Survey of Quantum-Inspired Evolutionary Algorithms Survey of Quantum-Inspired Evolutionary Algorithms Robert Nowotniak, MSc Supervisor: Jacek Kucharski, MSc, PhD, DSc Computer Engineering Department Technical University of Lodz � L´ od´ z, October 20, 2010 Robert Nowotniak L´ � od´ z, October 20, 2010
Survey of Quantum-Inspired Evolutionary Algorithms Outline 1 Background Information and Scope of Research 2 Quantum + Evolutionary Computing 3 Quantum Elements in Evolutionary Algorithms 4 Current problems 5 My Contributions 6 Preliminary Results and Selected Applications Robert Nowotniak L´ � od´ z, October 20, 2010 1 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum Computing Quantum Computing – branch of theoretical computer science dealing with application of quantum mechanical effects to solving computational problems. Robert Nowotniak L´ � od´ z, October 20, 2010 2 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum + Evolutionary Computing Possible interplay between quantum and evolutionary computing: 1 Evolutionary-Designed Quantum Algorithms Automatic synthesis of quantum algorithms 2 Quantum-Inspired Evolutionary Algorithms (QIEAs) Modification of existing EA algorithms by application of quantum- inspired concepts and principles 3 ,,True” Quantum Evolutionary Algorithms Ultimately, implementation of the algorithms in a ”true” quantum level hardware is the biggest challenge for the future Robert Nowotniak L´ � od´ z, October 20, 2010 3 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum + Evolutionary Computing Possible interplay between quantum and evolutionary computing: 1 Evolutionary-Designed Quantum Algorithms Automatic synthesis of quantum algorithms 2 Quantum-Inspired Evolutionary Algorithms (QIEAs) Modification of existing EA algorithms by application of quantum- inspired concepts and principles 3 ,,True” Quantum Evolutionary Algorithms Ultimately, implementation of the algorithms in a ”true” quantum level hardware is the biggest challenge for the future Robert Nowotniak L´ � od´ z, October 20, 2010 3 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum + Evolutionary Computing Possible interplay between quantum and evolutionary computing: 1 Evolutionary-Designed Quantum Algorithms Automatic synthesis of quantum algorithms 2 Quantum-Inspired Evolutionary Algorithms (QIEAs) Modification of existing EA algorithms by application of quantum- inspired concepts and principles 3 ,,True” Quantum Evolutionary Algorithms Ultimately, implementation of the algorithms in a ”true” quantum level hardware is the biggest challenge for the future Robert Nowotniak L´ � od´ z, October 20, 2010 3 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum + Evolutionary Computing Possible interplay between quantum and evolutionary computing: 1 Evolutionary-Designed Quantum Algorithms Automatic synthesis of quantum algorithms 2 Quantum-Inspired Evolutionary Algorithms (QIEAs) Modification of existing EA algorithms by application of quantum-inspired concepts and principles 3 ,,True” Quantum Evolutionary Algorithms Ultimately, implementation of the algorithms in a ”true” quantum level hardware is the biggest challenge for the future Robert Nowotniak L´ � od´ z, October 20, 2010 3 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum + Evolutionary Computing Possible interplay between quantum and evolutionary computing: 1 Evolutionary-Designed Quantum Algorithms Automatic synthesis of quantum algorithms 2 Quantum-Inspired Evolutionary Algorithms (QIEAs) Modification of existing EA algorithms by application of quantum-inspired concepts and principles 3 ,,True” Quantum Evolutionary Algorithms Ultimately, implementation of the algorithms in a ”true” quantum level hardware is the biggest challenge for the future Robert Nowotniak L´ � od´ z, October 20, 2010 3 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Scope of Research Robert Nowotniak L´ � od´ z, October 20, 2010 4 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Scope of Research Robert Nowotniak L´ � od´ z, October 20, 2010 4 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Scope of Research Robert Nowotniak L´ � od´ z, October 20, 2010 4 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Literature Review 1 