An Evolutionary Algorithm for Large-Scale Sparse Multiobjective Optimization Problems

Abstract

In the last two decades, a variety of different types of multi-objective optimization problems (MOPs) have been extensively investigated in the evolutionary computation community. However, most existing evolutionary algorithms encounter difficulties in dealing with MOPs whose Pareto optimal solutions are sparse (i.e., most decision variables of the optimal solutions are zero), especially when the number of decision variables is large. Such large-scale sparse MOPs exist in a wide range of applications, for example, feature selection that aims to find a small subset of features from a large number of candidate features, or structure optimization of neural networks whose connections are sparse to alleviate overfitting. This paper proposes an evolutionary algorithm for solving large-scale sparse MOPs. The proposed algorithm suggests a new population initialization strategy and genetic operators by taking the sparse nature of the Pareto optimal solutions into consideration, to ensure the sparsity of the generated solutions. Moreover, this paper also designs a test suite to assess the performance of the proposed algorithm for large-scale sparse MOPs. Experimental results on the proposed test suite and four application examples demonstrate the superiority of the proposed algorithm over seven existing algorithms in solving large-scale sparse MOPs.

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

“…As reported in [42], a hybrid representation of solution is effective for solving sparse LMOPs, where each solution is represented by a binary vector denoting the mask and a real vector denoting the decision variables. Following this idea, the proposed MOEA/PSL adopts RBM and DAE to learn the Pareto optimal subspace from the solutions with hybrid representation.…”

“…Four state-of-the-art MOEAs are selected as baselines in the experiments, namely, LMEA [8], WOF-SMPSO [11], MaOEA-IT [41], and SparseEA [42]. LMEA is a divide-and-conquer MOEA tailored for LMOPs, which divides the decision variables into convergence-related variables and diversity-related variables and optimizes them separately.…”

“…For benchmark problems, the population size is set to 100 and the number of function evaluations is set to 100 × D, where D denotes the number of decision variables. Due to the computationally expensive objectives of real-world problems, the population size is set to 50 as suggested in [42]; besides, the number of function evaluations is set to 2.0 × 10 4 , 1.0 × 10 5 and 2.0 × 10 5 for problems with approximately 1000, 5000 and 10000 real variables, and set to 1.0 × 10 4 , 5.0 × 10 4 and 1.0×10 5 for problems with approximately 1000, 5000 and 10000 binary variables.…”

“…The sparse multi-objective test suite [42] is adopted to test the performance of the compared MOEAs, which contains eight benchmark problems SMOP1-SMOP8 with scalable number of decision variables. These problems are characterized by multi-modality, deception, epistasis, and low intrinsic dimensionality, posing various difficulties for MOEAs to obtain a set of sparse solutions.…”

Evolutionary Computation for Large-scale Multi-objective Optimization: A Decade of Progresses

“…There are also some attempts to customize search operators to improve the scalability of certain MOEAs [96,97] . The work in [98] focuses on a specific type of large-scale problems named large-scale sparse MOPs, where most decision variables of the optimal solutions are zero.…”