Planning and Optimization Francesco Leofante University of Sassari, - PowerPoint PPT Presentation

Planning and Optimization Francesco Leofante University of Sassari, Italy University of Genoa, Italy AI4CPS 2019

Why? Alice and The Cheshire Cat debating on the relevance of planning F. Leofante AI4CPS 2019 January 29, 2019 2 / 10

Why? Alice and The Cheshire Cat debating on the relevance of planning A : Would you tell me, please, which way I ought to go from here? TCC : That depends a good deal on where you want to get to. A : I don’t much care where. TCC : Then it doesn’t much matter which way you go. F. Leofante AI4CPS 2019 January 29, 2019 2 / 10

Why? “A goal without a plan is just a wish” from “50 Ways to Lose Ten Pounds” (1995) by Joan Horbiak, p. 95 F. Leofante AI4CPS 2019 January 29, 2019 2 / 10

What is planning? � � ↸ � � � F. Leofante AI4CPS 2019 January 29, 2019 3 / 10

What is planning? ? � � ↸ � � � F. Leofante AI4CPS 2019 January 29, 2019 3 / 10

What is planning? � � � ↸ � � � F. Leofante AI4CPS 2019 January 29, 2019 3 / 10

What is planning? � � � ↸ � � � F. Leofante AI4CPS 2019 January 29, 2019 3 / 10

What is planning? � � ↸ � � � � restrict search for a plan to paths with (predetermined) bound F. Leofante AI4CPS 2019 January 29, 2019 3 / 10

What is planning? � � ↸ � � � � restrict search for a plan to paths with (predetermined) bound Reductions of planning to SAT linear encodings [Kautz and Selman, 1992] later extended, e.g. , concurrency, theories... F. Leofante AI4CPS 2019 January 29, 2019 3 / 10

Planning as SAT � � ↸ � � � F. Leofante AI4CPS 2019 January 29, 2019 4 / 10

Planning as SAT � � � ↸ � � � F. Leofante AI4CPS 2019 January 29, 2019 4 / 10

Planning as SAT Classical planning as SAT: only Boolean variables � � � ↸ � � � hasFuel(car) : y or n? F. Leofante AI4CPS 2019 January 29, 2019 4 / 10

Planning as SAT CPSs need more expressive formalisms... � � � ↸ � � � F. Leofante AI4CPS 2019 January 29, 2019 4 / 10

Planning as SAT CPSs need more expressive formalisms... � � � ↸ � � � fuel(car) > 5 F. Leofante AI4CPS 2019 January 29, 2019 4 / 10

Planning as Satisfiability Modulo Theories F. Leofante AI4CPS 2019 January 29, 2019 5 / 10

Planning as Satisfiability Modulo Theories Planning problem Let F and A be the sets of fluents and actions . Let X = F ∪ A and X ′ = { x ′ : x ∈ X} be its next state copy. A planning problem is a triple of formulae Π = � I , T , G � where I ( F ) represents the set of initial states T ( X , X ′ ) describes how actions affect states G ( F ) represents the set of goal states F. Leofante AI4CPS 2019 January 29, 2019 5 / 10

Planning as Satisfiability Modulo Theories Planning problem Let F and A be the sets of fluents and actions . Let X = F ∪ A and X ′ = { x ′ : x ∈ X} be its next state copy. A planning problem is a triple of formulae Π = � I , T , G � where I ( F ) represents the set of initial states T ( X , X ′ ) describes how actions affect states G ( F ) represents the set of goal states Encoding Π in SMT - the formula The planning problem Π with makespan k is the formula k − 1 � ϕ ( Π , k ) : = I ( F 0 ) ∧ T ( X i , X i + 1 ) ∧ G ( F k ) i = 0 F. Leofante AI4CPS 2019 January 29, 2019 5 / 10

Planning as Satisfiability Modulo Theories Solving Π How to choose k ? � start with k = 1 � increase until ϕ ( Π , k ) becomes sat or upper bound on k is reached. ϕ ( Π , k ) is sat iff there exists a plan with length k � in that case, a plan can be extracted from the satisfying assignment F. Leofante AI4CPS 2019 January 29, 2019 5 / 10

Beyond satisfiability: planning as OMT Confragosa in fastigium dignitatis via est Seneca F. Leofante AI4CPS 2019 January 29, 2019 6 / 10

Beyond satisfiability: planning as OMT Confragosa in fastigium dignitatis via est Seneca It is a rough road that leads to optimality Francesco F. Leofante AI4CPS 2019 January 29, 2019 6 / 10

Optimal Numeric Planning Modulo Theories Idea : solve numeric planning problem while minimizing their total cost How : leverage Optimisation Modulo Theories (OMT) Challenges : several � currently focusing on... scalability termination conditions support for rich cost structures F. Leofante AI4CPS 2019 January 29, 2019 7 / 10

Planning & Execution Competition for Logistics Robots in Simulation BS RS 1 RS 2 RS 2 CS 2 F. Leofante AI4CPS 2019 January 29, 2019 8 / 10

PROCOMFORT: optimizing comfort in smart buildings � � � � � Smart building F. Leofante AI4CPS 2019 January 29, 2019 9 / 10

PROCOMFORT: optimizing comfort in smart buildings Database  � � � � � Smart building F. Leofante AI4CPS 2019 January 29, 2019 9 / 10

PROCOMFORT: optimizing comfort in smart buildings Database Learning �  � � � � � Smart building F. Leofante AI4CPS 2019 January 29, 2019 9 / 10

PROCOMFORT: optimizing comfort in smart buildings Database Learning �  � � � � � � Smart building Model F. Leofante AI4CPS 2019 January 29, 2019 9 / 10

PROCOMFORT: optimizing comfort in smart buildings Database Learning �  � � � � � � Smart building Model � � � Planner F. Leofante AI4CPS 2019 January 29, 2019 9 / 10

PROCOMFORT: optimizing comfort in smart buildings Database Learning �  � � � � � � Smart building Model � � � � Controller Planner F. Leofante AI4CPS 2019 January 29, 2019 9 / 10

PROCOMFORT: optimizing comfort in smart buildings Database Learning �  � � � � � � Smart building Model � � � � Controller Planner F. Leofante AI4CPS 2019 January 29, 2019 9 / 10

PROCOMFORT: optimizing comfort in smart buildings Database Learning �  � � � � � � � � � Smart building Model � � � � Controller Planner F. Leofante AI4CPS 2019 January 29, 2019 9 / 10

Questions? ? ? ? ? ? F. Leofante AI4CPS 2019 January 29, 2019 10 / 10