Anytime Planning for Web Service Composition via Alternative Plan - - PowerPoint PPT Presentation

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
• Problem formulation
• Related Work
• Non-Deterministic planning
• WSC
• Alternative plan generation and merging
• Example
• Evaluation
• Results
• Conclusion

ICTAI 2014 - Session A23. Planning 2/49

Introduction (1/2)

• Web Service Composition (WSC)  reductions in time / money

required to produce enterprise applications

• Number of WSs growing continuously  discovery phase more difficult
• Ever-changing environment: interfaces / usage
• Always possible that their execution is not successful
• Solution of non-deterministic WSC problem with complete

information is EXP-hard (Nam, Kil, and Lee 2011)

• Semantic WSs:
• Functionality level: defined in regards to preconditions /effects over
• ntological concepts
• Can have alternative outcomes, each with a probability of occurring

attached to it

ICTAI 2014 - Session A23. Planning 3/49

automatic non- deterministic fully

• bservable

probabilistic problem

Introduction (2/2)

• MAPPPA (anagram of Anytime Probabilistic Planning via

Alternative Plan Merging) planner

• Anytime contingent planning framework
• Inspired by FF-Replan (winner of the 2004 IPPC-04)
• Takes the probabilities of the original non-deterministic actions into

consideration while generating the contingent plan

• Specifically targeted for WSC problems

ICTAI 2014 - Session A23. Planning 4/49

• Introduction
• Background
• Problem formulation
• Related Work
• Non-Deterministic planning
• WSC
• Alternative plan generation and merging
• Example
• Evaluation
• Results
• Conclusion

ICTAI 2014 - Session A23. Planning 5/49

Background (1/3)

• View WSC as “planning for service chaining”
• Only take into account semantic WSs at their functionality level (described in

the service profile part of OWL-S)

• Technical details, e.g., data structures or WSDL schemata, are ignored
• WSs defined by name, Inputs/Outputs and Preconditions/Effects (IOPEs)

ICTAI 2014 - Session A23. Planning 6/49

Background (2/3)

• Translation from WS domain (OWL-S) to planning one (PPDDL)
• Inputs + preconditions (hasInput + hasPrecondition)  action’s preconditions
• Outputs + effects (hasOutput + hasEffect)  action’s add effects
• IOPEs comprise set of ontological concepts  domain’s predicates
• Initial state /problem’s goal : conjunction of literals, i.e., ontological concepts
• Solution: template for execution, necessary WSs and their order of execution
• Current web service repository
• OWL-S Service Retrieval Test Collection v. 4.0

ICTAI 2014 - Session A23. Planning 7/49

Background (3/3) – Problem Formulation

• Probabilistic planning domain is of the form D = S, A, γ, Pr, Co
• S is a finite set of states
• A is a finite set of actions
• γ ∶ S × A → 2S is the state-transition function
• Pr ∶ S × A × S → 0,1 is the probability-transition function
• Co ∶ S × A × S → ℕ is a bounded cost-function
• Planning problem is a triple P = s0, sg, D
• s0 ∈ S is the initial state
• closed world semantics
• only contains static propositions: truth value cannot change during the planning process
• sg ∈ S is the goal state
• FOP problem
• Solutions to non-deterministic problems
• weak
• strong
• strong cyclic

ICTAI 2014 - Session A23. Planning 8/49

• Introduction
• Background
• Problem formulation
• Related Work
• Non-Deterministic planning
• WSC
• Alternative plan generation and merging
• Example
• Evaluation
• Results
• Conclusion

ICTAI 2014 - Session A23. Planning 9/49

Related Work (1/2) – WSC

• Literature review suggests
• AI planning is the method of choice for WSC
• OWL-S to PDDL translation : Klusch, Gerber & Schmidt (2005), Hatzi et al. (2011)
• Gap in the evaluation process of current WSC systems
• Evaluation based on a single case study, without quantitative criteria is common,

e.g., Chen, Xu, and Reiff-Marganiec (2009)

• Scarcity of non-deterministic WSC approaches
• Exceptions, e.g., Hoffmann, et al. (2009)
• application of a web service as a belief update operation
• identify two tractable special cases of WSC under uncertainty

