A Multiform Optimization Framework for Constrained Multiobjective Optimization.

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Evolutionary Computation

Background:

• Constrained multiobjective optimization problems (CMOPs) present significant challenges for existing multiobjective evolutionary algorithms (MOEAs).
• Effective handling of constraints and balancing diversity with convergence are critical issues in MOEAs.
• Utilizing information from both feasible and infeasible regions is key to solving CMOPs.

Purpose of the Study:

• To propose a novel multiform optimization framework for solving CMOPs within a multitask learning setting.
• To design a framework that searches in varying feasible spaces derived from the original CMOP task.
• To leverage transferable knowledge between auxiliary and primary CMOP tasks to guide the search towards Pareto optimal solutions.

Main Methods:

• A multiform optimization framework is proposed, integrating a primary CMOP task with an auxiliary CMOP task.
• The framework searches in progressively larger feasible spaces derived from the original CMOP.
• The framework is instantiated with dominance-based, decomposition-based, and indicator-based MOEAs.

Main Results:

• Experiments on benchmark test problems show the proposed method outperforms four representative constraint-handling techniques.
• The approach demonstrates superior performance compared to five state-of-the-art constrained MOEAs.
• The method is successfully applied to a real-world antenna array synthesis problem.

Conclusions:

• The proposed multiform optimization framework effectively addresses challenges in CMOPs by utilizing information from feasible and infeasible regions.
• The framework enhances search efficiency and solution quality by leveraging knowledge transfer in a multitask setting.
• This approach offers a promising direction for tackling complex constrained optimization problems in both theoretical and practical applications.