Restricted Strip Covering and the Sensor Cover Problem

Given a set of objects with durations (jobs) that cover a base region, can we schedule the jobs to maximize the duration the original region remains covered? We call this problem the sensor cover problem. This problem arises in the context of covering a region with sensors. For example, suppose you wish to monitor activity along a fence by sensors placed at various fixed locations. Each sensor has a range and limited battery life. The problem is to schedule when to turn on the sensors so that the fence is fully monitored for as long as possible. This one dimensional problem involves intervals on the real line. Associating a duration to each yields a set of rectangles in space and time, each specified by a pair of fixed horizontal endpoints and a height. The objective is to assign a position to each rectangle to maximize the height at which the spanning interval is fully covered. We call this one dimensional problem restricted strip covering. If we replace the covering constraint by a packing constraint, the problem is identical to dynamic storage allocation, a scheduling problem that is a restricted case of the strip packing problem. We show that the restricted strip covering problem is NP-hard and present an O(log log n)-approximation algorithm. We present better approximations or exact algorithms for some special cases. For the uniform-duration case of restricted strip covering we give a polynomial-time, exact algorithm but prove that the uniform-duration case for higher-dimensional regions is NP-hard. Finally, we consider regions that are arbitrary sets, and we present an O(log n)-approximation algorithm.Comment: 14 pages, 6 figure

Computer-aided programming for multiprocessing systems

As both the number of processors and the complexity of problems to be solved increase, programming multiprocessing systems becomes more difficult and error-prone. This report discusses parallel models of computation and tools for computer-aided programming (CAP). Program development tools are necessary since programmers are not able to develop complex parallel programs efficiently. In particular, a CAP tool, named Hypertool, is described here. It performs scheduling and handles the communication primitive insertion automatically so that many errors are eliminated. It also generates the performance estimates and other program quality measures to help programmers in improving their algorithms and programs. Experiments have shown that up to a 300% performance improvement can be achieved by computer-aided programming

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Production planning in 3D printing factories

[EN] Production planning in 3D printing factories brings new challenges among which the scheduling of parts to be produced stands out. A main issue is to increase the efficiency of the plant and 3D printers productivity. Planning, scheduling, and nesting in 3D printing are recurrent problems in the search for new techniques to promote the development of this technology. In this work, we address the problem for the suppliers that have to schedule their daily production. This problem is part of the LONJA3D model, a managed 3D printing market where the parts ordered by the customers are reorganized into new batches so that suppliers can optimize their production capacity. In this paper, we propose a method derived from the design of combinatorial auctions to solve the nesting problem in 3D printing. First, we propose the use of a heuristic to create potential manufacturing batches. Then, we compute the expected return for each batch. The selected batch should generate the highest income. Several experiments have been tested to validate the process. This method is a first approach to the planning problem in 3D printing and further research is proposed to improve the procedure.This research has been partially financed by the project: “Lonja de Impresión 3D para la Industria 4.0 y la Empresa Digital (LONJA3D)” funded by the Regional Government of Castile and Leon and the European Regional Development Fund (ERDF, FEDER) with grant VA049P17.De Antón, J.; Senovilla, J.; González, J.; Acebes, F.; Pajares, J. (2020). Production planning in 3D printing factories. International Journal of Production Management and Engineering. 8(2):75-86. https://doi.org/10.4995/ijpme.2020.12944OJS758682Canellidis, V., Giannatsis, J., & Dedoussis, V. (2013). Efficient parts nesting schemes for improving stereolithography utilization. CAD Computer Aided Design, 45(5), 875-886. https://doi.org/10.1016/j.cad.2012.12.002Chergui, A., Hadj-Hamou, K., & Vignat, F. (2018). 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