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

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Jan 12, 2023 442 likes •778 views

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?

SLIDE 1

Planning and Optimization

Francesco Leofante

University of Sassari, Italy University of Genoa, Italy AI4CPS 2019

SLIDE 2

Why?

Alice and The Cheshire Cat debating

n the relevance of planning
F. Leofante

AI4CPS 2019 January 29, 2019 2 / 10

SLIDE 3

Why?

Alice and The Cheshire Cat debating

n 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

SLIDE 4

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

SLIDE 5

What is planning?

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F. Leofante

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SLIDE 6

What is planning?

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?
F. Leofante

AI4CPS 2019 January 29, 2019 3 / 10

SLIDE 7

What is planning?

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F. Leofante

AI4CPS 2019 January 29, 2019 3 / 10

SLIDE 8

What is planning?

↸

F. Leofante

AI4CPS 2019 January 29, 2019 3 / 10

SLIDE 9

What is planning?

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restrict search for a plan to paths with (predetermined) bound
F. Leofante

AI4CPS 2019 January 29, 2019 3 / 10

SLIDE 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...

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AI4CPS 2019 January 29, 2019 3 / 10

SLIDE 11

Planning as SAT

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F. Leofante

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SLIDE 12

Planning as SAT

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AI4CPS 2019 January 29, 2019 4 / 10

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Planning as SAT

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Classical planning as SAT: only Boolean variables

hasFuel(car): y or n?

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AI4CPS 2019 January 29, 2019 4 / 10

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Planning as SAT

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CPSs need more expressive formalisms...
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AI4CPS 2019 January 29, 2019 4 / 10

SLIDE 15

Planning as SAT

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CPSs need more expressive formalisms...

fuel(car) > 5

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AI4CPS 2019 January 29, 2019 4 / 10

SLIDE 16

Planning as Satisfiability Modulo Theories

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AI4CPS 2019 January 29, 2019 5 / 10

SLIDE 17

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

SLIDE 18

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

ϕ(Π,k) := I(F0) ∧

k−1

T(Xi, Xi+1) ∧ G(Fk)

F. Leofante

AI4CPS 2019 January 29, 2019 5 / 10

SLIDE 19

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

SLIDE 20

Beyond satisfiability: planning as OMT

Confragosa in fastigium dignitatis via est Seneca

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SLIDE 21

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

SLIDE 22

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

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AI4CPS 2019 January 29, 2019 7 / 10

SLIDE 23

Planning & Execution Competition for Logistics Robots in Simulation

BS RS 1 RS 2 RS 2 CS 2

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SLIDE 24

PROCOMFORT: optimizing comfort in smart buildings

Smart building
F. Leofante