Browsing by Subject "Column generation"

Now showing 1 - 3 of 3

Open Access
Generalized column generation for linear programming
(Institute for Operations Research and the Management Sciences (INFORMS), 2002) Oğuz, O.
Column generation is a well-known and widely practiced technique for solving linear programs with too many variables or constraints to include in the initial formulation explicitly. Instead, the required column information is generated at each iteration of the simplex algorithm. This paper shows that, even if the number of variables is low enough for explicit inclusion in the model with the available technology, it may still be more efficient to resort to column generation for some class of problems.
Open Access
Mathematical formulations and approaches to the brain tumour resection problem
(2024-07) İlhan, Sarp Bora
Brain tumors are the fifth most common tumors and the first line of treatment for a brain tumor is surgical resection. However, resecting an entire tumour mass may raise a problem when the tumour merges with healthy cells or it has formed around the brain region that is involved in vital functions. Our aim is to capture the results of resecting tumourous parts in these complex situations and selecting the tumour volume that will have the least disruption on the brain functionality. We propose three measures, namely, global efficiency, concurrent demand satisfaction and congestion, to quantify the brain functionality. We develop critical node detection based formulation for the first and multicommodity flow based models for other measures. We develop Benders decomposition and column generation algorithms to solve the mathematical models. We compare the algorithm performances with model formulations. We use a diverse range of instances to conduct detailed comparisons. Finally, we investigate the decision outputs and how they change in different cases.
Open Access
The network design problem with relays
(Elsevier, 2007) Cabral, E. A.; Erkut, E.; Laporte, G.; Patterson, R. A.
The network design problem with relays (NDPR) is defined on an undirected graph G = (V, E, K), where V = {1, ..., n} is a vertex set, E = {(i, j) : i, j ∈ V, i < j} is an edge set. The set K = {(o(k), d(k))} is a set of communication pairs (or commodities): o(k) ∈ V and d(k) ∈ V denote the origin and the destination of the kth commodity, respectively. With each edge (i, j) are associated a cost cij and a length dij. With vertex i is associated a fixed cost fi of locating a relay at i. The NDPR consists of selecting a subset over(E, -) of edges of E and of locating relays at a subset over(V, -) of vertices of V in such a way that: (1) the sum Q of edge costs and relay costs is minimized; (2) there exists a path linking the origin and the destination of each commodity in which the length between the origin and the first relay, the last relay and the destination, or any two consecutive relays does not exceed a preset upper bound λ. This article develops a lower bound procedure and four heuristics for the NPDR. These are compared on several randomly generated instances with |V| ≤ 1002 and |E| ≤ 1930.