ICTAI 2014 - Session A23. Planning 10/49

Related Work (2/2) – Non-Deterministic planning

• FF-Replan
• single plan for a deterministic version of the original problem
• determinizations
• single-outcome: select one probabilistic effect as the outcome of each action,
• all-outcomes: create new action for each of the outcomes of the probabilistic effect
• Ignores the probabilities attached to the probabilistic outcomes
• (Jiménez, Coles, and A. Smith 2006)
• all-outcomes determinization
• translation of probabilities to associated cost values ≈the risk of failing
• metric planner  minimize the product of the failure probabilities
• (Dearden et al. 2003)
• construct seed plan though deterministic planning
• additional (deterministic) branches added incrementally
• best place to insert branch computed based on (approximation of) the amount of

utility gained

ICTAI 2014 - Session A23. Planning 11/49

• Introduction
• Background
• Problem formulation
• Related Work
• Non-Deterministic planning
• WSC
• Alternative plan generation and merging
• Example
• Evaluation
• Results
• Conclusion

ICTAI 2014 - Session A23. Planning 12/49

Alternative plan generation and merging (1/3)

• Anytime contingent planning algorithm - Three steps:
• creates a determinized version of the problem
• generates multiple solutions to the new deterministic problem
• merges plans in a single decision tree / contingent plan
• Tailor-made for WSC problems. Assumptions:
• WSs do not produce irreversible results
• always possible, from any state in the problem, to return to the initial one
• once an action has been executed with a specific effect as an outcome, then for the

rest of the particular branch it cannot be executed again with a different outcome

• also holds for undesired effects; If it fails in a particular branch, it will always fail in it
• real-world example:
• e.g., network failure, is not probable to be available again in a very short amount of

time.

• consequence
• contingent plan can execute each of the actions at most once in each of its branches 

solutions do not contain infinite branches or cycles ICTAI 2014 - Session A23. Planning 13/49

Alternative plan generation and merging (2/3)

• MAPPPA: all-outcomes determinization + incorporation of probabilities
• each action from the original problem is associated with an aversion factor
• maintain the original probabilities and costs from the probabilistic domain
• combined into a single metric  how much the planner should try to avoid using this

action due to its high probability of failing or its high cost in case it succeeds

• Not guaranteed to converge to an optimal contingent plan
• probability monotonically increases as each new (deterministic) branch is added
• In general, the decision tree is a weak plan
• If all the decision tree branches achieve the goals, the DT is a strong plan
• Planning can be based on any search algorithm that returns multiple

deterministic plans

• we use a variation of A* algorithm: continues finding solutions after the first one
• aversion metric can be integrated both as the past path-cost function of A* during

planning, or as a sorting metric of the plans afterwards

ICTAI 2014 - Session A23. Planning 14/49

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 15/49 States represented by a circle

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 16/49 Deterministic actions denoted by a straight line (𝑏2 and 𝑏7)

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 17/49 Probabilistic actions denoted by a dotted line

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 18/49 Some probabilistic actions have a single effect executed with a probability 𝑞𝑠𝑝𝑐𝛽𝑗𝑘& with a probability of 1 − 𝑞𝑠𝑝𝑐𝛽𝑗𝑘 they fail

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 19/49 Other probabilistic actions have two different effects, each having a different probability of being produced

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 20/49 Cost associated with each action is shown opposite it, e.g., 𝑑𝑝𝑡𝑢𝛽11 = 4,𝑑𝑝𝑡𝑢𝛽7 = 2

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 21/49 For this example, we use as an aversion metric, 𝑕 = 𝑑𝑝𝑡𝑢𝑏𝑗𝑘 +

1 𝑞𝑠𝑝𝑐𝛽𝑗𝑘+1

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 22/49 For this example, we use as an aversion metric, 𝑕 = 𝑑𝑝𝑡𝑢𝑏𝑗𝑘 +

1 𝑞𝑠𝑝𝑐𝛽𝑗𝑘+1

Original probabilistic actions All-outcomes determinization a1 a2

*

a3 a4 a5 a6 a7

* *(deterministic)

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 22/49 For this example, we use as an aversion metric, 𝑕 = 𝑑𝑝𝑡𝑢𝑏𝑗𝑘 +

1 𝑞𝑠𝑝𝑐𝛽𝑗𝑘+1

Original probabilistic actions All-outcomes determinization a1 a2

*

a3 a4 a5 a6 a7

* *(deterministic)

a11 a12 a2 a31 a32 a41 a42 a51 a52 a61 a62 a7

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 22/49 For this example, we use as an aversion metric, 𝑕 = 𝑑𝑝𝑡𝑢𝑏𝑗𝑘 +

