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Anytime Planning for Web Service Composition via Alternative Plan Merging George Markou & Ioannis Refanidis Dept. of Applied Informatics, University of Macedonia, Greece ICTAI 2014 - Session A23. Planning Introduction Background

  1. Alternative plan generation and merging (3/3) - Example Original All-outcomes probabilistic determinization actions a 11 a 12 a 2 a 1 a 31 For this example, we use as an a 2 * aversion metric, a 32 1 𝑕 = 𝑑𝑝𝑑𝑒 𝑏 π‘—π‘˜ + a 3 π‘žπ‘ π‘π‘ π›½π‘—π‘˜ +1 a 41 a 4 a 42 a 5 a 6 a 51 a 7 * a 52 * (deterministic) a 61 a 62 a 7 ICTAI 2014 - Session A23. Planning 22/49

  2. Alternative plan generation and merging (3/3) - Example Original All-outcomes probabilistic determinization actions a 11 a 12 a 2 a 1 a 31 For this example, we use as an a 2 * aversion metric, a 32 1 𝑕 = 𝑑𝑝𝑑𝑒 𝑏 π‘—π‘˜ + a 3 π‘žπ‘ π‘π‘ π›½π‘—π‘˜ +1 a 41 a 4 a 42 a 5 a 6 a 51 a 7 * a 52 * (deterministic) a 61 a 62 a 7 ICTAI 2014 - Session A23. Planning 22/49

  3. Alternative plan generation and merging (3/3) - Example Original All-outcomes probabilistic determinization actions a 11 a 12 a 2 a 1 a 31 For this example, we use as an a 2 * aversion metric, a 32 1 𝑕 = 𝑑𝑝𝑑𝑒 𝑏 π‘—π‘˜ + a 3 π‘žπ‘ π‘π‘ π›½π‘—π‘˜ +1 a 41 a 4 a 42 a 5 a 6 a 51 a 7 * a 52 * (deterministic) a 61 a 62 a 7 ICTAI 2014 - Session A23. Planning 22/49

  4. Alternative plan generation and merging (3/3) - Example Original All-outcomes probabilistic determinization actions a 11 a 12 a 2 a 1 a 31 For this example, we use as an a 2 * aversion metric, a 32 1 𝑕 = 𝑑𝑝𝑑𝑒 𝑏 π‘—π‘˜ + a 3 π‘žπ‘ π‘π‘ π›½π‘—π‘˜ +1 a 41 a 4 a 42 a 5 a 6 a 51 a 7 * a 52 * (deterministic) a 61 a 62 a 7 ICTAI 2014 - Session A23. Planning 22/49

  5. Alternative plan generation and merging (3/3) - Example Plan Prob Cost Aversion 𝑏 11 0.8 4 4.55 ICTAI 2014 - Session A23. Planning 23/49

  6. Alternative plan generation and merging (3/3) - Example Plan Prob Cost Aversion 1 = 4 + 0.8 + 1 𝑏 11 0.8 4 4.55 𝑕 = 𝑑𝑝𝑑𝑒 𝑏 π‘—π‘˜ + 1 π‘žπ‘ π‘π‘ π›½π‘—π‘˜ +1 ICTAI 2014 - Session A23. Planning 23/49

  7. Alternative plan generation and merging (3/3) - Example Plan Prob Cost Aversion 1 = 4 + 0.8 + 1 𝑏 11 0.8 4 4.55 𝑏 2, 𝑏 31 0.8 5 6.05 ICTAI 2014 - Session A23. Planning 23/49

  8. Alternative plan generation and merging (3/3) - Example Plan Prob Cost Aversion = 1 βˆ— 0.8 1 = 2 + = 0.8 1 + 1 1 + 3 + 𝑏 11 0.8 4 4.55 0.8 + 1 𝑏 2, 𝑏 31 0.8 5 6.05 ICTAI 2014 - Session A23. Planning 23/49

