the reasoning and optimization...

The Reasoning and Optimization Theme

Joshua Knowles, Konstantin Korovin and Renate Schmidt

School of Computer ScienceThe University of Manchester

18 September 2012

J. Knowles, K. Korovin & R. Schmidt (Computer Science)Reasoning and Optimization Theme 18 Sep. 2012 1 / 24

Outline

1 Introduction and theme outline

2 Why Reasoning?

3 Why Optimization?

4 General practical remarks


Reasoning and Optimization

What is Reasoning?

Manipulating representations of data and information about a domain ofapplication in order to produce new information

101110

1101

If I live in Manchester then it rains a lotIf it rains a lot then I need an umbrellaIf I live in Manchester then I need an umbrella

Quantitative Reasoning Symbolic Reasoninganalytic/numerical methods,probabilistic/statistical methods,algorithmic methods

logical methods,allows incorporation of aspects ofintelligence into computer systems

What is Optimization?

Crucial for handling complexitySolving complex problems fast, finding optimal solutions

Maximising profit Scheduling problems


Theme outline

Period Course units

P3 COMP60332 – Automated Reasoning and Verification

Konstantin Korovin, Renate Schmidt

P4 COMP60342 – Optimization for learning, planning andproblem-solving

Joshua Knowles

Teaching day: FridayLectures: 2.15, Labs: 2.25


Automated Symbolic Reasoning is indispensible for . . .

Providing proofs of mathematical argumentsSolution of Robbins Algebra Problem, NYT Oct. 1996

Ensuring correct functioning of complex systemsSoftware + hardware verificationseL4 Microkernel verified correct, NiCTA, 2009Major companies intensively using AR tools:Intel, Microsoft, NASA, Mercedes, Toyota, Airbus

Manage and retrieve data in complex information systemsSemantic web, ontology reasoning

Performing combinatorial reasoning: constraint problemsSolving Sudoku and other puzzlesProfessional sports scheduling


The very early beginnings

Since long ago philosophers have dreamed of machines that can reason

1655– Leibniz (inspired by Hobbes) recognized reasoning/thinking isa form of calculation

Leibniz’s goal was to develop a universal logical notation andsymbolic calculus in which conceptual computation can be carriedout completely mechanicallyHe tried to do reasoning by mapping to numerical computationsbecause he knew these could be mechanized


History of automated reasoning

1957– When the first computers became common thefirst running reasoning systems were implementedResults were not encouraging

1960– Davis & Putnam invented the DPLL calculus(Has become basis for state-of-the-art SAT solvers)

1965– Robinson invented the resolution calculus and unification

Resolution rule:A ∨ B ¬B ∨ C

A ∨ C

Astonishingly many refinements were developed over the years:hyperresolution, SOS strategy, semantic resolution, lock resolution,linear resolution, . . . , paramodulation, . . .

Other deduction approaches were implemented


A new framework and new era for Automated Reasoning

1990– Bachmair & Ganzinger introduced a new framework of resolution

Generalizes and unifies all previous work onresolution (and equality reasoning)Remarkably simple and elegant, yet very pow-erful and flexible

Guiding principle: Avoid unnecessary inferences where possible2 simple, yet powerful search control mechanismsGeneral notion of redundancy

Several system implementing this framework: SPASS, VAMPIRE, EAre currently the best available

Led quickly to massive advances and has inspired many peopleDecision procedures for fragments of first-order logic, non-classicallogics, special theoriesCombination of specialised decision proceduresInstance-based methods: iProver. . .


COMP60332 – Automated Reasoning and Verification

Introduce the foundation of automated symbolic reasoning and discussverification as a major application

Syllabus:

Propositional logic = Boolean logicDPLL calculus & SAT solvingResolution

First-order logic = predicate logicThe basics of the resolution framework of Bachmair & Ganzinger

Verification


Assessment

Exam: 50%Closed book, 2 hours, choose 2 of 3 questions

Lab & coursework: 50%Pencil and paper assessed exercisesLabwork involving

the SAT solver MiniSATthe first-order resolution prover SPASS


Why Optimization?

