Computational Complexity and ILP Models for Pattern Problems in the Logical Analysis of Data

Logical Analysis of Data is a procedure aimed at identifying relevant features in data sets with both positive and negative samples. The goal is to build Boolean formulas, represented by strings over {0,1,-} called patterns, which can be used to classify new samples as positive or negative. Since a data set can be explained in alternative ways, many computational problems arise related to the choice of a particular set of patterns. In this paper we study the computational complexity of several of these pattern problems (showing that they are, in general, computationally hard) and we propose some integer programming models that appear to be effective. We describe an ILP model for finding the minimum-size set of patterns explaining a given set of samples and another one for the problem of determining whether two sets of patterns are equivalent, i.e., they explain exactly the same samples. We base our first model on a polynomial procedure that computes all patterns compatible with a given set of samples. Computational experiments substantiate the effectiveness of our models on fairly large instances. Finally, we conjecture that the existence of an effective ILP model for finding a minimum-size set of patterns equivalent to a given set of patterns is unlikely, due to the problem being NP-hard and co-NP-hard at the same time.

Pipe-Lining dynamic programming processes in order to synchronize energy and production and consumption

Synchronizing heterogeneous processes remains a difficult issue in Scheduling area. Related ILP models are in trouble, because of large gaps induced by rational relaxation. We choose here to deal with it while emulating the interactions which take place between the various players of such heterogeneous processes, and propose a pipe-line decomposition of a dynamic programming process designed in order to schedule energy production and energy consumption.

Finding efficient solutions in the interval multi-objective linear programming models

The aim of our paper is to obtain efficient solutions to the interval multi- objective linear programming (IMOLP) models. In this paper, we propose a new method to determine the efficient solutions in the IMOLP models by using the expected value and variance operators (EVV operators). First, we define concepts of the expected value, variance, and uncertainty distributions, and present some properties of the EVV operators. Then, we introduce the IMOLP model under these operators. An IMOLP model consist of separate ILPs, but using the EVV operators and the uncertainty distributions, it can be converted into the interval linear programming (ILP) models under the EVV operators (EVV-ILP model). We show that optimal solutions of the EEV-ILP model are the efficient solutions of IMOLP models with uncertainty variables. The proposed method, which is called EVV, is not hard to solve. Finally, Monte Carlo simulation is used to show its the performance assessment.

Spectrum-aware shared protection (SASP) algorithm for cognitive radio networks

Cognitive radio (CR) has become a key technology for addressing spectrum scarcity. In CR networks, spectrum access should not interfere the incumbent networks. Due to the requirement above, common control channel approaches, which are widely used in traditional multichannel environments, may face serious CR long-time blocking problem and control channel saturation problem. Although channel-hopping-based approaches can avoid these two problems, existing works still have significant drawbacks including long time-to-rendezvous, unbalance channel loading, and low channel utilization. This paper tends to the issue of range mindful survivable methodologies with disappointment likelihood limitations under static activity in adaptable transfer speed optical systems. The joint disappointment likelihood amongst essential and reinforcement ways must be beneath the most extreme fair joint disappointment likelihood for each activity request. It creates whole number direct program (ILP) models for committed way security and shared-way assurance with a specific end goal to limit the aggregate number of recurrence spaces expended, and furthermore propose a range mindful devoted insurance (SADP) calculation and a range mindful shared security (SASP) calculation. This demonstrates the ILP show arrangements devour least number of recurrence spaces, however prompt higher normal joint disappointment likelihood contrasted with the SADP and SASP calculations. In addition, both the SADP and SASP calculations accomplish a superior execution as far as aggregate number of recurrence openings expended when contrasted with a customary devoted way insurance calculation and an ordinary shared-way assurance calculation, separately, however prompt higher normal joint disappointment likelihood.

Optimal selective logging regime and log landing location models: a case study in the Amazon forest

ABSTRACT Reduced-impact logging is a well known practice applied in most sustainable forest management plans in the Amazon. Nevertheless, there are still ways to improve the operational planning process. Therefore, the aim of this study was to create an integer linear programming (ILP) to fill in the knowledge gaps in the decision support system of reduced impact logging explorations. The minimization of harvest tree distance to wood log landing was assessed. Forest structure aspects, income and wood production were set in the model, as well as the adjacency constraints. Data are from a dense ombrophylous forest in the western Brazilian Amazon. We applied the phytosociological analysis and BDq method to define the selective logging criteria. Then, ILP models were formulated to allow the application of the constraints. Finally, 32 scenarios (unbalanced forest, UF, and balanced forest, BF) were generated and compared with real executed plans (RE). Robust results were achieved and the expected finding of each scenario was met. The feasibility to integrate ILP models in uneven-aged forest management projects was endorsed. Consequently, the UF and BF scenarios tested were efficient and concise, introducing new advances for forest management plans in the Amazon. The proposed models have a high potential to improve the selective logging activities in the Amazon forest.