1. Determine the search scope and define the parameters.
Firstly, the parameters of the problem are defined, which can be continuous variables or discrete variables. Determine the search scope of each parameter. These ranges can be the upper and lower limits of the problem.
2. Construct the test function and determine the initial interval.
Construct a test function and map the value of each parameter to a numerical value. This value reflects the applicability of the parameter value to the optimization problem. Usually this function is designed according to the characteristics of the problem. Randomly select an initial point within the search range of each parameter, and then calculate the test function values of these points.
3. Iterative search and termination conditions
By constantly selecting new points in the current interval and calculating their test function values, the current optimal points are constantly updated and improved. Usually, this step is done by using a method called "trust region" or "interpolation". When a certain termination condition is reached, such as the number of iterations reaches the preset upper limit, or the current optimal point is close enough to the theoretical optimal solution, the search will stop.
Interval method from advantages and disadvantages to application fields
Advantages of 1 and interval method
Interval method can deal with many optimization problems, including nonlinear optimization and multimodal optimization. Able to deal with a large number of parameters.
2. Shortcomings of interval method
Interval method will fall into local optimal solution for some problems, but can not find global optimal solution. The efficiency of interval method is not always the highest, and some problems need more computational resources.
3, machine learning, operations research
Interval method is often used to optimize the parameters of various machine learning algorithms, such as linear regression, logical regression, decision tree parameters and so on. In operational research, interval method is used to solve various scheduling and assignment problems, such as vehicle routing problem (VRP) and traveling salesman problem (TSP).
4, control system, artificial intelligence
In the control system, the interval method is used to design the parameters of the controller to achieve the optimal performance of the system. The optimal parameters of PID controller can be found by interval method. In the field of artificial intelligence, interval method is used to optimize various algorithms and strategies, such as the parameters of reward function in reinforcement learning.