  9. Alternative plan generation and merging (3/3) - Example Plan Prob Cost Aversion = 1 βˆ— 0.8 1 = 2 + = 0.8 1 + 1 1 + 3 + 𝑏 11 0.8 4 4.55 0.8 + 1 𝑏 2, 𝑏 31 0.8 5 6.05 ICTAI 2014 - Session A23. Planning 23/49

  10. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 ICTAI 2014 - Session A23. Planning 24/49

  11. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 ICTAI 2014 - Session A23. Planning 25/49

  12. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 ICTAI 2014 - Session A23. Planning 26/49

  13. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 27/49

  14. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 Circular nodes 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 = Chance nodes 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 28/49

  15. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 Circular nodes 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 = Chance nodes 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 28/49

  16. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 Grey nodes 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 potentially lead 𝑏 42 , 𝑏 62 6 31.74 to the goal ICTAI 2014 - Session A23. Planning 29/49

  17. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 White nodes 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 don’t lead to the 𝑏 42 , 𝑏 62 6 31.74 goal ICTAI 2014 - Session A23. Planning 30/49

  18. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 Triangular nodes 19.91 𝑏 42 , 𝑏 62 6 = end nodes 31.74 ICTAI 2014 - Session A23. Planning 31/49

  19. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 Goal node 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 32/49

  20. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 Dead-end node 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 33/49

  21. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = a 11 First action = a 11 𝑏 11 1 4.55 Deterministic = a 11 οƒ  Probabilistic = a 1 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 34/49

  22. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = a 11 First action = a 11 𝑏 11 1 4.55 Deterministic = a 11 οƒ  Probabilistic = a 1 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 34/49

  23. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = a 11 First action = a 11 𝑏 11 1 4.55 Deterministic = a 11 οƒ  Probabilistic = a 1 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ ICTAI 2014 - Session A23. Planning 34/49

  24. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = a 11 First action = a 11 𝑏 11 1 4.55 Deterministic = a 11 οƒ  Probabilistic = a 1 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π‘”π‘π‘—π‘šπ‘“π‘’ π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ ICTAI 2014 - Session A23. Planning 34/49

  25. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = a 11 First action = a 11 𝑏 11 1 4.55 Deterministic = a 11 οƒ  Probabilistic = a 1 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π‘”π‘π‘—π‘šπ‘“π‘’ π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π»π‘π‘π‘š! ICTAI 2014 - Session A23. Planning 34/49

  26. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = a 11 First action = a 11 𝑏 11 1 4.55 Deterministic = a 11 οƒ  Probabilistic = a 1 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π‘”π‘π‘—π‘šπ‘“π‘’ π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ 𝑂𝑓𝑦𝑒? π»π‘π‘π‘š! ICTAI 2014 - Session A23. Planning 34/49

  27. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = a 11 First action = a 11 𝑏 11 1 4.55 Deterministic = a 11 οƒ  Probabilistic = a 1 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π‘”π‘π‘—π‘šπ‘“π‘’ π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ 𝑂𝑓𝑦𝑒? π»π‘π‘π‘š! Current plan = a 11 does not contain any more actions Compute possible valid plans ICTAI 2014 - Session A23. Planning 34/49

  28. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 If a plan in the set of valid plans contains at any point actions that have 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 already been executed in the current branch 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 𝑏 42 , 𝑏 62 6 31.74 is the only one contained in the current branch β€’ that has already been inserted ICTAI 2014 - Session A23. Planning 35/49

  29. Alternative plan generation and merging (3/3) - Example Remember assumption : β€’ If an action was executed with a particular result it has this result for its entire branch. β€’ No delete effects or negated Compute possible valid # Plan Aversion preconditions οƒ  output effects still hold; plans no need for re- execution 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 If a plan in the set of valid plans contains at any point actions that have 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 already been executed in the current branch 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 If executed action had the same outcome as the one in the plan οƒ  insert 1) 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 plan into branch without the particular action 𝑏 42 , 𝑏 62 6 31.74 is the only one contained in the current branch β€’ that has already been inserted ICTAI 2014 - Session A23. Planning 35/49