1 𝑞𝑠𝑝𝑐𝛽𝑗𝑘+1

Original probabilistic actions All-outcomes determinization a1 a2

*

a3 a4 a5 a6 a7

* *(deterministic)

a11 a12 a2 a31 a32 a41 a42 a51 a52 a61 a62 a7

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 22/49 For this example, we use as an aversion metric, 𝑕 = 𝑑𝑝𝑡𝑢𝑏𝑗𝑘 +

1 𝑞𝑠𝑝𝑐𝛽𝑗𝑘+1

Original probabilistic actions All-outcomes determinization a1 a2

*

a3 a4 a5 a6 a7

* *(deterministic)

a11 a12 a2 a31 a32 a41 a42 a51 a52 a61 a62 a7

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 22/49 For this example, we use as an aversion metric, 𝑕 = 𝑑𝑝𝑡𝑢𝑏𝑗𝑘 +

1 𝑞𝑠𝑝𝑐𝛽𝑗𝑘+1

Original probabilistic actions All-outcomes determinization a1 a2

*

a3 a4 a5 a6 a7

* *(deterministic)

a11 a12 a2 a31 a32 a41 a42 a51 a52 a61 a62 a7

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 23/49 Prob Cost Aversion 4.55 4 Plan 𝑏11 0.8

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 23/49 Prob Cost Aversion 4.55 4 Plan 𝑏11 0.8 = 4 + 1 0.8 + 1 𝑕 = 𝑑𝑝𝑡𝑢𝑏𝑗𝑘 +

1 𝑞𝑠𝑝𝑐𝛽𝑗𝑘+1

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 23/49 Prob Cost Aversion 4.55 4 Plan 𝑏11 0.8 = 4 + 1 0.8 + 1 𝑏2,𝑏31 0.8 5 6.05

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 23/49 Prob Cost Aversion 4.55 4 Plan 𝑏11 0.8 = 1 ∗ 0.8 = 0.8

= 2 + 1 1 + 1 + 3 + 1 0.8 + 1

𝑏2,𝑏31 0.8 5 6.05

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 23/49 Prob Cost Aversion 4.55 4 Plan 𝑏11 0.8 = 1 ∗ 0.8 = 0.8

= 2 + 1 1 + 1 + 3 + 1 0.8 + 1

𝑏2,𝑏31 0.8 5 6.05

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 24/49 Aversion 4.55 6.05 13.13 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 # 1 2 3

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 25/49 Aversion 4.55 6.05 13.13 17.96 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 # 1 2 3 4

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 26/49 Aversion 4.55 6.05 13.13 17.96 19.91 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 # 1 2 3 4 5

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 27/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 28/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Circular nodes = Chance nodes # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 28/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Circular nodes = Chance nodes # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 29/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Grey nodes potentially lead to the goal # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 30/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 White nodes don’t lead to the goal # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 31/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Triangular nodes = end nodes # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 32/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Goal node # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 33/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Dead-end node # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 34/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = a11 First action = a11 Deterministic = a11  Probabilistic = a1 # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 34/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = a11 First action = a11 Deterministic = a11  Probabilistic = a1 # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 34/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = a11 First action = a11 Deterministic = a11  Probabilistic = a1 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 34/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = a11 First action = a11 Deterministic = a11  Probabilistic = a1 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝑔𝑏𝑗𝑚𝑓𝑒 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 34/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = a11 First action = a11 Deterministic = a11  Probabilistic = a1 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝑔𝑏𝑗𝑚𝑓𝑒 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝐻𝑝𝑏𝑚! # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 34/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = a11 First action = a11 Deterministic = a11  Probabilistic = a1 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝑔𝑏𝑗𝑚𝑓𝑒 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝐻𝑝𝑏𝑚! 𝑂𝑓𝑦𝑢? # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 34/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = a11 First action = a11 Deterministic = a11  Probabilistic = a1 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝑔𝑏𝑗𝑚𝑓𝑒 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝐻𝑝𝑏𝑚! 𝑂𝑓𝑦𝑢? Current plan = a11 does not contain any more actions Compute possible valid plans # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 35/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans If a plan in the set of valid plans contains at any point actions that have already been executed in the current branch is the only one contained in the current branch

• that

has already been inserted # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 35/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans If a plan in the set of valid plans contains at any point actions that have already been executed in the current branch 1) If executed action had the same outcome as the one in the plan  insert plan into branch without the particular action Remember assumption:

• If an action was executed with a

particular result it has this result for its entire branch.

