Exponential neighborhood search for consecutive block minimization

Abstract

AbstractGiven binary matrix , the term refers to the matrix obtained by permuting the columns of according to permutation . A 1‐block in a binary matrix is any maximal sequence of consecutive 1s situated on the same row. Given binary matrix , consecutive block minimization (CBM) is a combinatorial optimization problem that seeks a permutation of columns such that the number of 1‐blocks in is minimum. Since CBM is NP‐hard, we solve it by iterating local search where the neighborhood is exponential in the instance size and is always constructed in the vicinity of the best current solution. Seeking a local optimum in the exponential neighborhood amounts to solving a small traveling salesman problem (TSP). Instead, we obtain a good near local optimal solution using an implementation of Lin–Kernighan heuristic. Our method is compared with a recently published iterated local search metaheuristic as well as with two TSP solvers. The comparison shows that the proposed method provides better quality solutions.