| 1 Pr | ( { 1 } ) = | | 2 3 | 0 + 1 | = | 1 | 2 2 - PowerPoint PPT Presentation

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary GPU- BASED T UNING OF Q UANTUM -I NSPIRED G ENETIC A LGORITHM FOR A C OMBINATORIAL O PTIMIZATION P ROBLEM Robert Nowotniak, Jacek Kucharski Computer Engineering Department The Faculty of Electrical, Electronic, Computer and Control Engineering Technical University of Lodz XIV INTERNATIONAL CONFERENCE SYSTEM MODELLING and CONTROL June 27-29, 2011 Ł´ od´ z Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 1 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary P RESENTATION O UTLINE 1 Q UANTUM -I NSPIRED G ENETIC A LGORITHMS 2 NV IDIA CUDA TM TECHNOLOGY 3 T UNING – E XPERIMENTAL R ESULTS 4 S UMMARY Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary P RESENTATION O UTLINE 1 Q UANTUM -I NSPIRED G ENETIC A LGORITHMS 2 NV IDIA CUDA TM TECHNOLOGY 3 T UNING – E XPERIMENTAL R ESULTS 4 S UMMARY Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UANTUM -I NSPIRED G ENETIC A LGORITHMS Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 2 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UANTUM -I NSPIRED G ENETIC A LGORITHMS Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 2 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UANTUM E LEMENTS IN E VOLUTIONARY A LGORITHMS 1 Representation of solutions Instead of exact points in a search space, probability distributions of sampling the space 2 Initialization 3 Genetic operators 4 Evaluation Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 3 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UANTUM E LEMENTS IN E VOLUTIONARY A LGORITHMS 1 Representation of solutions (bits → qubits) Instead of exact points in a search space, probability distributions of sampling the space 2 Initialization 3 Genetic operators 4 Evaluation Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 3 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UANTUM E LEMENTS IN E VOLUTIONARY A LGORITHMS 1 Representation of solutions (bits → qubits) Instead of exact points in a search space, probability distributions of sampling the space 2 Initialization 3 Genetic operators 4 Evaluation Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 3 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary C LASSICAL B ITS VS Q UBITS Geometrical representation of Qubit on the Bloch sphere Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 4 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary C LASSICAL B ITS VS Q UBITS Geometrical representation of Qubit on the Bloch sphere Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 4 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary C LASSICAL B ITS VS Q UBITS Geometrical representation of Qubit on the Bloch sphere Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 4 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UBITS AND B INARY Q UANTUM G ENES 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, Jacek Kucharski System Modelling and Control, 2011 5 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UBITS AND B INARY Q UANTUM G ENES 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, Jacek Kucharski System Modelling and Control, 2011 5 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UBITS AND B INARY Q UANTUM G ENES 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, Jacek Kucharski System Modelling and Control, 2011 5 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary Q UBITS AND B INARY Q UANTUM G ENES 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, Jacek Kucharski System Modelling and Control, 2011 5 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary S IMPLE G ENETIC A LGORITHM In Simple Genetic Algorithm , solutions to technical problems are encoded as binary strings, for example:  — binary gene  1 1 0 1 0 1 0       1 0 0 1 0 0 0 — chromosome     population 0 0 1 0 1 1 0 of solutions     1 0 0 0 1 0 1       0 0 1 0 0 0 1  Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 6 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary S IMPLE G ENETIC A LGORITHM In Simple Genetic Algorithm , solutions to technical problems are encoded as binary strings, for example:  — binary gene  1 1 0 1 0 1 0       1 0 0 1 0 0 0 — chromosome     population 0 0 1 0 1 1 0 of solutions     1 0 0 0 1 0 1       0 0 1 0 0 0 1  Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 6 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary S IMPLE G ENETIC A LGORITHM In Simple Genetic Algorithm , solutions to technical problems are encoded as binary strings, for example:  — binary gene  1 1 0 1 0 1 0       1 0 0 1 0 0 0 — chromosome     population 0 0 1 0 1 1 0 of solutions     1 0 0 0 1 0 1       0 0 1 0 0 0 1  Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 6 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary S IMPLE G ENETIC A LGORITHM In Simple Genetic Algorithm , solutions to technical problems are encoded as binary strings, for example:  — binary gene  1 1 0 1 0 1 0       1 0 0 1 0 0 0 — chromosome     population 0 0 1 0 1 1 0 of solutions     0 0 1 0 0 0 1       1 0 0 0 1 0 1  Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 6 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary S IMPLE G ENETIC A LGORITHM In Simple Genetic Algorithm , solutions to technical problems are encoded as binary strings, for example:  — binary gene  0 0 0 0 1 0 0       1 0 0 1 0 1 1 — chromosome     population 1 1 1 0 0 1 0 of solutions     1 1 0 0 0 1 0       0 0 1 0 1 1 0  Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 6 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary S IMPLE G ENETIC A LGORITHM In Simple Genetic Algorithm , solutions to technical problems are encoded as binary strings, for example:  — binary gene  0 0 0 0 1 0 1       0 1 1 0 1 1 0 — chromosome     population 1 0 0 1 1 1 0 of solutions     1 1 0 1 0 1 1       1 1 0 1 0 1 1  Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 6 / 19

2. NVidia CUDA TM 1. Quantum-Inspired Genetic Algorithms 3. Experimental Results 4. Summary S IMPLE G ENETIC A LGORITHM In Simple Genetic Algorithm , solutions to technical problems are encoded as binary strings, for example:  — binary gene  0 1 0 0 1 0 0       0 0 0 0 1 1 0 — chromosome     population 0 1 0 1 0 0 1 of solutions     1 0 0 1 0 0 1       0 1 0 0 0 1 0  Robert Nowotniak, Jacek Kucharski System Modelling and Control, 2011 6 / 19