• No delete effects or negated

preconditions  output effects still hold; no need for re- execution is the only one contained in the current branch

• that

has already been inserted # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 35/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans If a plan in the set of valid plans contains at any point actions that have already been executed in the current branch 1) If executed action had the same outcome as the one in the plan  insert plan into branch without the particular action 2) If executed action had a different outcome as the one in the plan  the entire plan is rejected for this particular branch Remember assumption:

• If an action was executed with a

particular result it has this result for its entire branch.

• No delete effects or negated

preconditions  output effects still hold; no need for re- execution is the only one contained in the current branch

• that

has already been inserted # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 35/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans If a plan in the set of valid plans contains at any point actions that have already been executed in the current branch 1) If executed action had the same outcome as the one in the plan  insert plan into branch without the particular action 2) If executed action had a different outcome as the one in the plan  the entire plan is rejected for this particular branch Set of valid plans may not be the same as the original one

• some actions may have been removed from the plans due to (1)
• their cost and probability of successful execution have also changed
• plans are sorted again by their ascending aversion factors
• some plans may have been removed from the set due to (2)

is the only one contained in the current branch

• that

has already been inserted # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 35/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans If a plan in the set of valid plans contains at any point actions that have already been executed in the current branch 1) If executed action had the same outcome as the one in the plan  insert plan into branch without the particular action 2) If executed action had a different outcome as the one in the plan  the entire plan is rejected for this particular branch Set of valid plans may not be the same as the original one

• some actions may have been removed from the plans due to (1)
• their cost and probability of successful execution have also changed
• plans are sorted again by their ascending aversion factors
• some plans may have been removed from the set due to (2)
• 𝑏 1 is the only one contained in

the current branch

• Action aa 1 1 is the only one

contained in the current branch

• that

has already been inserted # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 35/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans If a plan in the set of valid plans contains at any point actions that have already been executed in the current branch 1) If executed action had the same outcome as the one in the plan  insert plan into branch without the particular action 2) If executed action had a different outcome as the one in the plan  the entire plan is rejected for this particular branch Set of valid plans may not be the same as the original one

• some actions may have been removed from the plans due to (1)
• their cost and probability of successful execution have also changed
• plans are sorted again by their ascending aversion factors
• some plans may have been removed from the set due to (2)
• 𝑏 1 is the only one contained in

the current branch

• nly present in PPllaan 1

tha t has already been inserted

• inserted
• that

has already been inserted # 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 35/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans If a plan in the set of valid plans contains at any point actions that have already been executed in the current branch 1) If executed action had the same outcome as the one in the plan  insert plan into branch without the particular action 2) If executed action had a different outcome as the one in the plan  the entire plan is rejected for this particular branch Set of valid plans may not be the same as the original one

• some actions may have been removed from the plans due to (1)
• their cost and probability of successful execution have also changed
• plans are sorted again by their ascending aversion factors
• some plans may have been removed from the set due to (2)
• 𝑏 1 is the only one contained in

the current branch

• nly present in PPllaan 1

tha t has already been inserted

• All other plans
• can be inserted intact
• retain their aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 36/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = 𝑏2,𝑏31 First action = a2 # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 36/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = 𝑏2,𝑏31 First action = a2 # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 36/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = 𝑏2,𝑏31 First action = a2 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 36/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = 𝑏2,𝑏31 First action = a2 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝐸𝑓𝑢𝑓𝑠𝑛𝑗𝑜𝑗𝑡𝑢𝑗𝑑 𝑑𝑏𝑜𝑜𝑝𝑢 𝑔𝑏𝑗𝑚 # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 36/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Best plan = 𝑏2,𝑏31 First action = a2 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝐸𝑓𝑢𝑓𝑠𝑛𝑗𝑜𝑗𝑡𝑢𝑗𝑑 𝑑𝑏𝑜𝑜𝑝𝑢 𝑔𝑏𝑗𝑚 Next action in plan = a31 Deterministic = a31  Probabilistic = a3 # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 37/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 37/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 37/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑔𝑏𝑗𝑚𝑓𝑒 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 37/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑔𝑏𝑗𝑚𝑓𝑒 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝐻𝑝𝑏𝑚! # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 37/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑔𝑏𝑗𝑚𝑓𝑒 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝑂𝑓𝑦𝑢? 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝐻𝑝𝑏𝑚! # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 37/49 Aversion 6.05 13.13 17.96 19.91 31.74 Plan 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑔𝑏𝑗𝑚𝑓𝑒 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝑂𝑓𝑦𝑢? Current plan does not contain any more actions Compute possible valid plans 𝑡𝑣𝑑𝑑𝑓𝑡𝑡𝑔𝑣𝑚 𝑓𝑦𝑓𝑑𝑣𝑢𝑗𝑝𝑜 𝑝𝑔 𝑏𝑑𝑢𝑗𝑝𝑜 𝐻𝑝𝑏𝑚! # 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 38/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans Current branch contains actions 𝑏12, 𝑏2, 𝑏32

