Robert Nowotniak, MScrobert.nowotniak.com/wordpress/wp-content/uploads/2010/11/IWSNDP… · Robert...

1. Artificial Intelligence 2. Quantum Computing 3. Quantum-Inspired Evolutionary Algorithms

QUANTUM-INSPIRED EVOLUTIONARY

ALGORITHMS IN SEARCH AND OPTIMIZATION

Robert Nowotniak, MSc

Supervisor: Prof. Jacek Kucharski

Computer Engineering DepartmentThe Faculty of Electrical, Electronic, Computer and Control Engineering

Technical University of Lodz

Rogow, April 17-19, 2011

Robert Nowotniak Quantum-Inspired Evolutionary Algorithms in Search and Optimization

PRESENTATION OUTLINE

1 Artificial Intelligence2 Quantum Computing3 Quantum-Inspired Evolutionary Algorithms4 Selected Applications and Results

Robert Nowotniak Quantum-Inspired Evolutionary Algorithms in Search and Optimization 1 / 14

PRESENTATION OUTLINE

1 Artificial Intelligence2 Quantum Computing3 Quantum-Inspired Evolutionary Algorithms4 Selected Applications and Results

ARTIFICIAL INTELLIGENCE

Major subfields in Artificial Intelligence:1 Artificial Neural Networks2 Fuzzy Systems3 Evolutionary Computing4 Artificial Immune Systems5 Collective Intelligence6 Machine Learning7 ...

SIMPLE GENETIC ALGORITHM

Solutions to technical problems can be encoded asbinary strings, for example:

1 1 0 1 0 1 0

1 0 0 1 0 0 0

0 0 1 0 1 1 0

1 0 0 0 1 0 1

0 0 1 0 0 0 1

populationof solutions

— chromosome

— binary gene

1 1 0 1 0 1 0

1 0 0 1 0 0 0

0 0 1 0 1 1 0

1 0 0 0 1 0 1

0 0 1 0 0 0 1

— chromosome

— binary gene

1 1 0 1 0 1 0

1 0 0 1 0 0 0

0 0 1 0 1 1 0

1 0 0 0 1 0 1

0 0 1 0 0 0 1

— chromosome

— binary gene

1 1 0 1 0 1 0

1 0 0 1 0 0 0

0 0 1 0 1 1 0

0 0 1 0 0 0 1

1 0 0 0 1 0 1

— chromosome

— binary gene

0 0 0 0 1 0 0

1 0 0 1 0 1 1

1 1 1 0 0 1 0

1 1 0 0 0 1 0

0 0 1 0 1 1 0

— chromosome

— binary gene

0 0 0 0 1 0 1

0 1 1 0 1 1 0

1 0 0 1 1 1 0

1 1 0 1 0 1 1

— chromosome

— binary gene

0 1 0 0 1 0 0

0 0 0 0 1 1 0

0 1 0 1 0 0 1

1 0 0 1 0 0 1

0 1 0 0 0 1 0

— chromosome

— binary gene

1 Representation of solutions

2 Initialization3 Genetic operators4 Evaluation

1 Representation of solutions2 Initialization3 Genetic operators4 Evaluation

1 Representation of solutions

2 Initialization3 Genetic operators4 Evaluation

QUANTUM COMPUTING

Quantum Computing – branch of theoreticalcomputer science dealing with application ofquantum mechanical effects to solvingcomputational problems.

Selected quantum mechanical phenomena:1 quantum entanglement2 superposition of states3 interference4 probability amplitudes5 parallelism

QUANTUM COMPUTING

Quantum Computing – branch of theoreticalcomputer science dealing with application ofquantum mechanical effects to solvingcomputational problems.

Selected quantum mechanical phenomena:1 quantum entanglement2 superposition of states3 interference4 probability amplitudes5 parallelism

CLASSICAL BITS VS QUBITS

Geometrical representation of Qubit on the Bloch sphereRobert Nowotniak Quantum-Inspired Evolutionary Algorithms in Search and Optimization 6 / 14

QUANTUM-INSPIRED EVOLUTIONARY ALGORITHMS

QUBITS AND BINARY QUANTUM GENES

|ψ〉 =√32︸︷︷︸α

|0〉+ 12︸︷︷︸β

|ψ〉

qubit (quantum bit): |ψ〉 = α|0〉+ β|1〉where: α, β ∈ C, |α|2 + |β|2 = 1Pr|ψ〉 : F{0,1} 7→ [0,1]Pr|ψ〉({0}) = |α|2

