Solving the 0-1 Knapsack Problem Using Simulated Annealing Algorithm

Simulated annealing is a heuristic search method inspired by the metallurgical annealing process, particularly suitable for solving NP-hard combinatorial optimization problems like the 0-1 knapsack problem. The core algorithmic concept simulates temperature reduction in physical annealing to progressively approach optimal solutions, allowing acceptance of inferior solutions with certain probabilities during search to escape local optima. Code implementation typically involves temperature scheduling functions and probabilistic acceptance criteria using Boltzmann distribution calculations.

In the 0-1 knapsack problem context, each item's state (selected/not selected) represents a binary variable, with all item state combinations forming the solution space. The algorithm starts from a random initial solution and generates new solutions through neighborhood operations (e.g., flipping an item's selection status). Key parameters requiring code-level configuration include initial temperature, cooling rate, and termination conditions, which must be calibrated based on problem scale. Implementation often involves encoding solutions as binary arrays and designing fitness functions combining profit maximization with capacity constraints.

Compared to traditional greedy algorithms, simulated annealing's main advantage lies in escaping local optima traps. During high-temperature phases, the algorithm frequently accepts inferior solutions, gradually transitioning to accepting only improved solutions as temperature decreases—this characteristic enables superior global search capabilities for complex combinatorial problems. Constraint handling typically incorporates penalty functions that integrate capacity constraints into the objective function, often implemented through conditional checks and adaptive penalty coefficients in the evaluation module.

The implemented algorithm can be executed directly, allowing observation of solution quality under different parameters to intuitively understand simulated annealing's application characteristics in discrete optimization. It demonstrates significant educational value for learning combinatorial optimization algorithms, particularly suitable for engineering scenarios requiring balance between solution quality and computational efficiency. Code structure usually includes modular components for solution initialization, neighborhood generation, energy calculation, and temperature update loops.