An Adaptive Localized Decision Variable Analysis Approach to Large-Scale Multiobjective and Many-Objective...

Area of Science:

• Optimization algorithms
• Computational intelligence
• Mathematical programming

Background:

• Large-scale multiobjective optimization problems (MaOPs) present significant computational challenges.
• Existing methods often struggle with balancing solution convergence and diversity in high-dimensional objective spaces.
• Decomposition-based frameworks offer a promising avenue but require refined variable analysis.

Purpose of the Study:

• To propose an adaptive localized decision variable analysis approach for MaOPs.
• To enhance the performance of decomposition-based optimization frameworks.
• To effectively manage large numbers of decision variables and objectives.

Main Methods:

• Incorporating reference vector guidance into control variable analysis.
• Employing a projection-based detection method to measure decision variable convergence relevance.
• Utilizing an adaptive scalarization strategy for optimizing grouped decision variables.
• Balancing convergence and diversity adaptively in the objective space.

Main Results:

• The proposed algorithm demonstrates effectiveness on test problems with 2-10 objectives and 200-1000 variables.
• Experimental results validate the algorithm's efficiency in solving large-scale multiobjective and many-objective optimization problems.
• The adaptive strategy successfully balances solution convergence and diversity.

Conclusions:

• The adaptive localized decision variable analysis approach is effective for large-scale MaOPs.
• The method offers an efficient way to handle complex optimization landscapes.
• This work contributes a novel strategy for improving multiobjective optimization performance.