Ising Model Permutation Optimization via Redundant State Variables
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Solution Overview
Problem
Existing methods for solving combinatorial optimization problems with 2-Way 1-Hot constraints, such as permutation optimization, often get stuck in local solutions due to limited changes in state variables, hindering the escape from suboptimal states.
Innovation Solution
An information processing apparatus that employs a dual process approach, fixing and non-fixing the value of state variables in specific rows and columns, allowing changes in four state variables to satisfy the 2-Way 1-Hot constraint, and using redundant elements to facilitate state transitions and escape local solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the values of state variables are changed to satisfy the 2-Way 1-Hot constraint, then the constraint is maintained, but the ability to escape local solutions is limited
Solution Approach 1:
The patent dynamically adjusts the constraint satisfaction level by introducing a constraint violation parameter that allows temporary relaxation of the 2-Way 1-Hot constraint. This enables the system to transition from a rigid constraint-following mode to a more flexible exploration mode, allowing state variables to change beyond traditional constraint boundaries while still maintaining solution validity through controlled violation and recovery mechanisms.
Solution Approach 2:
The patent changes the parameter representation by introducing redundant elements and modifying how state variables are encoded. Instead of directly representing permutations with N elements, the system uses N+1 elements where one element is redundant, allowing additional degrees of freedom in state transitions while maintaining the underlying permutation structure through controlled transformations.
2Adaptability or versatility
If redundant elements are introduced to facilitate state transitions, then the ability to escape local optima improves, but the complexity of the system increases
Solution Approach 1:
The patent extracts the constraint satisfaction logic into a separate mechanism that operates independently from the state transition process. By separating the concern of maintaining 2-Way 1-Hot constraints from the exploration of state space, the system can use redundant elements for exploration while a dedicated constraint management layer ensures validity, reducing the apparent complexity in the main transition logic.
Solution Approach 2:
The redundant element acts as an intermediary that mediates between the need for flexible state transitions and the requirement for constraint satisfaction. This intermediate element absorbs the complexity of coordinate transformations, allowing seamless transitions between different state representations while maintaining constraint validity through controlled interactions with the redundant element.
3Adaptability or versatility
If the value range of coefficients in the Ising model is extended to arbitrary values, then the problem representation flexibility improves, but the difficulty of finding ground state increases
Solution Approach 1:
The patent performs preliminary transformations on the energy function and coefficient values before initiating the ground state search. By pre-processing the problem representation to normalize coefficient ranges and transform the energy landscape, the system prepares the search space to be more amenable to exploration, reducing the effective difficulty of finding ground states while maintaining the ability to represent arbitrary optimization problems.
Data Source
AI summary
An information processing apparatus configured to: store N2 state variables included in an energy function of an Ising model, values of the N2 state variables being determined based on a constraint that the N2 state variables are arranged in N rows and N columns, and search for a solution to a permutation optimization problem by switching fixing and non-fixing a value of a state variable of a K-th row and an L-th column in N rows and N columns to 1; and repeating changing values of four state variables of the N2 state variables in accordance with a change amount of a value of the energy function when the values of the four state variables are changed to satisfy the constraint.