Simulated Annealing Temperature Range Determination
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing simulated annealing methods for solving combinatorial optimization problems lack a systematic approach to determine the temperature parameter range, especially for models with variables having discrete multiple values or continuous values, leading to inefficiencies in finding global optimal solutions.
Innovation Solution
A simulation apparatus and method that calculates the maximum and minimum values of the temperature parameter range by analyzing statistics from local optimal solutions and probability distribution functions of variables, allowing for multiple iterations of simulated annealing within this range to efficiently find better solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the temperature parameter range is set too wide to ensure global optimal solution is reached, then the reliability of finding global optimal solution is improved, but the calculation amount and time required increases significantly
Solution Approach 1:
The patent performs preliminary actions by calculating statistics (mean and standard deviation) from local optimal solutions obtained through local search methods before executing simulated annealing. This preliminary statistical analysis enables the system to determine an appropriate temperature parameter range in advance, avoiding the need to use an excessively wide temperature range during the actual simulated annealing process. By preparing this statistical information beforehand, the system can set a sufficiently wide temperature range to ensure global optimal solution is reached while minimizing unnecessary calculation time.
Solution Approach 2:
The patent dynamically determines the temperature parameter range by changing parameters based on statistical characteristics of the problem. Specifically, it calculates the temperature range using the formula T_range = k × σ (where σ is the standard deviation and k is a coefficient), thereby adapting the temperature parameter to the specific characteristics of each optimization problem. This parameter change approach allows the system to use the minimum necessary temperature range for each problem type, balancing between ensuring global optimal solution and reducing calculation time.
2Productivity
If the temperature parameter range is set too narrow to reduce calculation amount, then the productivity is improved, but the reliability of reaching global optimal solution deteriorates
Solution Approach 1:
The patent changes the temperature parameter based on statistical characteristics of the optimization problem by calculating T_range = k × σ, where σ represents the standard deviation of the objective function values from local optimal solutions. This dynamic parameter adjustment ensures the temperature range is sufficiently wide to maintain reliability of finding global optimal solution while being narrow enough to improve simulation efficiency and productivity.
Solution Approach 2:
The patent uses feedback from local search results to determine the temperature parameter range. By performing local search first and calculating statistics (mean and standard deviation) from the obtained local optimal solutions, the system receives feedback about the problem's characteristics. This feedback is then used to set an appropriate temperature range that balances reliability and efficiency, avoiding both excessively wide and unnecessarily narrow temperature ranges.
3Ease of operation
If existing simulated annealing methods are used without systematic temperature parameter determination, then the ease of operation is maintained, but the productivity and efficiency deteriorate
Solution Approach 1:
The patent implements self-service by enabling the system to automatically determine the appropriate temperature parameter range without requiring manual intervention or expert knowledge. The system performs local search, calculates statistics (mean and standard deviation) from the results, and automatically computes the temperature range using T_range = k × σ. This self-service capability maintains ease of operation while dramatically improving productivity and efficiency compared to methods requiring manual temperature parameter tuning.
Data Source
AI summary
A simulation apparatus is an apparatus that obtains a solution of a combinatorial optimization problem by SA, in which a local optimal solution of an objective function is acquired by using a local search method of changing a temperature parameter, a statistic is calculated based on the local optimal solution and a probability distribution function of a variable included in the objective function, a maximum value (temperature parameter when a standard deviation related to a state of the local optimal solution is large) and a minimum value (temperature parameter when the standard deviation is small) as a search range for the temperature parameter are obtained based on the calculated statistic (standard deviation), and a good solution is obtained by executing the simulated annealing a plurality of times in the search range having the maximum value and the minimum value for the temperature parameter.