Binary Decision Diagram Search for Combinatorial Optimization
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Solution Overview
Problem
In combinatorial optimization problems, especially those involving large datasets like gene control networks, existing methods struggle to efficiently search for optimal solutions due to exponential growth in computation complexity, leading to difficulties in evaluating solution candidates with high degrees of divergence and extracting entire solution spaces.
Innovation Solution
An optimal solution search method utilizing a binary decision diagram (BDD) data structure that enumerates and indexes solution candidates with a degree of divergence equal to or smaller than a specified range, employing tree pruning and node sharing to reduce pattern identification and extract common patterns, allowing for efficient evaluation and updating of solution candidates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If comprehensive full search is performed to find optimal solutions in combinatorial optimization problems, then solution accuracy is improved, but computation complexity increases exponentially making it almost impossible for large-scale problems
Solution Approach 1:
The patent segments the solution space by representing it as a binary decision diagram (BDD), which divides the combinatorial search space into hierarchical binary decisions. This segmentation allows the system to navigate the solution space efficiently without enumerating all possible combinations, thereby maintaining solution accuracy while reducing computational complexity from exponential to polynomial levels.
Solution Approach 2:
The patent transforms the combinatorial optimization problem from a high-dimensional discrete search space into a structured binary decision diagram representation. By mapping solution candidates onto BDD nodes and edges, the system adds a dimensional transformation that enables efficient traversal and evaluation, converting an intractable combinatorial problem into a manageable graph-based search problem.
2Adaptability or versatility
If the degree of divergence N is increased to enumerate more solution candidates, then solution coverage is improved, but the number of next solution candidate groups explodes making enumeration difficult
Solution Approach 1:
The patent segments the enumeration process by using BDD to represent solution candidate groups at different divergence levels. Instead of explosively generating all candidates at once, the system segmentally traverses the BDD structure, evaluating solution candidates in a controlled manner that maintains coverage while preventing combinatorial explosion during enumeration.
Solution Approach 2:
The patent performs preliminary action by pre-structuring the solution space into a binary decision diagram before enumeration begins. This preliminary organization of solution candidates into a hierarchical BDD structure enables efficient traversal and evaluation, allowing the system to handle large divergence levels without suffering from enumeration explosion during the actual search process.
3Quantity of substance
If the number of genes N increases in gene control network analysis, then data comprehensiveness is improved, but the number of possible graphs diverges ultra-exponentially making it difficult to extract entire solution space
Solution Approach 1:
The patent applies dimensionality change by transforming the ultra-exponentially growing graph solution space into a structured binary decision diagram representation. By mapping graph structures onto BDD nodes and transitions, the system converts an intractable combinatorial explosion into a manageable polynomial-scale graph traversal problem, enabling extraction of entire solution spaces even for large numbers of genes.
Solution Approach 2:
The patent segments the graph solution space extraction by using BDD to represent graphs as sequences of binary decisions. This segmentation allows the system to handle large-scale gene control networks by breaking down the ultra-exponential graph enumeration into hierarchical binary choices, making the entire solution space extractable even when the number of genes becomes large.
Data Source
AI summary
An optimal solution search method for searching for an optimal solution in a combinatorial optimization problem using a computer, includes: acquiring a first solution candidate; and enumerating and indexing solution candidate groups of which the degree of divergence from the first solution candidate is equal to or smaller than a predetermined range; equally extracting second solution candidates from the enumerated and indexed solution candidate groups assigning evaluation values to the second solution candidates; and determining whether the search for the optimal solution is terminated on the basis of the evaluation value. In a case where the search for the optimal solution is not terminated, the current first solution candidate is updated as the best second solution candidate selected from the second solution candidates, and the processes are repeated until the search for the first optimal solution is terminated.