Optimization

• Number Partitioning
  • Overview of the Number Partitioning Problem
    • Example
  • Mathematical Model
  • Modeling by JijModeling
  • Instance
    • Conversion to PyQUBO by JijModeling Transpiler
    • Optimization by OpenJij
    • Decoding and Displaying the Solution
• Knapsack Problem
  • Overview of the Knapsack Problem
    • Example
    • Generalizing the Problem
  • Modeling by JijModeling
    • Variables
    • Objective Function
    • Constraint
    • Instance
    • Undetermined Multiplier
    • Conversion to PyQUBO by JijModeling Transpiler
    • Optimization by OpenJij
    • Decoding and Displaying the Solution
• Graph Coloring Problem
  • Overview of the Graph Coloring Problem
    • Example
    • Generalizing the Problem
      • Constraint
      • Objective Function
  • Modeling by JijModeling
    • Variables
    • Constraint
    • Objective Function
    • Instance
    • Undetermined Multiplier
    • Conversion to PyQUBO by JijModeling Transpiler
    • Optimization by OpenJij
    • Decoding and Displaying the Solution
• Clique Cover Problem
  • Overview of the Clique Cover Problem
    • Complete Graph
    • Binary Variable
    • Constraint
    • Objective Function
  • Modeling by JijModeling
    • Variables
    • Constraints
    • Objective Function
    • Instance
    • Undetermined Multiplier
    • Conversion to PyQUBO by JijModeling Transpiler
    • Optimization by OpenJij
    • Decoding and Displaying the Solution
• Job Sequencing Problem with Integer Lengths
  • Overview of the Job Sequencing Problem with Integer Lengths
    • Example
    • Mathematical Model
      • Constraint
      • Objective Function
  • Modeling by JijModeling
    • Constraint
    • Objective Function
    • Instance
    • Undefined Multiplier
    • Conversion to PyQUBO by JijModeling Transpiler
    • Optimization by OpenJij
    • Decoding and Displaying the Solution
• Protein Folding Problem
  • Typical Models
    • HP Model
    • MJ Model
  • Solution Overview
    • 1. Bit Representation of Lattice Folding
    • 2. Cost Function Formulation
    • 3. Direct Solving with HUBO
    • 4. Comparison of the Results: the Direct HUBO Solving and the Reference Paper [1]
  • References
• Portfolio Optimization using Reverse Quantum Annealing
  • Introduction
  • Portfolio Optimization
    • Sharpe Ratio
    • Portfolio Evaluation and Optimization
  • Portfolio Optimization with Reverse Quantum Annealing
    • Reverse Quantum Annealing
    • Portfolio Optimization Procedure with Reverse Quantum Annealing
  • Generation of stock data and implementation of classical algorithms
    • Generation of stock data to be optimized
    • Search with Classical Algorithms
      • Greedy Method
      • Genetic Algorithm
  • Implementation of quantum annealing method using OpenJij
    • Method for quantum annealing
      • For forward annealing
      • For reverse quantum annealing
    • Checking reverse quantum annealing
    • Parameter search for specifying RQA schedule
      • In reverse phase
      • For pause phase
      • For forward phase
  • Concluding remarks
  • Appendix A: if the simulation results are not good…
  • Appendix B: Executing RQA on the D-Wave machine
  • References