...we recognize efficiency, strength, compactness in these designs. Howcan we mechanize the design process?


Why Optimization?

It means finding the best; a fundamental aim in all human endeavour

Optimization saves and makes money; underpins engineering; helpsorganize, manage and plan; supports machine learning; solvesproblems

Computers can do it fast

It is deeply linked with Reasoning by the structure of problems

It is philosophically linked with mathematics, intelligence,computation, e.g., through the theory of NP-completeness


Optimization in Machine Learning

Hamiltonian

of a double pendulum discovered by

computer

Computer Derives Physical Laws for ItelfIn 2009, Cornell researchers, Schmidt andLipson, used an optimization method based onadvanced symbolic regression to “discover”physical laws automatically from motion data.(Science, 2009)


Optimization in Machine Learning

Researchers at Manchester in 2011, developed optimization techniquesto discover combination therapies to treat brain inflammation, a majorfactor in Alzheimer’s and other diseases. (Nature Chemical Biology, 2011)


Optimization in Planning

The Hubble Space Telescope is a scarceresource.

Advanced optimization algorithms are used toschedule time on the telescope, sharing theresource between different groups and takingaccount of constraints


Optimization Saves Money

IcoSystem (a US optimization andcomplexity science company) set outto improve drug developmentprocesses at Eli Lilly.

‘Compared to a standard 40 months androughly £25 million, ...[we] reached thesame amount of technical success in a yearand a day with a total expenditure on theorder of £2.7 million.’ –Neil Bodick, COO,Eli Lilly Chorus


Optimization in Problem Solving

What is the minimum number ofmoves (from here) to obtain asolved cube?

What about from ANYconfiguration?


COMP60342 – What You Will Learn

The course aims to have a practical outcome

You will learn

How to approach a wide variety of problems, and how to developyour own code to solve them

You will understand some of the most general and flexible optimizationalgorithms, and how and why they work


What You Will Learn 2

Some important and interesting mathematical theory behind the practice

This links optimization fundamentally to computation and the notion ofcomplexity


How You Will Learn It

Answering thought-provoking questions (often not assessed)

Doing LAB work, where YOU MUST CODE for yourself

Running experiments in LABs where you test and compare methods


Structure of the Course

Week 1: Introduction to OptimizationProblems: from MAX-SAT to TSP to Optimal BettingBasic exact methods: Enumeration and Greedy

Week 2: Branch-and-BoundComplexity/NP-Completeness

Week 3: Dynamic ProgrammingStochastic DP Problems

Week 4: Evolutionary Algorithms and Local SearchWeek 5: Multiobjective Optimization

Assessments:

1st Lab (two weeks) Packing a Knapsack with Applications in Finance 10%2nd Lab (one week) Hospital Resource Management, and Optimal Stopping 10%3rd Lab (one week) Assigning Students to Projects (Project ‘Dating’) 10%4th Lab (one week) Multiobjective Maximum Satisfiability 10%Examination Multiple Choice plus 2 Questions from 5 (2 hours) 60%


The Course Text

Costs about £10. Copies available inSchool and University Library.


Some advice on choosing themes

The R&O theme can be combined with any other theme

Has no prerequisites, no pre/co-requisite to any theme

It goes well with these themes

Advanced Web TechnologiesData EngineeringManaging DataLearning from DataSecuritySoftware Engineering

Core in the Semantic Technologies Pathway


Finally. . .

Contacting usIf you are unsure about your theme selection do contact us, either inour offices or send us an email

Renate Schmidt Room 2.42, [email protected] Korovin Room 2.40, [email protected] Knowles Room G13, [email protected]

Up-to-date detailsSee timetable and course unit descriptions on the webSee also separate webpages for individual course units: containadditional material such as slides, links to tools, etc


[email protected]

[email protected]

[email protected]

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