• All actions are only present in 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2;
• 𝑏2 has already been executed with the same result  removed
• and 𝑏3 have already been inserted with different results
• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• All other plans
• can be inserted intact
• retain their aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 38/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans 𝑏 1 and 𝑏 3 𝑏𝑏 𝑏 3 3 𝑏 3 have already been inserted with different results Current branch contains actions 𝑏12, 𝑏2, 𝑏32

• All actions are only present in 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2;
• 𝑏2 has already been executed with the same result  removed
• 𝑏 1 1 1 and 𝑏3 have already been inserted with different

results

• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• All other plans
• can be inserted intact
• retain their aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 38/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans 𝑏 1 and 𝑏 3 𝑏𝑏 𝑏 3 3 𝑏 3 have already been inserted with different results Current branch contains actions 𝑏12, 𝑏2, 𝑏32

• All actions are only present in 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2;
• 𝑏2 has already been executed with the same result  removed
• 𝑏 1 1 1 and 𝑏3 have already been inserted with different

results

• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• All other plans
• can be inserted intact
• retain their aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 38/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans 𝑏 1 and 𝑏 3 𝑏𝑏 𝑏 3 3 𝑏 3 have already been inserted with different results Current branch contains actions 𝑏12, 𝑏2, 𝑏32

• All actions are only present in 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2;
• 𝑏2 has already been executed with the same result  removed
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 are rejected
• 𝑏𝑜 1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• All other plans
• can be inserted intact
• retain their aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 38/49 Aversion 4.55 6.05 13.13 17.96 19.91 31.74 Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans 𝑏 1 and 𝑏 3 𝑏𝑏 𝑏 3 3 𝑏 3 have already been inserted with different results Current branch contains actions 𝑏12, 𝑏2, 𝑏32

• All actions are only present in 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2;
• 𝑏2 has already been executed with the same result  removed
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 are rejected
• All other plans
• can be inserted intact
• retain their aversion factor
• can be inserted intact
• retain their aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑒𝑓𝑏𝑒 − 𝑓𝑜𝑒! # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑒𝑓𝑏𝑒 − 𝑓𝑜𝑒! # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑒𝑓𝑏𝑒 − 𝑓𝑜𝑒! # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑒𝑓𝑏𝑒 − 𝑓𝑜𝑒! 𝑒𝑓𝑏𝑒 − 𝑓𝑜𝑒! # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝑡𝑣𝑑𝑑𝑓𝑡𝑡 𝐻𝑝𝑏𝑚! 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑒𝑓𝑏𝑒 − 𝑓𝑜𝑒! 𝑒𝑓𝑏𝑒 − 𝑓𝑜𝑒! # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 39/49 Aversion 13.13 17.96 19.91 31.74 Plan 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 𝑔𝑏𝑗𝑚𝑣𝑠𝑓 𝑂𝑓𝑦𝑢? Current plan does not contain any more actions Compute possible valid plans # 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• and 𝑄𝑚𝑏𝑜2 contain 𝑏1 and 𝑏3 with different results
• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 contain 𝑏 1 and 𝑏 3 with different

results

• contain 𝑏1 and 𝑏3 with different results
• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 contain 𝑏 1 and 𝑏 3 with different

results

• contain 𝑏1 and 𝑏3 with different results
• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 contain 𝑏 1 and 𝑏 3 with different

results

• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 are rejected
• 𝑏𝑜 1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans lt Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 contain 𝑏 1 and 𝑏 3 with different

results

• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 are rejected
• PPllaan 3 and 𝑄𝑚𝑏𝑜 5 contain 𝑏 4 with a different res𝑣

contain 𝑏4 with a different result

• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans lt Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 contain 𝑏 1 and 𝑏 3 with different

