Simulated Annealing [SA]

Simulated Annealing [SA] is a powerful optimization algorithm inspired by the process of annealing in metallurgy. Known for its ability to escape local optima and find near-global solutions, SA is widely used in solving challenging optimization problems across various domains.

Key Terms/Concepts in SA:

• Objective Function: The cost function to minimize or maximize, representing the quality of a solution.
• Solution Space: The entire set of possible solutions.
• Temperature (T): A control parameter that starts high and gradually decreases to guide the search process.
• Cooling Schedule: The rate at which the temperature decreases (e.g., T = T × α).
• Neighboring Solution: A slightly modified version of the current solution, ensuring exploration of the solution space.
• Acceptance Probability: Determines whether a worse solution is accepted, calculated as
  P = e^(-Δf / T)
• Exploration vs. Exploitation: Balancing the search for new solutions (exploration) with refinement of current solutions (exploitation).

Applications of SA:

• Traveling Salesman Problem (TSP): Finding the shortest route that visits all cities and returns to the starting point.
• Resource Allocation: Efficient distribution of limited resources.
• Job Scheduling: Optimizing task assignments to minimize time or cost.
• Portfolio Optimization: Allocating investments to maximize returns while minimizing risks.
• Control System Design: Tuning system parameters for optimal performance.

Advantages of SA:

• Highly effective for large, complex, and nonlinear optimization problems.
• Can escape local optima to find near-global solutions.
• Flexible and adaptable, requiring minimal problem-specific knowledge.