Biobjective optimization problems on matroids with binary costs

Like most multiobjective combinatorial optimization problems, biobjective problems on matroids are in general intractable and their corresponding decision NP-hard. In this paper, we consider where one of the objective functions is restricted to binary cost coefficients. We show that case problem has a connected efficient set with respect natural definition neighborhood structure hence, can be solved efficiently using search approach. This is, best our knowledge, first non-trivial connectedness established. The theoretical results validated by numerical experiments minimum spanning tree (graphic matroids) knapsack cardinality constraint (uniform matroids). context problem, coloring all edges 0 green 1 red leads an equivalent want simultaneously minimize number (which defines second objective) Pareto sense.