results

• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 are rejected
• PPllaan 3 and 𝑄𝑚𝑏𝑜 5 are rejected
• 𝑏𝑜 3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans lt Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 contain 𝑏 1 and 𝑏 3 with different

results

• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 are rejected
• PPllaan 3 and 𝑄𝑚𝑏𝑜 5 are rejected
• PPllaan 3 and 𝑄𝑚𝑏𝑜 5 contain 𝑏 4 with the same resul𝑢 contain 𝑏4

with the same result

• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans 2 𝑏 42 is removed, as it has already been executed lt Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 contain 𝑏 1 and 𝑏 3 with different

results

• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 are rejected
• PPllaan 3 and 𝑄𝑚𝑏𝑜 5 are rejected
• 𝑏 4 42 42 is removed, as it has already been executed
• 𝑄𝑚𝑏𝑜1 and 𝑄𝑚𝑏𝑜2 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 40/49 Aversion Plan 𝑏11 𝑏2,𝑏31 𝑏41, 𝑏51, 𝑏61, 𝑏7 𝑏42, 𝑏61, 𝑏7 𝑏41, 𝑏51, 𝑏62 𝑏42, 𝑏62 Compute possible valid plans 2 𝑏 42 is removed, as it has already been executed lt Current branch contains actions 𝑏12, 𝑏2, 𝑏32, 𝑏42

• All plans contain one of those actions
• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 contain 𝑏 1 and 𝑏 3 with different

results

• PPllaan 1 and 𝑄𝑚𝑏𝑜 2 are rejected
• PPllaan 3 and 𝑄𝑚𝑏𝑜 5 are rejected
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with a different result
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 are rejected
• 𝑄𝑚𝑏𝑜3 and 𝑄𝑚𝑏𝑜5 contain 𝑏4 with the same result
• 𝑏42 is removed, as it has already been executed
• Since they now comprise different actions
• new (smaller, as they are more probable) aversion factor

# 1 2 3 4 5 6 17.96 31.74 7.05 20.83

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 41/49 Aversion 7.05 20.83 Plan 𝑏42, 𝑏61, 𝑏7 𝑏42, 𝑏62 # 4 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 41/49 Aversion 7.05 20.83 Plan 𝑏42, 𝑏61, 𝑏7 𝑏42, 𝑏62

𝑡𝑣𝑑𝑑𝑓𝑡𝑡

# 4 6

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 41/49 Aversion 7.05 20.83 Plan 𝑏42, 𝑏61, 𝑏7 𝑏42, 𝑏62

𝑡𝑣𝑑𝑑𝑓𝑡𝑡

# 4 6

𝑡𝑣𝑑𝑑𝑓𝑡𝑡

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 41/49 Aversion 7.05 20.83 Plan 𝑏42, 𝑏61, 𝑏7 𝑏42, 𝑏62

𝑡𝑣𝑑𝑑𝑓𝑡𝑡

𝐻𝑝𝑏𝑚! # 4 6 Current plan does not contain any more actions Compute possible valid plans

𝑡𝑣𝑑𝑑𝑓𝑡𝑡

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 41/49 Aversion 7.05 20.83 Plan 𝑏42, 𝑏61, 𝑏7 𝑏42, 𝑏62

𝑡𝑣𝑑𝑑𝑓𝑡𝑡

𝐻𝑝𝑏𝑚! # 4 6 Current plan does not contain any more actions Compute possible valid plans

𝑡𝑣𝑑𝑑𝑓𝑡𝑡

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 41/49 Aversion 7.05 20.83 Plan 𝑏42, 𝑏61, 𝑏7 𝑏42, 𝑏62 # 4 6 Current plan does not contain any more actions Compute possible valid plans

Alternative plan generation and merging (3/3) - Example

ICTAI 2014 - Session A23. Planning 41/49 Aversion 7.05 20.83 Plan 𝑏42, 𝑏61, 𝑏7 𝑏42, 𝑏62 # 4 6 Current plan does not contain any more actions Compute possible valid plans 𝐻𝑝𝑏𝑚!

