Exactly Computing the Tail of the Poisson-Binomial Distribution

We present ShiftConvolvePoibin, a fast exact method to compute the tail of a Poisson-binomial distribution (PBD). Our method employs an exponential shift to retain its accuracy when computing a tail probability, and in practice we find that it is immune to the significant relative errors that other methods, exact or approximate, can suffer from when computing very small tail probabilities of the PBD. The accompanying R package is also competitive with the fastest implementations for computing the entire PBD.

Optimization of Carsharing Fleet Placement in Round-Trip Carsharing Service

In a round-trip carsharing system, stations must be located in such a way that allow for maximum user coverage with the least walking distance as well as offer certain degrees of flexibility for returning. Therefore, a balance must be stricken between these factors. Providing a satisfactory system can be translated into an optimization problem and belongs to an NP-hard class. In this article, a novel optimization model for the round-trip carsharing fleet placement problem, called Fleet Placement Problem (FPP), is proposed. The optimization in this work is multiobjective and its NP-hard nature is proven. Three different optimization algorithms: PolySCIP (exact method), heuristics, and NSGA-II (metaheuristic) are investigated. This work adopts three real instances for the study, instead of their abstracts where they are most commonly used. They are two instance:, in the city of Luxembourg (smaller and larger) and a much larger instance in the city of Munich. Results from each algorithm are validated and compared with solution from human experts. Superiority of the proposed FPP model over the traditional methods is also demonstrated.

A Matheuristic approach for the maximum balanced subgraph of a signed graph

A graph G=(V,E) with its edges labeled in the set {+, -} is called a signed graph. It is balanced if its set of vertices V can be partitioned into two sets V 1 and V 2 , such that all positive edges connect nodes within V 1 or V 2 , and all negative edges connect nodes between V 1 and V 2 . The maximum balanced subgraph problem (MBSP) for a signed graph is the problem of finding a balanced subgraph with the maximum number of vertices. In this work, we present the first polynomial integer linear programming formulation for this problem and a matheuristic to obtain good quality solutions in a short time. The results obtained for different sets of instances show the effectiveness of the matheuristic, optimally solving several instances and finding better results than the exact method in a much shorter computational time.

Multi-objective Optimization of Data Placement in a Storage-as-a-Service Federated Cloud

Cloud federation enables service providers to collaborate to provide better services to customers. For cloud storage services, optimizing customer object placement for a member of a federation is a real challenge. Storage, migration, and latency costs need to be considered. These costs are contradictory in some cases. In this article, we modeled object placement as a multi-objective optimization problem. The proposed model takes into account parameters related to the local infrastructure, the federated environment, customer workloads, and their SLAs. For resolving this problem, we propose CDP-NSGAII IR , a Constraint Data Placement matheuristic based on NSGAII with Injection and Repair functions. The injection function aims to enhance the solutions’ quality. It consists to calculate some solutions using an exact method then inject them into the initial population of NSGAII. The repair function ensures that the solutions obey the problem constraints and so prevents from exploring large sets of unfeasible solutions. It reduces drastically the execution time of NSGAII. Experimental results show that the injection function improves the HV of NSGAII and the exact method by up to 94% and 60%, respectively, while the repair function reduces the execution time by an average of 68%.

Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- and higher-dimensional continuous-space facility location problems when the Manhattan distance is considered. Before we propose the exact method, we start with the continuous-space single-facility location problem and obtain the global minimizer for the problem using a statistical approach. Then, an exact method is developed to determine the globally optimal solution for the two- and higher-dimensional continuous-space facility location problem, which is different from the previous clustering algorithms. Based on the newly investigated properties of the minimizer, we extend it to multi-facility problems and transfer the continuous-space facility location problem to the discrete-space location problem. To illustrate the effectiveness and efficiency of the proposed method, several instances from a benchmark are provided to compare the performances of different methods, which illustrates the superiority of the proposed exact method in the decision-making of the continuous-space facility location problems.

Cannons and sparrows II: the enhanced Bernoulli exact method for determining statistical significance and effect size in the meta-analysis of k 2 × 2 tables

Background The use of meta-analysis to aggregate the results of multiple studies has increased dramatically over the last 40 years. For homogeneous meta-analysis, the Mantel–Haenszel technique has typically been utilized. In such meta-analyses, the effect size across the contributing studies of the meta-analysis differs only by statistical error. If homogeneity cannot be assumed or established, the most popular technique developed to date is the inverse-variance DerSimonian and Laird (DL) technique (DerSimonian and Laird, in Control Clin Trials 7(3):177–88, 1986). However, both of these techniques are based on large sample, asymptotic assumptions. At best, they are approximations especially when the number of cases observed in any cell of the corresponding contingency tables is small. Results This research develops an exact, non-parametric test for evaluating statistical significance and a related method for estimating effect size in the meta-analysis of k 2 × 2 tables for any level of heterogeneity as an alternative to the asymptotic techniques. Monte Carlo simulations show that even for large values of heterogeneity, the Enhanced Bernoulli Technique (EBT) is far superior at maintaining the pre-specified level of Type I Error than the DL technique. A fully tested implementation in the R statistical language is freely available from the author. In addition, a second related exact test for estimating the Effect Size was developed and is also freely available. Conclusions This research has developed two exact tests for the meta-analysis of dichotomous, categorical data. The EBT technique was strongly superior to the DL technique in maintaining a pre-specified level of Type I Error even at extremely high levels of heterogeneity. As shown, the DL technique demonstrated many large violations of this level. Given the various biases towards finding statistical significance prevalent in epidemiology today, a strong focus on maintaining a pre-specified level of Type I Error would seem critical. In addition, a related exact method for estimating the Effect Size was developed.

On the spleen diet in pulmonary tuberculosis

Pulmonary tuberculosis with its most complex symptom complex and various effects of tuberculosis toxaemia on almost all major organs of the human body, although it has created its own huge therapy problem, however, to date it has not yet found its definite and exact method of treatment. Among a number of various methods of treatment of pulmonary tuberculosis only collapsotherapy, and mainly artificial pneumothorax, has recently managed, indeed, to take a rather solid, solid and almost true place in the problem of tuberculosis therapy. Some limited use of pneumothorax continues to encourage a number of clinicians and researchers, both in your Union and in Western Europe, to look for more and more new and more correct ways to treat tuberculosis in general and pulmonary tuberculosis in particular.

SELECTION OF THE OPTIMUM ROUTE IN AN EXTENDED TRANSPORTATION NETWORK UNDER UNCERTAINTY

Relevance. For a given values set of extensive transport network sections lengths an exact method has been developed for finding optimal routes. The method provides an approximate solution when the initial data - are random variables with known distribution laws, as well as if these data are not clearly specified. Fora special case with a normal distribution of the numerical characteristics of the network, solution is brought to the final results. Method. An exact method of deterministic routing is proposed, which gives an approximate solution in case of random initial data. The method is extended to the case when the initial data are described in theory of fuzzy sets terms. The problem of stability assessing of solutions to problems of control the theory under conditions of uncertainty of initial data is considered. Results. A method of optimal routes finding is proposed when the initial data are deterministic or random variables with known distribution densities. A particular case of a probabilistic - theoretical description of the initial data is considered when can be obtained a simple solution of problem. Proposed method for obtaining an approximate solution in the general case for arbitrary distribution densities of random initial data. The situation is common when the initial data are not clearly defined. A simple computational procedure proposed for obtaining a solution. A method for stability assessing of solutions to control problems adopted under conditions of uncertainty in the initial data, is considered.