Upper bounds and exact algorithms for -dispersion problems

Constrained 0–1 quadratic programming: Basic approaches and extensions

“…This problem, given a complete weighted undirected graph G with node set N and an integer p 6 n, calls for a subgraph of p nodes such that the sum of the costs of the edges internal to the subgraph is maximized, and can be formulated as the QP with F given by (4) and the cost of each edge (i, j) by c ij + c ji . This problem is discussed in [25].…”

Demand Point Aggregation Analaysis for Location Models

“…Díaz-Báňez et al (2005) computed shortest paths for transportation of hazardous material in continuous spaces. They proposed an approximate algorithm based on the bisection method and reduced the optimization problem to a decision problem, where one needs to compute the shortest path such that the minimum distance to the demand points is not smaller than a certain amount r. Pisinger (2006) present an exact algorithm for finding a number of fast upper bounds for P -dispersion problems in which these bounds can be derived in O.n/ time. Bell (2006) considered mixed rout strategies for the risk-averse shipment of hazardous materials.…”

“…This heuristic exploits the network flow structure at both levels to overwhelm the difficulty and instability of the bilevel integer programming model. Pisinger (2006) present an exact algorithm for finding a number of fast upper bounds for P-dispersion problems in which these bounds can be derived in O.n/ time. Bell (2006) considered mixed rout strategies for the Risk-Averse shipment of hazardous materials.…”

A general heuristic for vehicle routing problems

“…A greedy heuristic for this problem running in O(n 3 ) was presented in [37] together with a more time-consuming exact algorithm. If n is large, it may be too time-consuming even to compute the whole matrix (r ij ) and one will instead choose related variables according to some heuristics.…”