  30. Alternative plan generation and merging (3/3) - Example Remember assumption : β€’ If an action was executed with a particular result it has this result for its entire branch. β€’ No delete effects or negated Compute possible valid # Plan Aversion preconditions οƒ  output effects still hold; plans no need for re- execution 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 If a plan in the set of valid plans contains at any point actions that have 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 already been executed in the current branch 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 If executed action had the same outcome as the one in the plan οƒ  insert 1) 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 plan into branch without the particular action 𝑏 42 , 𝑏 62 6 31.74 If executed action had a different outcome as the one in the plan οƒ  the 2) entire plan is rejected for this particular branch is the only one contained in the current branch β€’ that has already been inserted ICTAI 2014 - Session A23. Planning 35/49

  31. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 If a plan in the set of valid plans contains at any point actions that have 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 already been executed in the current branch 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 If executed action had the same outcome as the one in the plan οƒ  insert 1) 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 plan into branch without the particular action 𝑏 42 , 𝑏 62 6 31.74 If executed action had a different outcome as the one in the plan οƒ  the 2) entire plan is rejected for this particular branch Set of valid plans may not be the same as the original one β€’ some actions may have been removed from the plans due to (1) is the only one β€’ their cost and probability of successful execution have also changed contained in the current branch β€’ plans are sorted again by their ascending aversion factors β€’ that β€’ some plans may have been removed from the set due to (2) has already been inserted ICTAI 2014 - Session A23. Planning 35/49

  32. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 If a plan in the set of valid plans contains at any point actions that have 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 already been executed in the current branch 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 If executed action had the same outcome as the one in the plan οƒ  insert 1) 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 plan into branch without the particular action 𝑏 42 , 𝑏 62 6 31.74 If executed action had a different outcome as the one in the plan οƒ  the 2) entire plan is rejected for this particular branch Set of valid plans may not be the same as the original one β€’ some actions may have been removed from the plans due to (1) 𝑏 1 is the only one contained in β€’ β€’ their cost and probability of successful execution have also changed the current branch β€’ plans are sorted again by their ascending aversion factors β€’ Action aa 1 1 is the only one β€’ some plans may have been removed from the set due to (2) contained in the current branch that β€’ has already been inserted ICTAI 2014 - Session A23. Planning 35/49

  33. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 If a plan in the set of valid plans contains at any point actions that have 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 already been executed in the current branch 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 If executed action had the same outcome as the one in the plan οƒ  insert 1) 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 plan into branch without the particular action 𝑏 42 , 𝑏 62 6 31.74 If executed action had a different outcome as the one in the plan οƒ  the 2) entire plan is rejected for this particular branch Set of valid plans may not be the same as the original one β€’ some actions may have been removed from the plans due to (1) 𝑏 1 is the only one contained in β€’ β€’ their cost and probability of successful execution have also changed the current branch β€’ plans are sorted again by their ascending aversion factors β€’ only present in PPllaan 1 β€’ some plans may have been removed from the set due to (2) tha t has already been inserted β€’ inserted that β€’ has already been inserted ICTAI 2014 - Session A23. Planning 35/49

  34. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 If a plan in the set of valid plans contains at any point actions that have 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 already been executed in the current branch 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 If executed action had the same outcome as the one in the plan οƒ  insert 1) 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 plan into branch without the particular action 𝑏 42 , 𝑏 62 6 31.74 If executed action had a different outcome as the one in the plan οƒ  the 2) entire plan is rejected for this particular branch Set of valid plans may not be the same as the original one β€’ some actions may have been removed from the plans due to (1) 𝑏 1 is the only one contained in β€’ β€’ their cost and probability of successful execution have also changed the current branch β€’ plans are sorted again by their ascending aversion factors β€’ only present in PPllaan 1 β€’ some plans may have been removed from the set due to (2) tha t has already been inserted β€’ All other plans β€’ can be inserted intact β€’ retain their aversion factor ICTAI 2014 - Session A23. Planning 35/49

