Discrete Optimization Decomposition via Variable Fixing
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Solution Overview
Problem
Large-scale discrete optimization problems are often NP-hard, making it impractical to find optimal solutions due to exponential time growth, necessitating the use of heuristic methods that sacrifice optimality for efficiency.
Innovation Solution
A method that preprocesses discrete optimization problems by converting them into subproblems using an optimization oracle, such as a quantum annealer, by fixing variables based on sub-optimal or near-optimal solutions, allowing the decomposition of problems into smaller, solvable subproblems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If heuristic methods are used to solve large-scale discrete optimization problems, then computational efficiency is improved, but solution optimality deteriorates
Solution Approach 1:
The patent applies segmentation by decomposing a large-scale discrete optimization problem into multiple smaller subproblems through variable fixing. By identifying variables that remain constant across multiple near-optimal solutions and fixing them, the original problem is divided into smaller subproblems that can be solved more efficiently while maintaining solution quality.
2Adaptability or versatility
If the size of discrete optimization problems increases, then the practical applicability is improved, but the time needed to find optimal solutions worsens due to exponential growth
Solution Approach 1:
The patent applies preliminary action by performing variable fixing based on analysis of near-optimal solutions before solving the main optimization problem. By pre-identifying and fixing variables that are likely to remain constant, the system reduces the problem size in advance, enabling practical application to larger problems without incurring exponential time costs.
Data Source
AI summary
A method is disclosed for preprocessing a problem involving discrete optimization over a plurality of variables, the method comprising obtaining an indication of a problem involving discrete optimization; converting the problem involving discrete optimization into a problem suitable for a given optimization oracle architecture of an optimization oracle; providing a given number of times M the problem suitable for the given optimization oracle architecture to the optimization oracle; for each providing of the problem, performing a given number K of calls to the optimization oracle; each call generating a given configuration; obtaining a variable selection criterion, the variable selection criterion for determining at least one variable of the plurality of generated configurations that can be fixed; determining at least one variable that matches the variable selection criterion and a corresponding value for each variable; fixing the at least one determined variable at the corresponding value in the problem involving discrete optimization to thereby preprocess the problem to generate at least one subproblem and providing an indication of the at least one generated subproblem and an indication of the at least one fixed variable.