Application of Particle Swarm Simulated Annealing Algorithm in Function Optimization

The Particle Swarm Simulated Annealing algorithm (PSO-SA) is a hybrid optimization approach combining Particle Swarm Optimization (PSO) with Simulated Annealing (SA), demonstrating superior performance in function optimization problems. By integrating the strengths of both classical optimization methods, this algorithm effectively balances global exploration and local exploitation capabilities.

The PSO component simulates bird flock foraging behavior, where each particle adjusts its velocity and position based on personal best (pBest) and global best (gBest) positions. This mechanism, typically implemented with velocity update equations (v = w*v + c1*rand()*(pBest - x) + c2*rand()*(gBest - x)), provides strong global exploration but may lead to premature convergence. The SA component adopts metallurgical annealing principles, incorporating probabilistic acceptance of worse solutions through the Metropolis criterion (if exp(-ΔE/T) > random(0,1): accept worse solution), enabling escape from local optima.

In practical function optimization, PSO-SA typically employs a two-phase hybrid strategy: initial coarse-grained global search using PSO, followed by SA-based fine-grained local exploitation when particle swarm convergence is detected. Temperature parameter configuration is critical, with exponential cooling schedules (T_new = α*T_old, where α ∈ [0.95, 0.99]) ensuring thorough exploration in early stages and precise convergence later. Implementation often involves monitoring convergence criteria through position variance thresholds or iteration limits.

Key advantages of this hybrid approach include: 1) Enhanced local optimum escape capability compared to pure PSO; 2) Significantly improved convergence speed versus standalone SA; 3) Particular suitability for multimodal function optimization problems. Practical implementation requires coordinated tuning of parameters including inertia weight (w), acceleration coefficients (c1, c2), and annealing schedule parameters, as these directly impact the exploration-exploitation balance. Code implementation typically involves nested loops with conditional switching between PSO velocity updates and SA metropolis acceptance tests.