First suggestion: (Narayanan, 1996) 2 First early studies: (Han and Kim, 2000) 3 Currently, over 160 papers Quantum binary coding: about 130 papers Quantum real coding: 12 papers Applications: 79 Theoretical analysis: 5 papers Surveys: 2 papers Robert Nowotniak L´ � od´ z, October 20, 2010 5 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Literature Review 1 First suggestion: (Narayanan, 1996) 2 First early studies: (Han and Kim, 2000) 3 Currently, over 160 papers Quantum binary coding: about 130 papers Quantum real coding: 12 papers Applications: 79 Theoretical analysis: 5 papers Surveys: 2 papers Robert Nowotniak L´ � od´ z, October 20, 2010 5 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Literature Review 1 First suggestion: (Narayanan, 1996) 2 First early studies: (Han and Kim, 2000) 3 Currently, over 160 papers Quantum binary coding: about 130 papers Quantum real coding: 12 papers Applications: 79 Theoretical analysis: 5 papers Surveys: 2 papers Robert Nowotniak L´ � od´ z, October 20, 2010 5 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Annual Distribution of Papers on QIEAs 40 35 30 Papers on QIEAs 25 Real-Coded QiEA 20 (Han and Kim, 2000) 15 (Narayanan, 1996) 10 5 0 6 0 1 2 3 4 5 6 7 8 9 9 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2 2 2 2 Year Robert Nowotniak L´ � od´ z, October 20, 2010 6 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum Elements in Evolutionary Algorithms 1 Representation of solutions Instead of exact points in a search space, probability distributions of sampling the space 2 Initialization 3 Genetic operators 4 Fitness evaluation Robert Nowotniak L´ � od´ z, October 20, 2010 7 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum Elements in Evolutionary Algorithms 1 Representation of solutions Instead of exact points in a search space, probability distributions of sampling the space 2 Initialization 3 Genetic operators 4 Fitness evaluation Robert Nowotniak L´ � od´ z, October 20, 2010 7 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Quantum Elements in Evolutionary Algorithms 1 Representation of solutions Instead of exact points in a search space, probability distributions of sampling the space 2 Initialization 3 Genetic operators 4 Fitness evaluation Robert Nowotniak L´ � od´ z, October 20, 2010 7 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Qubits and Binary Quantum Genes Robert Nowotniak L´ � od´ z, October 20, 2010 8 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Qubits and Binary Quantum Genes qubit (quantum bit): | ψ � = α | 0 � + β | 1 � where: α, β ∈ C , | α | 2 + | β | 2 = 1 Pr | ψ � : F { 0 , 1 } �→ [0 , 1] Pr | ψ � ( { 0 } ) = | α | 2 | 1 � Pr | ψ � ( { 1 } ) = | β | 2 √ 3 | 0 � + 1 | ψ � = | 1 � | ψ � 2 2 ���� ���� β α | 0 � β α Robert Nowotniak L´ � od´ z, October 20, 2010 8 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Qubits and Binary Quantum Genes qubit (quantum bit): | ψ � = α | 0 � + β | 1 � where: α, β ∈ C , | α | 2 + | β | 2 = 1 Pr | ψ � : F { 0 , 1 } �→ [0 , 1] Pr | ψ � ( { 0 } ) = | α | 2 | 1 � Pr | ψ � ( { 1 } ) = | β | 2 √ √ | ψ � 2 2 | ψ � = | 0 � + | 1 � 2 2 β ���� ���� α | 0 � β α Robert Nowotniak L´ � od´ z, October 20, 2010 8 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Qubits and Binary Quantum Genes qubit (quantum bit): | ψ � = α | 0 � + β | 1 � where: α, β ∈ C , | α | 2 + | β | 2 = 1 Pr | ψ � : F { 0 , 1 } �→ [0 , 1] Pr | ψ � ( { 0 } ) = | α | 2 | 1 � Pr | ψ � ( { 1 } ) = | β | 2 | ψ � √ 1 | 0 � + 2 2 | ψ � = | 1 � β 3 3 ���� � �� � α | 0 � β α Robert Nowotniak L´ � od´ z, October 20, 2010 8 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Qubits and Binary Quantum Genes qubit (quantum bit): | ψ � = α | 0 � + β | 1 � where: α, β ∈ C , | α | 2 + | β | 2 = 1 Pr | ψ � : F { 0 , 1 } �→ [0 , 1] Pr | ψ � ( { 0 } ) = | α | 2 | 1 � Pr | ψ � ( { 1 } ) = | β | 2 | ψ � | ψ � = | 0 � + 1 | 1 � 0 β ���� ���� α β | 0 � α Robert Nowotniak L´ � od´ z, October 20, 2010 8 / 15
Survey of Quantum-Inspired Evolutionary Algorithms Situation for Simple Genetic Algorithm 1 1 0 1 0 1 0 — binary gene 1 0 0 1 0 0 0 — chromosome population 0 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 Robert Nowotniak L´ � od´ z, October 20, 2010 9 / 15
Recommend
More recommend