  35. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = 𝑏 2, 𝑏 31 𝑏 2, 𝑏 31 2 6.05 First action = a 2 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 36/49

  36. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = 𝑏 2, 𝑏 31 𝑏 2, 𝑏 31 2 6.05 First action = a 2 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 36/49

  37. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = 𝑏 2, 𝑏 31 𝑏 2, 𝑏 31 2 6.05 First action = a 2 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ ICTAI 2014 - Session A23. Planning 36/49

  38. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = 𝑏 2, 𝑏 31 𝑏 2, 𝑏 31 2 6.05 First action = a 2 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ πΈπ‘“π‘’π‘“π‘ π‘›π‘—π‘œπ‘—π‘‘π‘’π‘—π‘‘ π‘‘π‘π‘œπ‘œπ‘π‘’ π‘”π‘π‘—π‘š ICTAI 2014 - Session A23. Planning 36/49

  39. Alternative plan generation and merging (3/3) - Example # Plan Aversion Best plan = 𝑏 2, 𝑏 31 𝑏 2, 𝑏 31 2 6.05 First action = a 2 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ πΈπ‘“π‘’π‘“π‘ π‘›π‘—π‘œπ‘—π‘‘π‘’π‘—π‘‘ π‘‘π‘π‘œπ‘œπ‘π‘’ π‘”π‘π‘—π‘š Next action in plan = a 31 Deterministic = a 31 οƒ  Probabilistic = a 3 ICTAI 2014 - Session A23. Planning 36/49

  40. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 ICTAI 2014 - Session A23. Planning 37/49

  41. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ ICTAI 2014 - Session A23. Planning 37/49

  42. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π‘”π‘π‘—π‘šπ‘“π‘’ π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ ICTAI 2014 - Session A23. Planning 37/49

  43. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π‘”π‘π‘—π‘šπ‘“π‘’ π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π»π‘π‘π‘š! ICTAI 2014 - Session A23. Planning 37/49

  44. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π‘”π‘π‘—π‘šπ‘“π‘’ π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ 𝑂𝑓𝑦𝑒? π»π‘π‘π‘š! ICTAI 2014 - Session A23. Planning 37/49

  45. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 2, 𝑏 31 2 6.05 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 𝑏 42 , 𝑏 61 , 𝑏 7 4 17.96 5 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 𝑏 42 , 𝑏 62 6 31.74 π‘‘π‘£π‘‘π‘‘π‘“π‘‘π‘‘π‘”π‘£π‘š π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ π‘”π‘π‘—π‘šπ‘“π‘’ π‘“π‘¦π‘“π‘‘π‘£π‘’π‘—π‘π‘œ 𝑝𝑔 π‘π‘‘π‘’π‘—π‘π‘œ 𝑂𝑓𝑦𝑒? π»π‘π‘π‘š! Current plan does not contain any more actions Compute possible valid plans ICTAI 2014 - Session A23. Planning 37/49

  46. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 All actions are only present in π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 ; β€’ 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 𝑏 2 has already been executed with the same result οƒ  removed β€’ 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 and 𝑏 3 have already been inserted with different results β€’ 𝑏 42 , 𝑏 62 6 31.74 β€’ π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ All other plans β€’ can be inserted intact β€’ retain their aversion factor ICTAI 2014 - Session A23. Planning 38/49

  47. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 1 and 𝑏 3 𝑏𝑏 𝑏 3 3 𝑏 3 have already been inserted with different 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 results 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 All actions are only present in π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 ; β€’ 𝑏 42 , 𝑏 62 6 31.74 β€’ 𝑏 2 has already been executed with the same result οƒ  removed β€’ 𝑏 1 1 1 and 𝑏 3 have already been inserted with different results π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ β€’ All other plans β€’ can be inserted intact β€’ retain their aversion factor ICTAI 2014 - Session A23. Planning 38/49

