Local Global Search for Combinatorial Optimization
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Solution Overview
Problem
Current local search algorithms for large scale combinatorial optimization problems are limited by their small window sizes, which restrict the solution space and require exponentially increased computational resources, making it difficult to find feasible solutions that satisfy constraints efficiently.
Innovation Solution
The proposed method, Local Global Search, uses a Quadratic Unconstrained Binary Optimization (QUBO) solver to iteratively cluster nodes into larger windows, allowing for the exploration of an exponentially larger solution space with the same quantum hardware, and provides adjustable parameters to control resource usage, enabling easier constraint satisfaction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If larger window sizes are used in local search algorithms, then the solution space coverage is improved, but the computational resources required increase exponentially
Solution Approach 1:
The patent divides the large-scale combinatorial optimization problem into multiple smaller sub-problems by partitioning the solution space into clusters or groups. Each quantum processor handles a subset of variables, allowing the overall problem to be solved through coordinated local searches across multiple segments rather than requiring a single processor to handle the entire problem space.
Solution Approach 2:
The patent implements a hierarchical structure where quantum processors operate at multiple levels of abstraction. Local search operations are nested within broader optimization frameworks, with quantum processors performing detailed local searches that are coordinated at higher levels. This nested approach allows exponential solution space coverage through compositional integration of multiple quantum processors rather than requiring a single exponentially larger processor.
2Quantity of substance
If quantum local search methods are used to solve larger problems, then the problem size that can be solved is improved, but the hardware requirements increase
Solution Approach 1:
The patent combines multiple quantum processors to work collectively on a single large-scale optimization problem. By merging the computational capabilities of multiple processors and coordinating their local search operations, the system can solve problems larger than any single processor could handle independently, achieving scalable problem size growth without requiring a single exponentially larger hardware unit.
Solution Approach 2:
The patent designs a universal quantum processing framework that can handle various types of combinatorial optimization problems using the same underlying architecture. The system employs standardized interfaces and coordination mechanisms that allow different quantum processors to work together on diverse problem types, reducing the need for specialized hardware configurations for each problem size or type.
3Device complexity
If standard local search algorithms are used with limited window sizes, then the computational resources required are reduced, but the solution space explored is limited
Solution Approach 1:
The patent implements feedback mechanisms where quantum processors exchange information about their local search results and coordinate their operations. This feedback allows the system to guide the exploration of the solution space more effectively, with processors adjusting their search strategies based on information from other processors, thereby achieving broader solution space coverage without requiring each processor to independently explore the entire space.
Data Source
AI summary
A method of solving a large scale combinatorial optimization problem including inputting, via at least one processor, an objective function and an initial solution as a mapping from a plurality of n nodes, randomly clustering the plurality of nodes into k clusters of n/k nodes each, for each cluster of the k clusters, assigning binary variables to denote each possible permutation of a label set within the cluster, determining that there are u=k2 variables if k>2, and u=1 variables if k=2, expressing the objective function in terms of the un/k variables, solving the objective function in terms of the un/k variables using a Quadratic Unconstrained Binary Optimization (QUBO) solver to obtain an updated solution, determining whether a convergence criteria is satisfied for the updated solution, and upon a determination that a convergence criteria is satisfied, outputting the updated solution to the objective function.