Optimal Solution Determination in Combinatorial Optimization
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Solution Overview
Problem
Combinatorial optimization problems, such as gene control networks, face challenges in determining optimality due to the exponential growth of solution spaces and the difficulty in extracting and analyzing large numbers of solution candidates, especially with complex constraint conditions, which hinders the determination of optimal solutions in fields like drug development.
Innovation Solution
A method for determining optimality in combinatorial optimization problems involves uniformly extracting solutions, estimating maximum evaluation values, and determining whether candidate solutions fall within confidence intervals, using techniques like generalized extreme value distribution and zero-suppressed binary decision diagrams to efficiently analyze and validate solution optimality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exhaustive full search is performed to determine optimal solution, then solution optimality is guaranteed, but calculation amount explodes exponentially making it infeasible for large-scale problems
Solution Approach 1:
The patent segments the solution space into multiple regions and performs uniform extraction of solution candidates from different regions. This allows statistical analysis to be conducted on a manageable subset of solutions while still providing reliability guarantees for the overall optimal solution determination.
Solution Approach 2:
The patent introduces statistical analysis as an intermediary mechanism between exhaustive search and heuristic methods. By using statistical techniques to analyze uniformly extracted solutions, it provides reliability assessment without requiring complete enumeration of all possible solutions.
2Productivity
If heuristic methods are used to calculate approximate solutions, then calculation efficiency is improved, but solution optimality cannot be determined as only local solutions are obtained
Solution Approach 1:
The patent implements feedback through statistical analysis of uniformly extracted solutions. The statistical results provide information about the quality of heuristic solutions and enable determination of whether a solution is likely to be optimal, creating a feedback loop that improves reliability without sacrificing efficiency.
Solution Approach 2:
The patent changes the parameter of solution extraction from random or heuristic-based selection to uniform extraction across the solution space. This parameter change enables statistical analysis to provide reliability assessment while maintaining computational efficiency.
3Measurement precision
If statistical analysis is performed on solution candidates, then optimality estimation is possible, but difficulty in uniformly extracting large amounts of solutions from complex solution spaces with constraint conditions prevents practical application
Solution Approach 1:
The patent performs preliminary uniform extraction of solution candidates before statistical analysis. By pre-selecting solutions uniformly from the solution space using ZDD techniques, it simplifies the subsequent statistical analysis step and makes the overall process practically applicable even with complex constraints.
Solution Approach 2:
The patent replaces complex mechanical extraction processes with ZDD-based uniform extraction methods. This substitution enables efficient and systematic extraction of solution candidates that satisfies the requirements for statistical analysis while handling complex constraint conditions.
Data Source
AI summary
Provided is an optimal solution determination method for determining optimality of a solution in a combinatorial optimization problem using a computer, including uniformly extracting a plurality of solutions in a solution space of the combinatorial optimization problem as a plurality of first solutions, and estimating a maximum evaluation value in a case where solutions of a number that exceeds the number of the plurality of first solutions are assumed, on the basis of a plurality of first evaluation values respectively corresponding to the plurality of first solutions that are uniformly extracted, as a first maximum evaluation value Z. Further, in a case where a solution candidate (graph G_1) that belongs to a solution space is input (step S18), an evaluation value S_1 corresponding to the graph G_1 is acquired, the acquired evaluation value S_1 is compared with the first maximum evaluation value Z, and it is determined whether the evaluation value S_1 of the input graph G_1 is within a confidence interval of the first maximum evaluation value Z (whether the graph G_1 is a first optimal value or not).