  48. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 1 and 𝑏 3 𝑏𝑏 𝑏 3 3 𝑏 3 have already been inserted with different 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 results 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 All actions are only present in π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 ; β€’ 𝑏 42 , 𝑏 62 6 31.74 β€’ 𝑏 2 has already been executed with the same result οƒ  removed β€’ 𝑏 1 1 1 and 𝑏 3 have already been inserted with different results π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ β€’ All other plans β€’ can be inserted intact β€’ retain their aversion factor ICTAI 2014 - Session A23. Planning 38/49

  49. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 1 and 𝑏 3 𝑏𝑏 𝑏 3 3 𝑏 3 have already been inserted with different 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 results 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 All actions are only present in π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 ; β€’ 𝑏 42 , 𝑏 62 6 31.74 β€’ 𝑏 2 has already been executed with the same result οƒ  removed β€’ PPllaan 1 and π‘„π‘šπ‘π‘œ 2 are rejected π‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ β€’ All other plans β€’ can be inserted intact β€’ retain their aversion factor ICTAI 2014 - Session A23. Planning 38/49

  50. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 4.55 𝑏 2, 𝑏 31 2 6.05 𝑏 1 and 𝑏 3 𝑏𝑏 𝑏 3 3 𝑏 3 have already been inserted with different 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 13.13 results 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 𝑏 41 , 𝑏 51 , 𝑏 62 5 19.91 All actions are only present in π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 ; β€’ 𝑏 42 , 𝑏 62 6 31.74 β€’ 𝑏 2 has already been executed with the same result οƒ  removed β€’ PPllaan 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ All other plans β€’ can be inserted intact β€’ retain their aversion factor β€’ can be inserted intact β€’ retain their aversion factor ICTAI 2014 - Session A23. Planning 38/49

  51. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 ICTAI 2014 - Session A23. Planning 39/49

  52. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 ICTAI 2014 - Session A23. Planning 39/49

  53. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 ICTAI 2014 - Session A23. Planning 39/49

  54. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 π‘”π‘π‘—π‘šπ‘£π‘ π‘“ 𝑒𝑓𝑏𝑒 βˆ’ π‘“π‘œπ‘’! ICTAI 2014 - Session A23. Planning 39/49

  55. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 π‘”π‘π‘—π‘šπ‘£π‘ π‘“ 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑒𝑓𝑏𝑒 βˆ’ π‘“π‘œπ‘’! ICTAI 2014 - Session A23. Planning 39/49

  56. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 π‘”π‘π‘—π‘šπ‘£π‘ π‘“ 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑒𝑓𝑏𝑒 βˆ’ π‘“π‘œπ‘’! π‘”π‘π‘—π‘šπ‘£π‘ π‘“ ICTAI 2014 - Session A23. Planning 39/49

  57. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 π‘”π‘π‘—π‘šπ‘£π‘ π‘“ 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑒𝑓𝑏𝑒 βˆ’ π‘“π‘œπ‘’! π‘”π‘π‘—π‘šπ‘£π‘ π‘“ 𝑒𝑓𝑏𝑒 βˆ’ π‘“π‘œπ‘’! ICTAI 2014 - Session A23. Planning 39/49

  58. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 π‘”π‘π‘—π‘šπ‘£π‘ π‘“ 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑒𝑓𝑏𝑒 βˆ’ π‘“π‘œπ‘’! π‘”π‘π‘—π‘šπ‘£π‘ π‘“ 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑒𝑓𝑏𝑒 βˆ’ π‘“π‘œπ‘’! π»π‘π‘π‘š! ICTAI 2014 - Session A23. Planning 39/49

  59. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 π‘”π‘π‘—π‘šπ‘£π‘ π‘“ ICTAI 2014 - Session A23. Planning 39/49

  60. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 13.13 3 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 4 𝑏 41 , 𝑏 51 , 𝑏 62 19.91 5 𝑏 42 , 𝑏 62 31.74 6 π‘”π‘π‘—π‘šπ‘£π‘ π‘“ 𝑂𝑓𝑦𝑒? Current plan does not contain any more actions Compute possible valid plans ICTAI 2014 - Session A23. Planning 39/49

