Permutation Optimization Using Redundant State Variables
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Solution Overview
Problem
Existing methods for solving permutation optimization problems with 2-Way 1-Hot constraints face challenges in efficiently escaping local solutions and finding optimal permutations due to limited state transitions, particularly when only changing values of up to four state variables at a time.
Innovation Solution
The introduction of redundant elements into the permutation optimization problem allows for the generation of an energy function with additional state variables, enabling more extensive state transitions and increasing the number of candidate solutions by transforming the problem into one with N2 state variables, where N is greater than M, thereby avoiding local solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If redundant elements are added to the permutation optimization problem, then the number of candidate solutions and state transitions increase, but the problem size and computational complexity increase
Solution Approach 1:
The patent introduces redundant elements as intermediary components that facilitate state transitions in the permutation optimization problem. These redundant elements act as mediators that enable multi-bit transitions by providing additional state variables, thereby increasing the number of candidate solutions without directly modifying the core problem structure. The redundant elements can be systematically removed or mapped back to the original problem after optimization.
2Reliability
If the search unit changes values of four state variables at a time, then local constraints are satisfied, but the ability to escape local solutions is limited
Solution Approach 1:
The patent extends the search space by adding redundant elements that create additional dimensions in the state variable space. This dimensionality expansion allows the search unit to perform multi-bit transitions that effectively explore the solution landscape more efficiently. By operating in this expanded N-dimensional space (where N > M), the system can escape local solutions while still satisfying the original 2-Way 1-Hot constraints when projected back to the M-dimensional problem space.
Data Source
AI summary
An apparatus of acquiring a solution to a permutation optimization problem represented by an energy function of an Ising model, the apparatus being configured to perform processing including: obtaining problem information which indicates M2 state variables (M is an integer equal to or more than 3) in the permutation optimization problem; generating information on a first energy function which includes N2 state variables obtained by adding (N2−M2) state variables (N is an integer more than M) to the M2 state variables, based on the problem information; inputting the information on the first energy function to a search unit; obtaining, from the search unit based on the first energy function, a first solution represented by values of the N2 state variables; and generating a second solution to the permutation optimization problem by removing values of the (N2−M2) state variables from the first solution.