Path Relinking Initialization for Diverse Combinatorial Search
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Solution Overview
Problem
Conventional path relinking methods for combinatorial optimization problems often confine the initial solution to the vicinity of the best solution, limiting the search space and hindering the discovery of diverse and potentially better solutions.
Innovation Solution
A computer program that determines higher-ranked solutions based on evaluation function values, adjusts selection probabilities to favor solutions closer to the best solution, and generates an initial solution using path relinking with a second, diverse solution, thereby expanding the search space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the best solution is used to generate the initial solution in path relinking, then the initial solution is similar to the best solution, but the search space is limited and diversity is reduced
Solution Approach 1:
The patent changes the selection parameter from deterministic (always selecting the best solution) to probabilistic (selecting from multiple high-ranking solutions based on probability). This allows the system to balance between exploiting known good solutions and exploring diverse regions of the search space, resolving the contradiction between solution quality and search space coverage.
Solution Approach 2:
The patent introduces dynamic selection where the choice of initial solution varies probabilistically based on ranking probabilities. Instead of a static rule always selecting the best solution, the system dynamically selects from multiple candidates, enabling adaptability between exploitation and exploration phases of the search.
2Adaptability or versatility
If two solutions are randomly selected from the solution pool, then the search space is expanded, but good solutions are searched to the same extent as other solutions, reducing efficiency
Solution Approach 1:
The patent transforms the uniform random selection parameter into a non-uniform probability distribution where selection probability is inversely related to the rank of the solution. This ensures that higher-quality solutions have higher probabilities of being selected, maintaining search efficiency while still allowing diverse solutions to be chosen occasionally for exploration.
3Reliability
If the best solution is always selected, then solution quality is maintained, but diversity in initial solutions is reduced
Solution Approach 1:
The patent introduces dynamic probabilistic selection that balances reliability and diversity. The selection process is dynamic rather than static, allowing the system to maintain reliability by favoring high-ranking solutions while simultaneously preserving diversity through probabilistic variation in selection outcomes.
Data Source
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AI summary
A processing unit determines, from a plurality of solutions to a combinatorial optimization problem stored in a storage unit, a plurality of higher-ranked solutions based on evaluation function values of the plurality of solutions, determines, for each of the plurality of higher-ranked solutions, a selection probability such that higher-ranked solutions having evaluation function values closer to that of the highest-ranked solution among the plurality of higher-ranked solutions are more likely to be selected, selects a first solution from the plurality of higher-ranked solutions according to the selection probabilities, selects a second solution different from the first solution, from the plurality of solutions, generates a third solution with a path relinking method using the selected first solution and second solution, and performs a solution search on the combinatorial optimization problem using the third solution as an initial solution.