Learning to Decompose: A Paradigm for Decomposition-Based Multiobjective Optimization

The decomposition-based evolutionary multiobjective optimization algorithm has become an increasingly popular choice for a posteriori multiobjective optimization. However, recent studies have shown that their performance strongly depends on the Pareto front shapes. This can be attributed to the decomposition method, of which the reference points and subproblem formulation settings are not well adaptable to various problem characteristics. In this paper, we develop a learning-to-decompose paradigm that adaptively sets the decomposition method by learning the characteristics of the estimated Pareto front. Specifically, it consists of two inter-dependent parts, i.e., a learning module and an optimization module. Given the current non-dominated solutions from the optimization module, the learning module periodically learns an analytical model of the estimated Pareto front. Thereafter, useful information is extracted from the learned model to set the decomposition method for the optimization module, including: 1) reference points compliant with the Pareto front shape; and 2) subproblem formulations whose contours and search directions are appropriate for the current status. Accordingly, the optimization module, which can be any decomposition-based evolutionary multiobjective optimization algorithm in principle, decomposes the multiobjective optimization problem into a number of subproblems and optimizes them simultaneously. To validate our proposed learning-to-decompose paradigm, we integrate it with two decomposition-based evolutionary multiobjective optimization algorithms, and compare them with four state-of-the-art algorithms on a series of benchmark problems with various Pareto front shapes.