𝑡𝑣𝑑𝑑𝑓𝑡𝑡

• Introduction
• Background
• Problem formulation
• Related Work
• Non-Deterministic planning
• WSC
• Alternative plan generation and merging
• Example
• Evaluation
• Results
• Conclusion

ICTAI 2014 - Session A23. Planning 42/49

Evaluation (1/4)

• Evaluation based on two domains
• Variation of the one presented as an example
• Modified version of the evaluation domain from Hatzi et al. (2011)
• A user desires to purchase a book through an electronic bookstore
• knows book title / author, credit card information, and shipping address
• result: book’s purchase, shipping date, and customs cost for the item
• Both domains have two versions
• uniform costs for the web services (Domx

uni)

• variant cost for each web service (Domx

var)

• Domain costs
• start from 1
• taken from exponential probability density function, f 𝑦 = 𝑓− 𝑦−1 , 𝑦 ≥ 1

ICTAI 2014 - Session A23. Planning 43/49

Evaluation (2/4)

• Different setup versions for A* (search algorithm)
• combinations of path-cost function / heuristic estimates
• heuristic estimates
• max heuristic (hmax) (not admissible in all settings)
• additive heuristic (hadd), with the extra assumption that the action costs are unary
• h = 0
• h𝑡𝑗𝑛𝑗 = 𝑞𝑠𝑓𝑒𝑗𝑑𝑏𝑢𝑓𝑡 ∈ sg/s𝑗 , i.e., number of goals that not yet achieved
• path-cost functions / aversion metrics for A*:
• 𝑕𝑏 = costaij +

1 probαij+1,

• 𝑕𝑐 =

costaij probaij+1

• 𝑕𝑑 =

costaij probaij+1,

• 𝑕𝑒 = costaij − probaij
• 𝑕𝑓 = 𝑏

ICTAI 2014 - Session A23. Planning 44/49 Bonet and Geffner (2001)

Evaluation (3/4) - Results

In all cases, the algorithm outputted all possible solutions

• the resulting decision trees varied according to the selected path-cost function
• all heuristics, in any combination with a path-cost function,

produce solutions quickly

• the simpler heuristics 𝑖 = 0 and hsim produce the plans in less time than the others
• 𝑖𝑏𝑒𝑒 and 𝑖𝑛𝑏𝑦 are more informed heuristics. Worse performance probably due to:
• combination of faster computation of simpler heuristics and hardness of domains

ICTAI 2014 - Session A23. Planning 45/49

Evaluation (3/4) - Results

=0 and h sim h h sim sim h sim produce the plans in less time than the others 𝐸𝑝𝑛 1 all heuristics, in any combination with a path-cost function, produce solutions

quickly In all cases, the algorithm outputted all possible solutions

• the resulting decision trees varied according to the selected path-cost function
• Heuristics
• the simpler heuristics 𝑖 = 0 and hsim produce the plans in less time than the others
• the simpler heuristics 𝑖 = 0 and hsim produce the plans in less time than the others
• 𝑖𝑏𝑒𝑒 and 𝑖𝑛𝑏𝑦 are more informed heuristics. Worse performance probably due to:
• combination of faster computation of simpler heuristics and hardness of domains

ICTAI 2014 - Session A23. Planning 45/49

Evaluation (3/4) - Results

𝑖 𝑏𝑒𝑒 𝑏𝑏𝑒𝑒𝑒𝑒 𝑖 𝑏𝑒𝑒 and 𝑖 𝑛𝑏𝑦 𝑖 𝑖 𝑛𝑏𝑦 𝑛𝑛𝑏𝑏𝑦𝑦 𝑖 𝑛𝑏𝑦 are more informed

• heuristics. Worse performance probably due to:

=0 and h sim h h sim sim h sim produce the plans in less time than the others

𝐸𝑝𝑛 1 all heuristics, in any combination with a path-cost function, produce solutions

quickly In all cases, the algorithm outputted all possible solutions

• the resulting decision trees varied according to the selected path-cost function
• Heuristics
• combination of faster computation of simpler heuristics and hardness of domains
• the simpler heuristics 𝑖 = 0 and hsim produce the plans in less time than the others
• 𝑖𝑏𝑒𝑒 and 𝑖𝑛𝑏𝑦 are more informed heuristics. Worse performance probably due to:
• combination of faster computation of simpler heuristics and hardness of domains

