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

Abstract

Decomposition-based evolutionary multi-objective optimization algorithms decompose a multi-objective optimization problem into subproblems using a set of predefined reference points. The convergence is guaranteed by optimizing the single-objective or simplified multi-objective subproblems while the diversity is handled by the evenly distributed reference points. Nevertheless, studies have shown that the performance of decomposition-based algorithms is strongly dependent on the Pareto front shapes due to unadaptable reference points and subproblem formulation. In this paper, we investigate the causes from three aspects and propose a learning-to-decompose paradigm consisting of a learning module and an optimization module to address these issues. Specifically, given the current non-dominated solutions from the optimization module, which can be any decomposition-based multi-objective optimizer, the learning module learns an analytical model that characterizes the estimated PF. Thereafter, useful information are extracted from the learned model to guide the decomposition in the optimization module. In particular, we utilize the learned model to sample reference points compliant to the PF and formulate subproblems with appropriate contours and search directions according to the current status. We integrate the learning-todecompose paradigm with two most popular decompositionbased evolutionary optimizers, i.e., MOEA/D and NSGA-III, and compare them with several state-of-the-art adaptive methods. The comprehensive experiments validate the effectiveness and robustness of the proposed paradigm on 14 test problems with various Pareto front shapes.

Visualisation of Pareto Front Approximation: A Short Survey and Empirical Comparisons

“…10, the performance of NSGA-III and MOEA/D are not as promising as HypE and IBEA. This can be explained as the distribution of weight vectors used in NSGA-III and MOEA/D does not fit the PF shapes of DTLZ5 and DTLZ7 [47,48]. Note that such observations are not clear when using MDS for visualisation as discussed in Section 3.1.1.…”

Which Surrogate Works for Empirical Performance Modelling? A Case Study with Differential Evolution

“…Gaussian process (GP), random forest (RF), support vector machine for regression (SVR), radial basis function networks (RBFN), are considered as the candidates for surrogate modelling of DE's empirical performance. Note that these regression algorithms have been widely used in the model-based PO in the algorithm configuration literature [34][35][36].…”

AREA: An adaptive reference-set based evolutionary algorithm for multiobjective optimisation

“…For example, a linear interpolation model was used in an approach specifically for problems with discontinuous PFs [41]. Wu et al introduced a Gaussian process regression model to aid reference sampling [37]. Similarly, an incremental learning model was employed for reference adaptation [9].…”