Abstract In this paper we introduce , a global optimization solver specifically designed for (continuous) polynomial programming problems with box-constrained variables. Written entirely in , is based on the Reformulation-Linearization (Sherali and Tuncbilek in J Glob Optim 103:225–249, 1992). We present a description of the main characteristics of along with a thorough analysis of the impact on its performance of various enhancements discussed in the literature, such as bound tightening and SDP cuts. We also present a comparative study with three of the main state-of-the-art global optimization solvers: , and .

SUMMARY Nowadays, parallel architectures are changing so fast that there is a need for scalable and efficient tools to analyze and predict the performance of parallel applications. Analytical models are proved to be a useful approximation for characterizing parallel algorithms, but developing accurate analytical models is a hard issue, and, in general, they provide coarse performance predictions due to their intrinsic lack of accuracy. In this paper, we describe in detail the Tools for Instrumentation and Analysis (TIA) framework, an easy‐to‐use tool that automatically obtains accurate performance models by means of analytical expressions. This framework automatizes most of its internal tasks, reducing opportunities for human error, and it only requires the user to focus on the metrics and execution parameters that might influence the performance, those that should be considered in the modeling process. Its main advantage over other tools is that TIA uses model selection techniques that allow the automation of the modeling process. As a case of study, the use of TIA to obtain analytical models of different implementations of the broadcast collective communication in a cluster of multicores is shown. The results obtained by TIA are evaluated and compared with theoretical approaches based on the LogGP model. Copyright © 2013 John Wiley & Sons, Ltd.

The TIA modeling framework provides analytical models of the performance of parallel applications. The resulting models are obtained using model selection techniques and are accurate enough for various purposes. Its main drawback is that the completion time depends on the number of candidate models and, in some situations, it becomes critical. In this work, a genetic algorithm is proposed for reducing the time for searching of the best candidate model. The use of this genetic algorithm to obtain the performance model of the linear implementation of the broadcast collective communication in a cluster of multicores is shown.

In this paper a methodology to characterize the influence of cache misses on the performance of parallel applications is presented. This methodology is based on analytical models provided by the TIA framework. This framework obtains analytical models of given observable quantities by instrumenting the source code and applying model selection techniques. In particular, two metrics related with the performance are considered in this work: the number of cache misses and the elapsed time. Based on both models, the influence in terms of execution time due to the cache misses can be inferred. Two different versions of the parallel product of dense matrices are used as case of study.

A new method for obtaining models of the performance of parallel applications based on statistical analysis is presented in this paper. This method is based on the Akaike's information criterion (AIC) that provides an objective mechanism to rank different models by means of an experimental data fit. The input of the modeling process is a set of variables and parameters that can a priori influence the performance of the application. This set can be provided by the user. Using this information, the method automatically generates a set of candidate models. These models are fit to the experimental data and the AIC score of each model is calculated. The model with the best AIC score is selected as the best model. Also, using the AIC scores of all candidate models, useful statistical information is provided to help the user to evaluate the quality of the selected model, as well as indications of how to interactively improve this modeling process. As a first case of study, statistical models obtained for different implementations of the broadcast collective communication in Open MPI are shown. These models are very accurate, exceeding its adjustment to theoretical approaches based on the LogGP model. Finally, the NAS Parallel Benchmark is also characterized using this new method with good results in terms of accuracy.

This paper presents a new LogP-based model, called LoOgGP, which allows an accurate characterization of MPI applications based on microbenchmark measurements. This new model is an extension of LogP for long messages in which both overhead and gap parameters perform a linear dependency with message size. The LoOgGP model has been fully integrated into a modelling framework to obtain statistical models of parallel applications, providing the analyst with an easy and automatic tool for LoOgGP parameter set assessment to characterize communications. The use of LoOgGP model to obtain a statistical performance model of an image deconvolution application is illustrated as a case of study.

This paper presents a framework based on a user driven methodology to obtain analytical models of MPI applications on parallel systems in a systematic and easy to use way. This methodology consists of two stages. In the first one, instrumentation of the source code is performed using CALL, which is a profiling tool for interacting with the code in an easy, simple and direct way. New features are added to CALL to obtain different performance metrics and store the performance information in XML files. Using this information, an analytical model of the performance behavior is obtained in the second stage by means of R, a language and environment for statistical analysis. The structure of the whole framework is detailed in this paper, and some selected examples are used to show its practical use.