A General Framework of Dynamic Constrained Multiobjective Evolutionary Algorithms for Constrained Optimization.

Area of Science:

• Optimization Techniques
• Computational Mathematics
• Evolutionary Algorithms

Background:

• Constrained optimization problems (COPs) present significant challenges in various scientific and engineering fields.
• Existing methods often struggle with complex constraints and multimodal search spaces.
• Developing robust techniques for solving COPs, especially in high dimensions, remains an active research area.

Purpose of the Study:

• To propose a novel multiobjective technique for solving constrained optimization problems (COPs).
• To introduce a general framework for dynamic constrained multiobjective evolutionary algorithms (DCMOEA) to address COPs.
• To enhance the handling of constraint difficulty and multimodal search spaces within optimization algorithms.

Main Methods:

• A COP is transformed into a dynamic constrained multiobjective optimization problem (DCMOP) with three objectives: original objective, constraint-violation objective, and niche-count objective.
• A strategy of gradually reducing the constraint boundary is employed to manage constraint difficulty.
• A method of gradually reducing niche size is utilized to address multimodal difficulty.
• A general framework for DCMOEAs is proposed, instantiated with Pareto ranking-based, decomposition-based, and hypervolume indicator-based algorithms.

Main Results:

• The proposed DCMOEA framework demonstrates competitive or superior performance compared to state-of-the-art constraint optimizers.
• The technique shows particular effectiveness on COPs with a large number of dimensions.
• Experimental results on two benchmark suites validate the efficacy of the proposed approach.

Conclusions:

• The novel multiobjective technique offers an effective approach to solving constrained optimization problems.
• The proposed framework and its instantiations provide a robust solution for handling complex constraints and multimodal landscapes.
• The method shows promise for applications requiring high-dimensional constrained optimization.