Kernels in linear algebra are memory-bounded routines and their performance is dependent on the sparsity pattern of the matrix operands. Since memory is many times slower than arithmetic operations these kernels tend to exploit small fractions of the peak performance of modern architectures such as GPUs. In this sense, the improvement of the storage of the matrices to reduce the memory accesses is a main line of work.The problem of finding an exact solution for the best permutation of a matrix is computationally prohibitive thus it is interesting to explore metaheuristic approaches. Previous work found good results with evolutionary algorithms but with high execution time. In this context, it is compelling to explore trajectory-based metaheuristics as a way to reduce execution time since they require evaluating only one solution per iteration. In this work, we continue the efforts and present heuristics based on VNS and ILS which outperform the evolutionary algorithm in the majority of the instances evaluating half of the solutions.