  61. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 β€’ All plans contain one of those actions 4 𝑏 42 , 𝑏 61 , 𝑏 7 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different results β€’ 𝑏 41 , 𝑏 51 , 𝑏 62 5 π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ 𝑏 42 , 𝑏 62 6 β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ 𝑏 42 is removed, as it has already been executed β€’ β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  62. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 β€’ All plans contain one of those actions 4 𝑏 42 , 𝑏 61 , 𝑏 7 PPllaan 1 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different β€’ 𝑏 41 , 𝑏 51 , 𝑏 62 5 results 𝑏 42 , 𝑏 62 6 β€’ contain 𝑏 1 and 𝑏 3 with different results β€’ π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ β€’ 𝑏 42 is removed, as it has already been executed β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  63. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 β€’ All plans contain one of those actions 4 𝑏 42 , 𝑏 61 , 𝑏 7 PPllaan 1 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different β€’ 𝑏 41 , 𝑏 51 , 𝑏 62 5 results 𝑏 42 , 𝑏 62 6 β€’ contain 𝑏 1 and 𝑏 3 with different results β€’ π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ β€’ 𝑏 42 is removed, as it has already been executed β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  64. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 β€’ All plans contain one of those actions 4 𝑏 42 , 𝑏 61 , 𝑏 7 PPllaan 1 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different β€’ 𝑏 41 , 𝑏 51 , 𝑏 62 5 results 𝑏 42 , 𝑏 62 6 β€’ PPllaan 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ π‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ 𝑏 42 is removed, as it has already been executed β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  65. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 lt 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 4 𝑏 42 , 𝑏 61 , 𝑏 7 β€’ All plans contain one of those actions 𝑏 41 , 𝑏 51 , 𝑏 62 5 PPllaan 1 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different β€’ 𝑏 42 , 𝑏 62 6 results β€’ PPllaan 1 and π‘„π‘šπ‘π‘œ 2 are rejected PPllaan 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different res 𝑣 β€’ contain 𝑏 4 with a different result π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ 𝑏 42 is removed, as it has already been executed β€’ β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  66. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 lt 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 4 𝑏 42 , 𝑏 61 , 𝑏 7 β€’ All plans contain one of those actions 𝑏 41 , 𝑏 51 , 𝑏 62 5 PPllaan 1 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different β€’ 𝑏 42 , 𝑏 62 6 results β€’ PPllaan 1 and π‘„π‘šπ‘π‘œ 2 are rejected PPllaan 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ π‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ 𝑏 42 is removed, as it has already been executed β€’ β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  67. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 lt 4 𝑏 42 , 𝑏 61 , 𝑏 7 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 𝑏 41 , 𝑏 51 , 𝑏 62 5 β€’ All plans contain one of those actions 𝑏 42 , 𝑏 62 6 β€’ PPllaan 1 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different results PPllaan 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ PPllaan 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ PPllaan 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same resul 𝑒 contain 𝑏 4 β€’ with the same result β€’ π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ β€’ 𝑏 42 is removed, as it has already been executed β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  68. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 2 𝑏 42 is removed, as it has already been executed 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 4 𝑏 42 , 𝑏 61 , 𝑏 7 lt 𝑏 41 , 𝑏 51 , 𝑏 62 5 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 𝑏 42 , 𝑏 62 6 β€’ All plans contain one of those actions β€’ PPllaan 1 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different results PPllaan 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ PPllaan 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ β€’ 𝑏 4 42 42 is removed, as it has already been executed β€’ π‘„π‘šπ‘π‘œ 1 and π‘„π‘šπ‘π‘œ 2 are rejected π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ β€’ 𝑏 42 is removed, as it has already been executed β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  69. Alternative plan generation and merging (3/3) - Example Compute possible valid # Plan Aversion plans 𝑏 11 1 𝑏 2, 𝑏 31 2 2 𝑏 42 is removed, as it has already been executed 𝑏 41 , 𝑏 51 , 𝑏 61 , 𝑏 7 3 4 𝑏 42 , 𝑏 61 , 𝑏 7 17.96 7.05 lt 𝑏 41 , 𝑏 51 , 𝑏 62 5 Current branch contains actions 𝑏 12 , 𝑏 2 , 𝑏 32 , 𝑏 42 𝑏 42 , 𝑏 62 6 31.74 20.83 β€’ All plans contain one of those actions β€’ PPllaan 1 and π‘„π‘šπ‘π‘œ 2 contain 𝑏 1 and 𝑏 3 with different results PPllaan 1 and π‘„π‘šπ‘π‘œ 2 are rejected β€’ PPllaan 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with a different result β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 are rejected β€’ π‘„π‘šπ‘π‘œ 3 and π‘„π‘šπ‘π‘œ 5 contain 𝑏 4 with the same result β€’ β€’ 𝑏 42 is removed, as it has already been executed β€’ Since they now comprise different actions β€’ new (smaller, as they are more probable) aversion factor ICTAI 2014 - Session A23. Planning 40/49

