A Decomposition-Based Multiobjective Evolutionary Algorithm for Sparse Reconstruction

Sparse reconstruction is an important method aiming at obtaining an approximation to an original signal from observed data. It can be deemed as a multiobjective optimization problem for the sparsity and the observational error terms, which are considered as two conflicting objectives in evolutionary algorithm. In this paper, a novel decomposition based multiobjective evolutionary algorithm is proposed to optimize the two objectives and reconstruct the original signal more exactly. In our algorithm, a sparse constraint specific differential evolution is designed to guarantee that the solution remains sparse in the next generation. In addition, a neighborhood-based local search approach is proposed to obtain better solutions and improve the speed of convergence. Therefore, a set of solutions is obtained efficiently and is able to closely approximate the original signal.