Mixed Integer Quadratic Programming Calculation System
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Solution Overview
Problem
Current techniques are inefficient in solving mixed binary quadratic programming problems, particularly in finding the ground state of the Ising model at high speeds, which is crucial for applications like social network analysis and financial portfolio optimization.
Innovation Solution
A calculation system comprising a variable memory, state transition calculation block, nonlinear coefficient memory, linear coefficient memory, weight input line, and temperature input line, which performs random sampling and next state determination using difference calculations to efficiently solve mixed binary quadratic programming problems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional methods are used to solve mixed binary quadratic programming problems, then the problems can be solved, but the calculation speed is slow and convergence to optimal solutions is inefficient
Solution Approach 1:
The patent divides the calculation system into distinct functional blocks: a difference calculation block that computes energy differences, a sampling block that performs stochastic sampling, and a next state determination block that updates variable states. This segmentation allows each block to be optimized independently and enables parallel processing, significantly improving calculation speed for mixed binary quadratic programming problems.
Solution Approach 2:
The patent implements dynamic temperature scheduling where the temperature parameter is adjusted during the optimization process to control the sampling probability distribution. The system transitions from high-temperature stochastic sampling that explores the solution space to low-temperature sampling that converges to optimal solutions, enabling efficient convergence while maintaining calculation speed.
2Productivity
If the number of variables in mixed binary quadratic programming problems is reduced, then calculation efficiency improves, but the ability to represent complex optimization problems decreases
Solution Approach 1:
The patent transforms mixed binary quadratic programming variables into a unified representation suitable for the Ising model and quantum annealing. By changing the parameter representation of variables and using auxiliary variables with constraint equations, the system maintains the ability to represent complex optimization problems while improving calculation efficiency through standardized processing.
Solution Approach 2:
The patent introduces auxiliary variables and constraint equations as intermediaries to represent complex optimization problems. These intermediary elements enable the transformation of general mixed binary quadratic programming problems into a form suitable for quantum annealing and simulated annealing, preserving problem representation capability while enhancing calculation efficiency.
Data Source
AI summary
A calculation system includes a variable memory storing a value indicating a state of a variable of a mixed integer quadratic programming problem; a state transition calculation block that calculates the next state of the value indicating the state of the variable; a nonlinear coefficient memory that stores a nonlinear coefficient of the state transition calculation block; a linear coefficient memory that stores a linear coefficient of the state transition calculation block; a weight input line that receives a weight signal of the state transition calculation block; and a temperature input line that receives a temperature signal of the state transition calculation block. The state transition calculation block includes a difference calculation block that calculates a difference calculation by using the weight signal, the nonlinear coefficient, and the linear coefficient. A next state determination block calculates the next state of the variable using the value read from the variable memory.