  70. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 42 , 𝑏 61 , 𝑏 7 7.05 4 𝑏 42 , 𝑏 62 20.83 6 ICTAI 2014 - Session A23. Planning 41/49

  71. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 42 , 𝑏 61 , 𝑏 7 7.05 4 𝑏 42 , 𝑏 62 20.83 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 ICTAI 2014 - Session A23. Planning 41/49

  72. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 42 , 𝑏 61 , 𝑏 7 7.05 4 𝑏 42 , 𝑏 62 20.83 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 ICTAI 2014 - Session A23. Planning 41/49

  73. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 42 , 𝑏 61 , 𝑏 7 7.05 4 𝑏 42 , 𝑏 62 20.83 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 π»π‘π‘π‘š! Current plan does not contain any more actions Compute possible valid plans ICTAI 2014 - Session A23. Planning 41/49

  74. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 42 , 𝑏 61 , 𝑏 7 7.05 4 𝑏 42 , 𝑏 62 20.83 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 π»π‘π‘π‘š! Current plan does not contain any more actions Compute possible valid plans ICTAI 2014 - Session A23. Planning 41/49

  75. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 42 , 𝑏 61 , 𝑏 7 7.05 4 𝑏 42 , 𝑏 62 20.83 6 Current plan does not contain any more actions Compute possible valid plans ICTAI 2014 - Session A23. Planning 41/49

  76. Alternative plan generation and merging (3/3) - Example # Plan Aversion 𝑏 42 , 𝑏 61 , 𝑏 7 7.05 4 𝑏 42 , 𝑏 62 20.83 6 𝑑𝑣𝑑𝑑𝑓𝑑𝑑 π»π‘π‘π‘š! Current plan does not contain any more actions Compute possible valid plans ICTAI 2014 - Session A23. Planning 41/49

  77. β€’ Introduction β€’ Background o Problem formulation β€’ Related Work o Non-Deterministic planning o WSC β€’ Alternative plan generation and merging o Example Evaluation β€’ o Results β€’ Conclusion ICTAI 2014 - Session A23. Planning 42/49

  78. Evaluation (1/4) Evaluation based on two domains β€’ o Variation of the one presented as an example o Modified version of the evaluation domain from Hatzi et al. (2011) o A user desires to purchase a book through an electronic bookstore o knows book title / author, credit card information, and shipping address o r esult: book’s purchase, shipping date, and customs cost for the item o Both domains have two versions uni ) o uniform costs for the web services ( Dom x var ) o variant cost for each web service ( Dom x o Domain costs o start from 1 o taken from exponential probability density function, f 𝑦 = 𝑓 βˆ’ π‘¦βˆ’1 , 𝑦 β‰₯ 1 ICTAI 2014 - Session A23. Planning 43/49

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