Optimal Computing Budget Allocation for Particle Swarm Optimization in Stochastic Optimization.

Area of Science:

• Computational intelligence
• Optimization algorithms
• Metaheuristics

Background:

• Particle Swarm Optimization (PSO) is a metaheuristic for deterministic problems.
• Real-world applications often involve stochastic optimization, where standard PSO is inefficient.
• Current PSO methods for stochastic problems equally allocate computational effort, wasting resources.

Purpose of the Study:

• To enhance the computational efficiency of Particle Swarm Optimization (PSO) for stochastic optimization problems.
• To integrate Optimal Computing Budget Allocation (OCBA) principles into PSO.
• To develop an intelligent sampling strategy for PSO in noisy environments.

Main Methods:

• Integration of Optimal Computing Budget Allocation (OCBA) into Particle Swarm Optimization (PSO).
• Derivation of an asymptotically optimal allocation rule for sampling.
• Proposal of an easy-to-implement sequential procedure for sample allocation.

Main Results:

• The proposed method significantly improves the computational efficiency of PSO for stochastic problems.
• Intelligent sample allocation leads to more effective selection of personal and global best solutions.
• Numerical tests demonstrate superior performance compared to standard PSO with equal effort allocation.

Conclusions:

• The integration of OCBA with PSO offers a more efficient approach to stochastic optimization.
• The derived allocation rule and sequential procedure enhance PSO's ability to handle noisy fitness evaluations.
• This approach yields better results for the same computational budget in stochastic optimization tasks.