To extend the PFN-based CBO framework for multi-objective optimization, several modifications and enhancements can be implemented:
Objective Transformation: One approach is to transform the multi-objective problem into a single-objective problem using scalarization techniques like weighted sum or Tchebycheff method. This transformed objective can then be optimized using the existing PFN-based CBO framework.
Pareto Optimization: Another method is to incorporate Pareto optimization techniques into the PFN-based CBO framework. This involves optimizing multiple objectives simultaneously to find a set of solutions that represent the Pareto front, where no solution can be improved in one objective without degrading in another.
Acquisition Function Modification: The acquisition function used in PFN-based CBO can be adapted to handle multiple objectives. This may involve developing new acquisition functions that consider the trade-offs between different objectives and guide the search towards the Pareto front.
Constraint Handling: Extending the constraint-handling capabilities of the PFN-based CBO framework to handle multiple constraints associated with each objective is crucial for multi-objective optimization. This may involve developing new constraint-handling methods that can effectively manage the trade-offs between objectives and constraints.
By incorporating these enhancements, the PFN-based CBO framework can effectively handle multi-objective optimization problems, providing a powerful tool for optimizing complex engineering systems with competing objectives.