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.
Bibliographical noteThis work was supported in part by the Hong Kong Research Grants Council (RGC) General Research Fund under Grant 9042038 (CityU 11205314), in part by the ANR/RCC Joint Research Scheme through the Hong Kong RGC and the France National Research Agency under Project A-CityU101/16, in part by the Royal Society under Grant IEC/NSFC/170243, and in part by the Chinese National Science Foundation of China under Grant 61672443 and Grant 61473241.
- evolutionary computation
- Gaussian process (GP) regression
- multiobjective optimization
- reference points generation