The Hitting Set Problem and Evolutionary Algorithmic Techniques with ad-hoc Viruses (HEAT-V)

Introduction. The Weighted Minimum Hitting Set Problem (WMHSP) and the standard Minimum Hitting Set Problem (MHSP), are combinatorial problems of great interest for many applications. Although, these problems lend themselves quite naturally to an evolutionary approach. To our knowledge, there are no significant results of evolutionary algorithms applied to either the WMHSP or the MHSP, except for the results contained in Cutello et al., (2002). We will now formally introduce the optimization problem and recall that the corresponding decision problem is NP-complete – Instance: A finite set U, with | U |= m; a collection of sets C = {S1, . . . , Sn} such that Si ⊆ U ∀i = {1, . . . , n}. A weight function w : U → +. – Solution: A hitting set for C, that is to say H ⊆ U such that H ∩ Si = ∅, ∀i = 1, . . . , n. – Optimal Solution: a hitting set H such that w(H) = ∑ s∈H w(s) is minimal.