Quality Metric Estimation for NP-Hard Combinatorial Scheduling
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current scheduling systems for complex projects, such as aircraft construction, face inefficiencies due to the inability to calculate optimal solutions for NP-hard combinatorial problems within practical time and resource constraints, leading to suboptimal schedules and increased costs.
Innovation Solution
A method that estimates the quality metric value of optimal solutions for combinatorial problems using a function established for families of problems, allowing for the evaluation and improvement of solutions without finding the optimal solution, thereby guiding the search for better solutions and reformulating problems to make them more tractable.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional scheduling systems attempt to calculate optimal solutions for NP-hard combinatorial problems, then solution quality improves, but computational time and resource requirements become impractical
Solution Approach 1:
The patent extracts the quality metric value calculation from the complete optimal solution search process. By separating the quality assessment function from the full optimization problem, the system can evaluate solution quality without completing the computationally expensive optimal search, thus resolving the contradiction between solution quality and computational time
Solution Approach 2:
The patent performs preliminary establishment of quality metric functions based on problem characteristics before the actual solving process. This preliminary action creates a framework that allows rapid quality assessment during solution search, avoiding the need to compute complete optimal solutions at each evaluation step
2Measurement precision
If more computational resources are allocated to solve combinatorial problems, then solution optimality improves, but system cost and complexity increase
Solution Approach 1:
The patent employs approximate quality metric functions that are computationally inexpensive to evaluate, replacing expensive exact optimization computations. These simplified quality assessments provide sufficient guidance for finding good solutions without requiring the complex computational infrastructure needed for guaranteed optimality
Solution Approach 2:
The patent introduces quality metric functions as intermediary tools between the problem definition and complete solution search. These functions serve as mediators that provide quality guidance without requiring direct computation of optimal solutions, thus reducing system complexity while maintaining solution quality
3Manufacturing precision
If exact optimal solutions are computed for complex projects, then schedule quality improves, but preparation time exceeds construction time
Solution Approach 1:
The patent applies partial action by computing quality metric values rather than complete optimal solutions. This partial computation provides sufficient quality information for practical scheduling decisions without requiring the excessive computation time needed for exact optimality, thus resolving the contradiction between schedule quality and preparation time
Data Source
AI summary
A method is provided for solving a given combinatorial problem includes providing a function that has been established for a family of combinatorial problems including the given combinatorial problem. For each problem in the family, the function relates a secondary measure of the problem to a quality metric of a characteristic solution to the problem. The function may be applied to a value of the secondary measure for the given problem to obtain a value of the quality metric of the characteristic solution to the given problem. The given problem may be solved to obtain a solution to the given problem; and the solution evaluated based on comparison of a value of the quality metric of the solution, and the value of the quality metric of the characteristic solution. And in at least one instance based on the evaluation, the solution may be communicated to guide performance of a task.