We propose general separation procedures for generating cuts for the stable set polytope, inspired by a procedure by Rossi and Smriglio and applying a lifting method by Xavier and Campêlo. In contrast to existing cut-generating procedures, ours generate both rank and non-rank valid inequalities, hence they are of a more general nature than existing methods. This is accomplished by iteratively solving a lifting problem, which consists of a maximum weighted stable set problem on a smaller graph. Computational experience on DIMACS benchmark instances shows that the proposed approach may be a useful tool for generating cuts for the stable set polytope. 1 This work has been partially supported by the Stic/AmSud joint program by CAPES (Brazil), CNRS and MAE (France), CONICYT (Chile) and MINCYT (Argentina) -project 13STIC-05-and the Pronem program by FUNCAP/CNPq (Brazil) -project ParGO.
Artículo de publicación ISISalmon farming in Chile constitutes one of the nation's principal food exporting sectors. In the seawater stage, one of the most
important in the farm production chain, salmon are cultivated in floating cages fitted with nets that hold the fish during the entire
grow-out process. The maintenance of the cage nets is carried out at land-based facilities. This article reports on the creation of
an integer programming tool for grow-out centres that optimizes resource use, improves planning and generates economic
evaluations for supporting analysis and decision-making relating to the maintenance, repair and periodic changing of cage nets.
The tool prototype was tested in a single operating area of one of Chile's largest salmon farmers. The results demonstrated a
reduction in net maintenance costs of almost 18%, plus a series of important qualitative benefits. Implementation of the tool by
farm operators awaits the end of the current crisis in the industry
One of the logistical challenges in planning a population census is determining which dwellings each enumerator must visit within a census tract. This is known as the dwelling segmentation problem, which generally includes a set of constraints on the enumerators' assigned routes and various criteria regarding the homogeneity and uniformity of the segmentation solutions. In this work, we present a computational approach for this problem, which represents an improvement over manual methods and existing software. The resulting method was successfully applied to the Province of Buenos Aires in the 2010 Argentinian census.
A solution strategy based on integer linear programming models has been developed for leaf sweeping operations in the Argentine city of Trenque Lauquen. The aim is to achieve efficiency in the assignment of sweepers to city blocks, the identification of leaf bag deposit points and the routes to be followed by collection trucks for leaf bag pickup. Previous to this strategy, sweeper assignments were improvised and inefficient, with blocks often left unswept. Furthermore, no method was available for accurately determining the number of sweepers needed to ensure either full coverage of all city zones within the working day or a balanced work load distribution across all sweepers. Application of the solution strategy by the city has resulted in efficient definitions of sweeper requirements while optimizing sweeper assignments such that all blocks are covered. Once the strategy is fully implemented, the number of bag deposit points under the manual definitions should be reduced by roughly one-half and the total travel distance of the truck routes, modelled as an asymmetric travelling salesman problem, should be cut by 10–15% with the consequent savings in time, vehicle use and fuel consumption.
We consider an optimization problem posed by an actual newspaper company, which consists of computing a minimum length route for a delivery truck, such that the driver only stops at street crossings, each time delivering copies to all customers adjacent to the crossing. This can be modeled as an abstract problem that takes an unweighted simple graph G = (V, E) and a subset of edges X and asks for a shortest cycle, not necessarily simple, such that every edge of X has an endpoint in the cycle. We show that the decision version of the problem is strongly NP-complete, even if G is a grid graph. Regarding approximate solutions, we show that the general case of the problem is APX-hard, and thus no PTAS is possible unless P = NP. Despite the hardness of approximation, we show that given any α-approximation algorithm for metric TSP, we can build a 3α-approximation algorithm for our optimization problem, yielding a concrete 9/2-approximation algorithm. The grid case is of particular importance, because it models a city map or some part of it. A usual scenario is having some neighborhood full of customers, which translates as an instance of the abstract problem where almost every edge of G is in X. We model this property as |E−X| = o(|E|), and for these instances we give a (3/2 + ε)-approximation algorithm, for any ε > 0, provided that the grid is sufficiently big.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.