ICTAI 2014 - Session A23. Planning 45/49

Evaluation (4/4) - Results

• 𝐸𝑝𝑛 1 the choice of path-cost function is not as important as the heuristic in regard to

the required time

• Path-cost functions
• In (the simpler) 𝐸𝑝𝑛 1𝑝𝑛 1 1 the choice of path-cost function is not as important

as the heuristic in regard to the required time

• 𝑕 = 𝑏 ) as the path-cost function

regardless of the heuristic  most effective

ICTAI 2014 - Session A23. Planning 46/49

Evaluation (4/4) - Results

• 𝑕𝑕= 𝑏 𝑏𝑏 𝑏 ) as the path-cost function regardless of the heuristic most

effective

• 𝐸𝑝𝑛 1 the choice of path-cost function is not as important as the heuristic in regard to

the required time

• Path-cost functions
• However, using the number of actions (𝑕 = 𝑏 ) as the path-cost function

regardless of the heuristic  most effective

• Overall
• the approach is efficient in the evaluation domains tested
• simple, non-time-consuming heuristics, are the method of choice

ICTAI 2014 - Session A23. Planning 46/49 In regard to time and amount

• f expanded states

• Introduction
• Background
• Problem formulation
• Related Work
• Non-Deterministic planning
• WSC
• Alternative plan generation and merging
• Example
• Evaluation
• Results
• Conclusion
• Future work

ICTAI 2014 - Session A23. Planning 47/49

• MAPPPA:
• Anytime probabilistic planner
• Produces a contingent plan by integrating alternative

deterministic solutions to a determinized probabilistic problem

• determinized problem does not disregard WSs reliability or cost
• promising results in our evaluation
• integrated into our prototype WSC platform, MADSWAN*

*(alpha version available currently only contains deterministic WSC algorithm)

Conclusion

ICTAI 2014 - Session A23. Planning 48/49

• MAPPPA:
• Anytime probabilistic planner
• Produces a contingent plan by integrating alternative

deterministic solutions to a determinized probabilistic problem

• determinized problem does not disregard WSs reliability or cost
• promising results in our evaluation
• integrated into our prototype WSC platform, MADSWAN*

*(alpha version available currently only contains deterministic WSC algorithm)

Conclusion

ICTAI 2014 - Session A23. Planning 48/49 gmarkou@uom.gr http://goo.gl/mqyEOX http://goo.gl/IBgax3

Future work

• Planning:
• Use an existing deterministic planner to generate the alternative plans
• Optimized existing implementation of A*
• prune paths subsumed by others  check if all previously added actions in path already form

another, shorter, solution

• prune paths trying to add a deterministic action 𝑏𝑦𝑗, , if 𝑏𝑦𝑘 is already in the same path

ICTAI 2014 - Session A23. Planning 49/49

Future work

• Planning:
• Use an existing deterministic planner to generate the alternative plans
• Optimized existing implementation of A*
• prune paths subsumed by others  check if all previously added actions in path already form

another, shorter, solution

• prune paths trying to add a deterministic action 𝑏𝑦𝑗, , if 𝑏𝑦𝑘 is already in the same path

ICTAI 2014 - Session A23. Planning 49/49 same non-deterministic action with a different alternative outcome

Future work

• Planning:
• Use an existing deterministic planner to generate the alternative plans
• Optimized existing implementation of A*
• prune paths subsumed by others  check if all previously added actions in path already form

another, shorter, solution

• prune paths trying to add a deterministic action 𝑏𝑦𝑗, , if 𝑏𝑦𝑘 is already in the same path
• OWL-S
• Consider ontological concepts’ matches covering plug-in or subsumes relationships
• Support OWL-S extensions that allows description of WS QoS elements, e.g., OWL-Q

ICTAI 2014 - Session A23. Planning 49/49

Thank you for your attention!

Questions?

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service composition”, Proc. IEEE International Conference on Web Services (ICWS'09), July 2009, pp. 9-16.

• R. Dearden, N. Meuleau, S. Ramakrishnan, D.E. Smith, and Washington, R. “Incremental contingency planning,” in
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• O. Hatzi, D. Vrakas, M. Nikolaidou, et al., “An integrated approach to automated semantic web service composition

through planning”, IEEE Trans. Service Computing, April 2011, pp. 301-308.

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constraints, and planning under uncertainty: a new connection”, J. Artif. Intell. Res, vol. 35, May 2009, pp.49-117.

• S. Jiménez, A. Coles, and A. Smith, “Planning in probabilistic domains using a deterministic numeric planner, in
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International AAAI Fall Symposium on Agents and the Semantic Web, Nov. 2005.

• W. Nam, H. Kil, and D. Lee 2011, “On the computational complexity of behavioral description-based web service

composition,” Theor. Comput. Sci., vol. 412, no. 48, pp. 6736-6749, 2011. ICTAI 2014 - Session A23. Planning 51/49