The SBGD framework can be applied to various optimization problems beyond non-convex functions, including multi-objective optimization and stochastic optimization.
Multi-Objective Optimization:
Weighted Sum Method: SBGD can be extended to handle multiple conflicting objectives by using a weighted sum method to combine the objectives into a single function.
Pareto Optimization: Implementing Pareto optimization techniques to find a set of solutions that represent the trade-off between different objectives.
Stochastic Optimization:
Incorporating Uncertainty: SBGD can be adapted to handle stochastic optimization problems by incorporating uncertainty in the objective function or constraints.
Evolutionary Strategies: Utilizing evolutionary strategies within the SBGD framework to handle stochasticity and randomness in the optimization process.
By adapting the communication and mass transition mechanisms in SBGD to suit the characteristics of multi-objective or stochastic optimization problems, the framework can effectively address a wider range of optimization challenges.