Multi-Objective Optimization in R

The 'rmoo' package is a framework for multi- and many-objective optimization, which allows researchers and users versatility in parameter configuration, as well as tools for analysis, replication and visualization of results. The 'rmoo' package was built as a fork of the 'GA' package by Luca Scrucca(2017) and implementing the Non-Dominated Sorting Genetic Algorithms proposed by K. Deb's.

C++ Header Files for Stan

The C++ header files of the Stan project are provided by this package, but it contains little R code or documentation. The main reference is the vignette. There is a shared object containing part of the 'CVODES' library, but its functionality is not accessible from R. 'StanHeaders' is primarily useful for developers who want to utilize the 'LinkingTo' directive of their package's DESCRIPTION file to build on the Stan library without incurring unnecessary dependencies. The Stan project develops a probabilistic programming language that implements full or approximate Bayesian statistical inference via Markov Chain Monte Carlo or 'variational' methods and implements (optionally penalized) maximum likelihood estimation via optimization. The Stan library includes an advanced automatic differentiation scheme, 'templated' statistical and linear algebra functions that can handle the automatically 'differentiable' scalar types (and doubles, 'ints', etc.), and a parser for the Stan language. The 'rstan' package provides user-facing R functions to parse, compile, test, estimate, and analyze Stan models.

Maximum Likelihood Estimation and Related Tools

Functions for Maximum Likelihood (ML) estimation, non-linear optimization, and related tools. It includes a unified way to call different optimizers, and classes and methods to handle the results from the Maximum Likelihood viewpoint. It also includes a number of convenience tools for testing and developing your own models.

Differential Evolution Optimization in Pure R

Differential Evolution (DE) stochastic heuristic algorithms for global optimization of problems with and without general constraints. The aim is to curate a collection of its variants that (1) do not sacrifice simplicity of design, (2) are essentially tuning-free, and (3) can be efficiently implemented directly in the R language. Currently, it provides implementations of the algorithms 'jDE' by Brest et al. (2006) for single-objective optimization and 'NCDE' by Qu et al. (2012) for multimodal optimization (single-objective problems with multiple solutions).

Discrete and Global Optimization Routines

The R package 'adagio' will provide methods and algorithms for (discrete) optimization, e.g. knapsack and subset sum procedures, derivative-free Nelder-Mead and Hooke-Jeeves minimization, and some (evolutionary) global optimization functions.

Time Series Clustering Along with Optimizations for the Dynamic Time Warping Distance

Time series clustering along with optimized techniques related to the Dynamic Time Warping distance and its corresponding lower bounds. Implementations of partitional, hierarchical, fuzzy, k-Shape and TADPole clustering are available. Functionality can be easily extended with custom distance measures and centroid definitions. Implementations of DTW barycenter averaging, a distance based on global alignment kernels, and the soft-DTW distance and centroid routines are also provided. All included distance functions have custom loops optimized for the calculation of cross-distance matrices, including parallelization support. Several cluster validity indices are included.

Functions for Optimal Non-Bipartite Matching

Perform non-bipartite matching and matched randomization. A "bipartite" matching utilizes two separate groups, e.g. smokers being matched to nonsmokers or cases being matched to controls. A "non-bipartite" matching creates mates from one big group, e.g. 100 hospitals being randomized for a two-arm cluster randomized trial or 5000 children who have been exposed to various levels of secondhand smoke and are being paired to form a greater exposure vs. lesser exposure comparison. At the core of a non-bipartite matching is a N x N distance matrix for N potential mates. The distance between two units expresses a measure of similarity or quality as mates (the lower the better). The 'gendistance()' and 'distancematrix()' functions assist in creating this. The 'nonbimatch()' function creates the matching that minimizes the total sum of distances between mates; hence, it is referred to as an "optimal" matching. The 'assign.grp()' function aids in performing a matched randomization. Note bipartite matching can be performed using the prevent option in 'gendistance()'.

Manly Mixture Modeling and Model-Based Clustering

The utility of this package includes finite mixture modeling and model-based clustering through Manly mixture models by Zhu and Melnykov (2016) . It also provides capabilities for forward and backward model selection procedures.

Header-Only C++ Mathematical Optimization Library for 'Armadillo'

'Ensmallen' is a templated C++ mathematical optimization library (by the 'MLPACK' team) that provides a simple set of abstractions for writing an objective function to optimize. Provided within are various standard and cutting-edge optimizers that include full-batch gradient descent techniques, small-batch techniques, gradient-free optimizers, and constrained optimization. The 'RcppEnsmallen' package includes the header files from the 'Ensmallen' library and pairs the appropriate header files from 'armadillo' through the 'RcppArmadillo' package. Therefore, users do not need to install 'Ensmallen' nor 'Armadillo' to use 'RcppEnsmallen'. Note that 'Ensmallen' is licensed under 3-Clause BSD, 'Armadillo' starting from 7.800.0 is licensed under Apache License 2, 'RcppArmadillo' (the 'Rcpp' bindings/bridge to 'Armadillo') is licensed under the GNU GPL version 2 or later. Thus, 'RcppEnsmallen' is also licensed under similar terms. Note that 'Ensmallen' requires a compiler that supports 'C++14' and 'Armadillo' 10.8.2 or later.

Adequacy of Probabilistic Models and General Purpose Optimization

The main application concerns to a new robust optimization package with two major contributions. The first contribution refers to the assessment of the adequacy of probabilistic models through a combination of several statistics, which measure the relative quality of statistical models for a given data set. The second one provides a general purpose optimization method based on meta-heuristics functions for maximizing or minimizing an arbitrary objective function.