By Giorgio Ausiello, Giuseppe F. Italiano, Luigi Laura, Umberto Nanni, Fabiano Sarracco (auth.), A. Ridha Mahjoub, Vangelis Markakis, Ioannis Milis, Vangelis Th. Paschos (eds.)
This e-book constitutes the completely refereed post-conference lawsuits of the second one overseas Symposium on Combinatorial Optimization, ISCO 2012, held in Athens, Greece, in April 2012. The 37 revised complete papers provided including four invited talks have been conscientiously reviewed and chosen from ninety four usual and 30 brief submissions. They current unique examine on all elements of combinatorial optimization, starting from mathematical foundations and concept of algorithms to computational reports and useful applications.
Read or Download Combinatorial Optimization: Second International Symposium, ISCO 2012, Athens, Greece, April 19-21, 2012, Revised Selected Papers PDF
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Sample text
N) is visited by at most uj paths whose overall capacity is at least rj , with the objective of minimizing the overall cost of the paths. For each k = 1, . . , the number of train units of type k that execute the trips sequence corresponding to P . Moreover, for each k = 1, . . , p and j = 1, . . , n, let Pjk ⊆ P k denote the subcollection of paths in P k that visit node j. The ILP model is the following: p ck xP , min (1) k=1 P ∈P k xP ≤ dk , k = 1, . . , p, (2) sk xP ≥ rj , j = 1, . . , n, (3) P ∈P k p k=1 P ∈Pjk Train Unit Assignment 27 p xP ≤ uj , j = 1, .
P and j = 1, . . , n, let Pjk ⊆ P k denote the subcollection of paths in P k that visit node j. The ILP model is the following: p ck xP , min (1) k=1 P ∈P k xP ≤ dk , k = 1, . . , p, (2) sk xP ≥ rj , j = 1, . . , n, (3) P ∈P k p k=1 P ∈Pjk Train Unit Assignment 27 p xP ≤ uj , j = 1, . . , n, (4) xP ≥ 0, integer , k = 1, . . , p, P ∈ P k . (5) k=1 P ∈Pjk The objective is to minimize the cost of the train units used. Constraints (2) require to respect the number of train units available for each type.
Otherwise, ⎧ ⎫ fj (k) k−1 ⎨ ⎬ P j = wj ∈ Rp+ : 2wj + wj ≥ 2, k = gj + 1, . . , tj + 1 . e. we want to minimize the number of train units used. For this formulation, we consider a slightly different graph representation of the problem given by a directed complete multigraph G = (V, A). The node set V corresponds to the set of trips, and the arc set A is partitioned into p subsets A1 , . . , Ap , where arc subset Ak is associated with train units of type k (k = 1, . . , p) and the simple directed graph Gk = (V, Ak ) is complete.