0-1 Integer Programming Variable Correlation Analysis
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Solution Overview
Problem
Conventional methods for solving 0-1 integer programming problems face difficulties when variables appear in only one constraint condition, leading to inadequate narrowing of the solution space and increased processing load, making it challenging to efficiently calculate accurate solutions.
Innovation Solution
The proposed method involves identifying pairings of variables that appear in a predetermined number of constraint conditions and registering correlation information based on both the frequency of appearance and degree of relationship between variables, allowing for targeted value inversion to search for solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional weighted local search method is used to solve 0-1 integer programming problems, then the solution space can be narrowed down based on variable relationships, but variables appearing in only one constraint condition cannot be effectively processed leading to increased processing load and reduced solution accuracy
Solution Approach 1:
The patent segments the variable set into two categories: variables appearing in multiple constraint conditions (processed using degree of relationship) and variables appearing in only one constraint condition (processed using appearance frequency). This segmentation allows each type of variable to be handled with the most appropriate metric, improving both solution accuracy and processing efficiency.
Solution Approach 2:
The patent changes the selection parameter from solely 'degree of relationship' to a dual-parameter system that includes both 'appearance frequency' and 'degree of relationship'. This parameter change enables the system to effectively process variables that appear in only one constraint condition by using appearance frequency as the selection criterion, thereby improving solution accuracy without significantly increasing processing load.
2Productivity
If variables appearing in only one constraint condition are excluded from correlation analysis, then processing load is reduced, but solution accuracy deteriorates due to inadequate solution space narrowing
Solution Approach 1:
The patent segments the correlation analysis process into two paths: one for variables appearing in multiple constraints (using degree of relationship) and another for variables appearing in single constraints (using appearance frequency). This segmentation ensures that variables appearing in only one constraint condition are included in the analysis with appropriate metrics, improving solution accuracy while maintaining processing efficiency.
Solution Approach 2:
The patent applies partial correlation analysis selectively: full degree of relationship analysis for variables in multiple constraints, and simplified appearance frequency analysis for variables in single constraints. This partial application of different analysis depths optimizes the balance between processing load and solution accuracy.
3Measurement precision
If correlation information is registered for all variable pairings, then solution accuracy is improved through comprehensive solution space narrowing, but device complexity increases due to extensive data storage requirements
Solution Approach 1:
The patent applies local quality by using different correlation information registration strategies for different variable types: degree of relationship information for variables appearing in multiple constraints, and appearance frequency information for variables appearing in single constraints. This localized approach reduces overall data storage requirements while maintaining comprehensive solution space narrowing capability.
Solution Approach 2:
The patent implements partial correlation registration by selectively registering correlation information based on variable characteristics. Not all variable pairings require full degree of relationship analysis; variables appearing in single constraints suffice with appearance frequency data. This partial registration reduces storage complexity while preserving solution accuracy.
Data Source
AI summary
A computer-readable recording medium storing therein a program for causing a computer to execute a process including: obtaining constraint conditions forming a 0-1 integer programming problem including variables each taking a value 0 or 1, each constraint condition including at least one of the variables; identifying pairings of a variable appearing only in a predetermined number of constraint conditions and the constraint conditions where the variable appears, the predetermined number being less than a total number of the constraint conditions; registering, in a storage unit, for each of the identified pairings, first correlation information correlating the variable of the pairing with another variable appearing in at least one of the constraint conditions of the pairing; registering, in the storage unit, second correlation information correlating, based on a degree of relationship between the variables, at least one of the variables and another variable having at least a predetermined degree of relationship with the at least one variable; and searching for a solution to the 0-1 integer programming problem by determining, based on the first and second correlation information, a group of any two or more correlated variables, for value inversion.