Adapting MOEA/D to CMA-ES for Dealing with Ill-conditioned Multiobjective Problems.

Area of Science:

• Evolutionary Computation
• Multiobjective Optimization
• Algorithm Design

Background:

• Ill-conditioned problems pose significant challenges in single-objective optimization.
• These challenges are largely unaddressed in evolutionary multiobjective optimization (EMO).
• Existing EMO approaches may compromise core evolutionary strategy features when integrating them.

Purpose of the Study:

• To introduce a novel decomposition-based multiobjective evolution strategy (MOES/D).
• To address non-separable and ill-conditioned multiobjective optimization problems.
• To develop tailored strategies for coordinating evolutionary algorithms.

Main Methods:

• Developed MOES/D, a decomposition-based multiobjective evolution strategy.
• Implemented an importance mixing algorithm for unbiased sample efficiency.
• Utilized a collaborative ascent method for simultaneous subproblem optimization.
• Applied expectation-maximization for principled resource allocation to prioritize models.

Main Results:

• MOES/D demonstrates superior performance on moderate- and ill-conditioned multiobjective problems.
• The algorithm significantly outperforms most state-of-the-art algorithms.
• Experiments were conducted on a novel benchmark suite of non-separable and ill-conditioned problems.

Conclusions:

• MOES/D effectively solves challenging non-separable and ill-conditioned multiobjective problems.
• The proposed tailored strategies enhance the efficiency and capabilities of evolutionary algorithms in EMO.
• This work bridges a critical gap in EMO research by addressing ill-conditioned instances.