Combinatorial Optimization Using Evolutionary Algorithm and QUBO Conversion
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Solution Overview
Problem
Existing methods for expressing combinatorial optimization problems, including array searches, in the QUBO format lead to increased calculation costs due to the need to search all possible combinations and formulate constraints, which reduces flexibility and increases problem scale.
Innovation Solution
The proposed solution involves using an evolutionary algorithm to optimize order information for a combinatorial optimization process that includes an array search, converting this information into a QUBO format, and performing combinatorial optimization using an Ising machine, thereby separating the optimization problem into order optimization and combinatorial optimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If combinatorial optimization problems including array searches are expressed in QUBO format, then the problem can be solved using standard optimization methods, but the calculation cost increases and the problem scale expands
Solution Approach 1:
The patent segments the combinatorial optimization problem into two distinct parts: array search (handled by evolutionary algorithms) and combination search (handled by QUBO formulation). This segmentation allows each part to be optimized independently, reducing the overall problem scale that needs to be expressed in QUBO format while maintaining solution quality.
Solution Approach 2:
The patent extracts the array search component from the combinatorial optimization problem and handles it separately using evolutionary algorithms. This extraction removes the array search portion from the QUBO formulation, thereby reducing the problem scale and calculation cost associated with expressing the entire problem in QUBO format.
2Reliability
If all possible combinations are searched in QUBO format, then complete optimization is achieved, but the calculation cost increases
Solution Approach 1:
The patent divides the search space into two segments: array configurations (explored via evolutionary algorithms with evaluation at each generation) and combinations (explored via QUBO optimization). This segmentation allows the system to achieve complete optimization by searching both segments, while reducing calculation cost by handling each segment with appropriately optimized methods rather than exhaustively searching all possible combinations in QUBO format.
Solution Approach 2:
The patent performs preliminary action by using evolutionary algorithms to evaluate individuals and update evaluation values as generations progress. This preliminary evaluation identifies promising solutions before the final QUBO optimization, reducing the need to exhaustively search all combinations while maintaining optimization completeness.
3Adaptability or versatility
If array search is included in QUBO formulation, then the problem is fully captured, but the time and effort for formulation increases
Solution Approach 1:
The patent extracts the array search component from the QUBO formulation and handles it separately using evolutionary algorithms. This extraction significantly reduces the formulation time and effort required for QUBO while maintaining full problem coverage, as the evolutionary algorithms naturally handle array search without requiring explicit QUBO constraints.
Solution Approach 2:
The patent segments the problem into array search (handled by evolutionary algorithms) and combination search (handled by QUBO). This segmentation allows each segment to be formulated with appropriate methods, reducing the overall formulation time while maintaining adaptability and versatility of the approach.
Data Source
AI summary
A non-transitory computer-readable storage medium storing an arithmetic operation program that causes at least one computer to execute a process, the process includes searching for first order information such that an evaluation value is updated as a generation progresses by using an evolutionary algorithm for a first individual that is a target of a combinatorial optimization process which includes an array search, the individual including the first order information; generating a first array by using the first order information; converting the first array into a QUBO format; and searching for a combination by using the converted first array.