Solving Large-Scale Multiobjective Optimization Problems With Sparse Optimal Solutions via Unsupervised Neural...

Area of Science:

• Computational Intelligence
• Optimization Theory
• Machine Learning

Background:

• Large-scale multiobjective optimization problems (LMOPs) present significant challenges due to the curse of dimensionality.
• Existing evolutionary algorithms struggle to find optimal solutions within limited evaluation budgets for LMOPs.
• Approximating the Pareto-optimal subspace can effectively reduce the search space and alleviate algorithmic difficulty.

Purpose of the Study:

• To propose an evolutionary algorithm capable of learning the Pareto-optimal subspace for solving sparse LMOPs.
• To reduce the computational complexity and improve the efficiency of evolutionary algorithms for high-dimensional optimization.
• To enhance the approximation of optimal solutions for LMOPs with a limited number of evaluations.

Main Methods:

• The proposed algorithm employs two unsupervised neural networks: a restricted Boltzmann machine and a denoising autoencoder.
• These networks collaboratively learn a sparse distribution and a compact representation of decision variables, approximating the Pareto-optimal subspace.
• Genetic operators are applied within the learned subspace, with solutions mapped back to the original search space via the neural networks.

Main Results:

• The algorithm demonstrated effectiveness in solving sparse LMOPs with 10,000 decision variables.
• Experiments were conducted on eight benchmark and eight real-world problems.
• The proposed method achieved results with a limited budget of only 100,000 evaluations.

Conclusions:

• The proposed evolutionary algorithm successfully learns the Pareto-optimal subspace to address sparse LMOPs.
• This approach significantly alleviates the difficulty associated with high-dimensional search spaces in multiobjective optimization.
• The method offers an efficient solution for complex optimization problems with a reduced number of evaluations.