UNIT 1

UNIT 2

Unit 3

Unit 4

Introduction

• Simulated Annealing (SA) is inspired by a physical process called annealing, where metals are heated and then cooled slowly to reach a stable, low-energy state (crystalline structure). This idea is applied to optimization problems, where the goal is to find the "optimal" or "near-optimal" solution.

Physical Annealing Process

1. Heating Phase: At high temperatures, particles in a metal gain energy and move randomly.
2. Cooling Phase: As the temperature drops, particles settle into a stable, low-energy configuration.
3. For this to work well, the cooling must be done very slowly; otherwise, the material may not reach its optimal state (ground energy).

Simulated Annealing Analogy

• In optimization problems:
  • The state of the metal corresponds to a potential solution to the problem.
  • The energy corresponds to the cost function being minimized.
  • The temperature controls the randomness of the search for better solutions.

Algorithm Overview

1. Start with a random solution and an initial high temperature.
2. Move to a neighboring solution:
   • If it improves the cost (lower energy), accept it.
   • If it’s worse, accept it with a certain probability, which decreases as temperature drops.
3. Gradually lower the temperature according to a cooling schedule.
4. Stop when the system is "frozen" (low temperature) or no better solutions are found.