Scatter search for the profile minimization problem

We study the problem of minimizing the profile of a graph and develop a solution method by following the tenets of scatter search. Our procedure exploits the network structure of the problem and includes strategies that produce a computationally efficient and agile search. Among several mechanisms, our search includes path relinking as the basis for combining solutions to generate new ones. The profile minimization problem (PMP) is NP‐Hard and has relevant applications in numerical analysis techniques that rely on manipulating large sparse matrices. The problem was proposed in the early 1970s but the state‐of‐the‐art does not include a method that could be considered powerful by today's computing standards. Extensive computational experiments show that we have accomplished our goal of pushing the envelope and establishing a new standard in the solution of the PMP.