RCSP are typically formulated as mixed integer problem. More than half of the researchers use a set covering problem formulation (SCP, 63 articles). The second most populat problem formulation is the related set partitioning problem (SPP, 25 articles). Both models represent a path-flow formulatio...
N. Bilal, P. Galinier and F. Guibault, "A New Formulation of the Set Covering Problem for Metaheuristic Approaches," International Scholarly Research Notices, pp.1-10, April 2013.N. Bilal, P. Galinier, and F. Guibault. A new formulation of the set covering problem for metaheuristic ...
As Fig. 4 shows, the set covering problem formulation (SCP) is by far the most popular model formulation among RCSP researchers: around 80% of the publications after 2000 use a variant of it. The set partitioning problem (SPP) is closely related to the SCP and the second most used ...
Instead, the restrictions imposed on the variables of the extended formulation are accounted for with respect to their impact in the set covering, packing or partitioning constraints. Based on this impact, the objective coefficients of the pricing problem are modified to favour columns that comply ...
We present a GRASP algorithm to Unicost Set Covering Problem, a special case of the Set Covering Problem where no dis- tinction is made between covering sets. The most signifi- cant contribution of the algorithm is the incorporation of a local improvement procedure based on the heuristics to ...
This paper proposes a covering problem in a discrete space where the covering radius is unknown and will be determined according to the distances among existing facilities and candidate points. On the other hand, cost of servicing is considered in our formulation as an important factor for allocati...
Let me take maximum coverage problem as an example, which given a set system with a number , we ask what is the largest amount of elements we can cover using sets. Theorem. Greedy covering gives a -approximation to the maximum coverage problem. Proof. Let be the number of elements newly...
This formulation allows us to transition from a fractional to an integer solution while managing the distribution of probabilities according to the given functionf. The expected value of\(SOL_{algo}\)can be calculated as follows: $$\begin{aligned} \mathbb {E}(SOL_{algo}) & = \sum _i \...
We examine a mixed-integer bilevel programming (MIBLP) formulation for a competitive set covering problem, assuming that both players seek to maximize their profit. This class of problems arises in several fields, including non-cooperative product introduction and facility location games. We develop ...
The set covering problem (SCP) is a well-known combinatorial optimization problem. This paper presents a GRASP algorithm to solve a special SCP case known in the literature as the unicost set covering problem. The algorithm incorporates a local improvement procedure based on the heuristics to solv...