1 Introduction
With the rapid development of computer technology, many methods for solving optimization problems have emerged. Among them, simulated annealing (SA), simulated quantum annealing (SQA) and path integral Monte Carlo (PIQMC) are one of the most popular randomization methods in the current field. The essence of these methods is to search on the probability distribution to find the optimal solution or approximately optimal solution to the problem. This article will delve into the basic principles, implementation processes and applications of these three methods.
2. Simulated annealing (SA)
Simulated annealing, inspired by the cooling process of solid matter in nature, is a probabilistic search algorithm used to find the global optimal solution to a given problem.
2.1 Basic Principles
During the annealing process, when a substance is heated to a certain temperature, its atoms begin to move randomly. As the temperature decreases, this random movement decreases, and the atoms gradually settle into lower energy positions. In the algorithm, this "temperature" concept corresponds to a control parameter that affects the randomness in the search process.
2.2 SA algorithm steps:
- Initialization parameters: Set the initial solution, initial temperature, cooling rate and other related parameters.
- When the temperature is greater than a certain threshold, repeat the following steps: a. Select a neighbor solution. b. Calculate the energy difference ΔE between the new solution and the current solution. c. If ΔE is less than 0 or meets a certain probability condition (usually based on the Metropolis criterion), accept the new solution. d. Lower the temperature (multiplied by the cooling rate).
- Output the current solution as the optimal solution.
def simulated_annealing(