Pr|ψ〉({1}) = |β|2

|ψ〉 =√22︸︷︷︸α

|0〉+√22︸︷︷︸β

|ψ〉

Pr|ψ〉({1}) = |β|2

|ψ〉 = 13︸︷︷︸α

|0〉+ 2√23︸︷︷︸β

|1〉|ψ〉

Pr|ψ〉({1}) = |β|2

|ψ〉 = 0︸︷︷︸α

|0〉+ 1︸︷︷︸β

|1〉|ψ〉

Pr|ψ〉({1}) = |β|2

SITUATION FOR SIMPLE GENETIC ALGORITHM

1 1 0 1 0 1 0

1 0 0 1 0 0 0

0 0 1 0 1 1 0

1 0 0 0 1 0 1

0 0 1 0 0 0 1

— chromosome

— binary gene

0 0 0 0 1 0 0

1 0 0 1 0 1 1

1 1 1 0 0 1 0

1 1 0 0 0 1 0

0 0 1 0 1 1 0

— chromosome

— binary gene

0 0 0 0 1 0 1

0 1 1 0 1 1 0

1 0 0 1 1 1 0

1 1 0 1 0 1 1

— chromosome

— binary gene

ILLUSTRATION OF QUANTUM POPULATION

quantumpopulation

— quantum chromosome

— quantum gene

quantumpopulation

— quantum gene

quantumpopulation

— quantum gene

Quantum-inspired elements bring a ”new dimension” intoEvolutionary Algorithms.

CURRENT PROBLEMS

1 How to use the ”new dimension” efficiently?2 Theoretical aspects of QIEAs have not been studied with

due attention.3 No general rules and guidelines for constructing QIEAs

have been identified.

CURRENT PROBLEMS

1 How to use the ”new dimension” efficiently?

2 Theoretical aspects of QIEAs have not been studied withdue attention.

3 No general rules and guidelines for constructing QIEAshave been identified.

CURRENT PROBLEMS

due attention.

3 No general rules and guidelines for constructing QIEAshave been identified.

CURRENT PROBLEMS

due attention.3 No general rules and guidelines for constructing QIEAs

have been identified.

THE PH.D. DISSERTATION

Analysis of Quantum-Inpsired Evolutionary Algorithms(to be finished by the end of 2011)

ORIGINAL CONTRIBUTIONS

1 Convergence analysis of Quantum-Inspired EvolutionaryAlgorithms based on Banach’s fixed point theorem

2 Building blocks propagation analysisin Quantum-Inspired Genetic Algorithms[1]

3 Implementation in massively parallel computingenvironment (nVidia CUDATM technology)

4 Tuning QIEAs: meta-optimization[2]

1Nowotniak, R., Kucharski, J.: Building Blocks Propagation in Quantum-InspiredGenetic Algorithm, Scientific Bulletin of Academy of Science and Technology, 2011

2Nowotniak, R., Kucharski, J.: Meta-optimization of Quantum-Inspired EvolutionaryAlgorithm, XVII International Conference on Information Technology Systems, 2010

SELECTED APPLICATIONS

1 Simultaneous Localization andMapping (SLAM) problem for mobilerobots[3]

2 Segmentation of titanium alloysimages obtained with X-Raymicrotomography[4]

3Jezewski, S., Łaski, M., Nowotniak, R.: Comparison of Algorithms forSimultaneous Localization and Mapping Problem for Mobile Robot, Scientific Bulletin ofAcademy of Science and Technology,. Automatics, 2011

4Jopek, Ł., Nowotniak, R., Postolski, M., Babout, L.., Janaszewski, M.: Applicationof Quantum Genetic Algorithms to Feature Selection Problem, Scientific Bulletin ofAcademy of Science and Technology, Automatics, 2010

MY RECENT PAPERS

1 R.Nowotniak, J. Kucharski, Meta-optimization of Quantum-InspiredEvolutionary Algorithm, 2010, Proceedings of the XVII InternationalConference on Information Technology Systems,ISBN 978-83-7283-378-5

2 R.Nowotniak, J. Kucharski, Building Blocks Propagation inQuantum-Inspired Genetic Algorithm, 2010, Scientific Bulletin ofAcademy of Science and Technology, Automatics, 2010,ISSN 1429-3447

3 R. Nowotniak, Survey of Quantum-Inspired Evolutionary Algorithms,2010, Proceedings of the FIMB PhD students conference,ISSN 2082-4831

4 S.Jezewski, M. Łaski, R. Nowotniak, Comparison of Algorithms forSimultaneous Localization and Mapping Problem for Mobile Robot,2010, Scientific Bulletin of Academy of Science and Technology,Automatics, ISSN 1429-3447

5 Ł. Jopek, R. Nowotniak, M. Postolski, L. Babout, M. Janaszewski,Application of Quantum Genetic Algorithms in Feature SelectionProblem, 2009, Scientific Bulletin of Academy of Science andTechnology, Automatics, ISSN 1429-3447

Thank you for your attention

Robert Nowotniak Quantum-Inspired Evolutionary Algorithms in Search and Optimization

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