Simulated Bifurcation Algorithm for Combinatorial Optimization
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Solution Overview
Problem
Combinatorial optimization problems are challenging due to the 'combinatorial explosion' issue, where the number of combinations increases exponentially, making it difficult to calculate optimal or approximate solutions within a practical time in various fields like finance, logistics, and life science.
Innovation Solution
An information processing system and method that uses a simulated bifurcation algorithm, updating first and second vectors based on weighted coefficients, incorporating constraint terms, and increasing coefficient values, to solve combinatorial optimization problems efficiently by parallel processing and distributed computing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional combinatorial optimization methods are used, then solution accuracy can be maintained, but calculation time becomes impractically long due to combinatorial explosion
Solution Approach 1:
The patent transforms the combinatorial optimization problem into a continuous optimization problem by changing the parameter space from discrete combinations to continuous variables. This allows the use of gradient-based optimization methods that can efficiently navigate the solution space without enumerating all possible combinations, thereby reducing calculation time while maintaining solution accuracy through the mathematical equivalence of the transformed problem.
2Adaptability or versatility
If the problem size increases, then more comprehensive solutions can be found, but the number of combinations increases exponentially making calculation infeasible
Solution Approach 1:
The patent replaces the mechanical enumeration approach (systematically checking each combination) with a mathematical transformation approach. By converting discrete combinatorial variables into continuous variables and using analytical optimization methods, the system achieves polynomial-time complexity instead of exponential-time complexity, enabling scalable solutions for large problem sizes.
3Reliability
If exhaustive search methods are used to ensure optimal solutions, then solution quality is guaranteed, but computational resources are exhausted
Solution Approach 1:
The patent changes the problem parameters from discrete to continuous domain, enabling the use of efficient gradient-based optimization algorithms. This transformation maintains solution optimality by preserving the mathematical structure of the original problem while allowing the optimizer to converge to the global optimum without exhaustive search, thereby dramatically reducing computational resource consumption.
Data Source
AI summary
An information processing device includes a storage unit and a processing circuit. The storage unit is configured to store a first variable and a second variable. The processing circuit is configured to update the first variable based on the second variable, which corresponds to the first variable, weight the first variable with a first coefficient and add the weighted first variable to the corresponding second variable, calculate a problem term using the plurality of first variables, add the problem term to the second variable, calculate a first correction term including a product of a constraint term and a second coefficient, add the first correction term to the second variable, and increase absolute values of the first coefficient and the second coefficient depending on the number of updates. The constraint term is based on a constraint condition and has the first variable as an argument.