Optimization Device Using Inner Product Maximization for Fast Pseudo-Optimal Solutions
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Solution Overview
Problem
Existing algorithms for solving optimization problems, such as the interior point method, simplex method, cutting plane method, branch-and-bound method, and branch-and-cut method, require significant computational resources and are not suitable for deriving a pseudo-optimal solution quickly.
Innovation Solution
An optimization device, method, and program that accepts input of multiple candidate solutions to an optimization problem with an objective function expressed as an inner product of features and weights, or in a bilinear form, and determines the candidate solution that maximizes the inner product or bilinear form with the weight of the objective function as a pseudo-optimal solution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing optimization algorithms (interior point method, simplex method, etc.) are used to solve optimization problems, then the solution accuracy is improved, but the computation time increases significantly
Solution Approach 1:
The patent applies partial action by computing only the necessary components for pseudo-optimal solutions rather than performing complete optimization. The system calculates inner products of feature vectors and weight vectors to identify candidate solutions without executing full optimization algorithms, thereby achieving acceptable solutions with reduced computation time.
Solution Approach 2:
The patent uses inexpensive computational operations (inner product calculations) that can be performed rapidly and discarded, rather than relying on expensive, time-consuming optimization algorithms. Multiple candidate solutions are evaluated using simple inner product computations to quickly identify pseudo-optimal solutions.
2Measurement precision
If interior point method is used for large-scale calculations, then the solution quality is improved, but the computation speed decreases due to cubic complexity
Solution Approach 1:
The patent substitutes the mechanical optimization process (iterative algorithms moving through solution space) with a direct computational approach using inner products. Instead of mechanically iterating through optimization steps with cubic complexity, the system directly computes scores for candidate solutions using vector inner products, achieving linear complexity.
3Measurement precision
If exact optimal solution is pursued using traditional algorithms, then the solution precision is improved, but the computational complexity increases enormously
Solution Approach 1:
The patent extracts the essential evaluation criterion from complex optimization algorithms - the inner product of feature and weight vectors. By taking out only the necessary computational element (inner product calculation) and discarding the complex iterative optimization process, the system achieves pseudo-optimal solutions with dramatically reduced computational complexity.
Data Source
AI summary
An AI (Artificial Intelligence) system comprising: the input means 81 accepts input of multiple candidate solutions to an optimization problem in which an objective function is express as an inner product of a feature and weight, or expressed in a bilinear form, and weight of the objective function; the optimal solution determination means 82 determines as an optimal solution, among the candidate solutions, the candidate solution that maximizes the inner product with the weight of the objective function or the candidate solution that maximizes a value of the bilinear form; and the output means 83 outputs the optimal solution.