Multiobjective memetic estimation of distribution algorithm based on an incremental tournament local searcher.

Area of Science:

• Optimization algorithms
• Computational intelligence
• Multiobjective optimization

Background:

• Multiobjective optimization problems (MOPs) often feature complex Pareto sets, such as low-dimensional continuous manifolds.
• Traditional estimation of distribution algorithms (EDAs) may not fully exploit promising individuals, hindering efficient search.
• Exploiting local information and ensuring well-distributed solutions are critical for effective MOPs.

Purpose of the Study:

• To introduce a novel hybrid multiobjective algorithm, MMEDA, combining EDAs, local search, and ε-dominance.
• To address the challenge of efficiently searching complex Pareto fronts in continuous MOPs.
• To improve both convergence speed and solution diversity in multiobjective optimization.

Main Methods:

• Developed a novel multiobjective estimation of distribution algorithm.
• Integrated an incremental tournament local searcher to exploit local search space efficiently.
• Combined the local searcher with ε-dominance for improved solution distribution and computational efficiency.
• Proposed two new MOPs with variable linkages based on manifold distributions.

Main Results:

• The proposed MMEDA algorithm demonstrated comparable performance against three state-of-the-art algorithms.
• Experiments on twenty-two test problems showed MMEDA's effectiveness in terms of convergence and diversity metrics.
• The algorithm showed robustness across problems with and without variable linkages of diverse complexities.

Conclusions:

• The hybrid MMEDA algorithm effectively balances global search (via EDA) and local search (via incremental tournament and ε-dominance).
• MMEDA offers a promising approach for tackling complex continuous multiobjective optimization problems.
• The proposed method contributes to advancing the field of multiobjective optimization algorithms.