥ ✆ ✌ ✌ ✍ ❢ ➪ ☎ ❡ ✌ ✟ ✂ ✄ ✌ ➢ ✞ ➶ ❈ ❄❅ ● ❋ ❀ ❁ ❂ ❉❊ ❈ ❅ ❆❇ ❃ ➶ ✿❀❁❂ ✾ ➫ ➴ ➹ ➫ ➹ ➶ ➶ ❨ ➚ ❀ ❚ P ▼❳ ❁ ❲ ❱ ✿ ❯ ❘❙ ❁ ❘ ◗ P ❖ ❊ ◆ ▼ ❃ ❈ ❋ ❑ ❬ ➥ ✆ ✌ ✌ ✄ ❞ ❙ ❭ ❳ ❲ P ❩ ❄ ◗ ❀ ❄ ❃ ❊ ❍▲ ❂ ✌ ❢ ✾ ✌ ☞ ➢ ➡ ☛ ➼ ✌ ✞ ❃ ✄ ☛ ✌ ❡ ➥ ✆ ✌ ✌ ✿❀❁❂ ❄❅ ❄ ❍ ✿ ❉ ❉ ❁ ❀ ❀ ❏ ■ ❈ ❆❇ ● ❋ ❀ ❁ ❂ ❉❊ ❈ ❅ ❡ ❨ ☛ ❀ ❍▲ ❑ ❂ ❄ ✿ ❉ ❉ ❁ ❀ ▼ ❏ ■ ❍ ✄ ● ❋ ❀ ❁ ❃ ◆ ❉❊ ❁ ❃ ❊ ❲ ❋ ❁ ❈ P ▼❳ ❲ ❊ ❱ ✿ ❯ ❚ ❘❙ ❘ ◗ P ❖ ❂ ❈ ❈ ❃ ✞ ❢ ✌ ➼ ☛ ➡ ➢ ☞ ✌ ✾ ✿❀❁❂ ◗ ❄❅ ❆❇ ❅ Arad Arad 366 366 Zerind Sibiu Timisoara Zerind Sibiu Timisoara 374 253 329 374 253 329 Rimnicu Rimnicu Arad Oradea Fagaras Arad Oradea Fagaras Vilcea Vilcea 366 380 178 193 366 380 178 193 Sibiu Bucharest 253 0 Complete ?? Complete : No–can get stuck in loops, e.g., Iasi Neamt Iasi Neamt Time ?? Complete in finite space with repeated-state checking Time : Space ?? , but a good heuristic can give dramatic improvement ➧➩➘➷➴ Space : Optimal ?? —keeps all nodes in memory ➧➩➘ Optimal : No