A hybrid genetic algorithm for computing the float of an activity in networks with imprecise durations

This paper deals with two relevant problems: calculating bounds on the float and determining the type of criticality, in the network with imprecise durations which are represented by means of intervals or fuzzy intervals. There exist different types of critical activity in the network with interval durations; an activity can be either necessarily noncritical, or necessarily critical, or possibly critical at the time. Lemmas, provided in this paper, elaborate on the connections between the notion of critical paths and critical activities. The minimal float problem is NP-hard while the maximal float problem is polynomial. Due to difficulty of obtaining the lower bound on the floats in medium and large-scaled networks, a hybrid genetic algorithm (HGA) is developed. The proposed HGA incorporates a neighbourhood search (NS) into a basic genetic algorithm that enables the algorithm to perform genetic search over the subspace of local optimum. Then the results are extended to network with fuzzy durations.