@article{Hindmarsh2005,
abstract = {SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordinary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL, CVODE, and IDA, respectively. The codes are written in ANSI standard C and are suitable for either serial or parallel machine environments. Common and notable features of these codes include inexact Newton-Krylov methods for solving large-scale nonlinear systems; linear multistep methods for time-dependent problems; a highly modular structure to allow incorporation of different preconditioning and/or linear solver methods; and clear interfaces allowing for users to provide their own data structures underneath the solvers. We describe the current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness. We also describe how the codes stem from previous and widely used Fortran 77 solvers, and how the codes have been augmented with forward and adjoint methods for carrying out first-order sensitivity analysis with respect to model parameters or initial conditions. {\textcopyright} 2005 ACM.},
author = {Hindmarsh, Alan C. and Brown, Peter N. and Grant, Keith E. and Lee, Steven L. and Serban, Radu and Shumaker, Dan E. and Woodward, Carol S.},
doi = {10.1145/1089014.1089020},
issn = {00983500},
journal = {ACM Transactions on Mathematical Software},
keywords = {Daes,Nonlinear systems,Odes,Sensitivity analysis},
number = {3},
pages = {363--396},
title = {{SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers}},
volume = {31},
year = {2005}
}
@article{Akman2018,
abstract = {Researchers using ordinary differential equations to model phenomena face two main challenges among others: implementing the appropriate model and optimizing the parameters of the selected model. The latter often proves difficult or computationally expensive. Here, we implement Particle Swarm Optimization, which draws inspiration from the optimizing behavior of insect swarms in nature, as it is a simple and efficient method for fitting models to data. We demonstrate its efficacy by showing that it outstrips evolutionary computing methods previously used to analyze an epidemic model.},
author = {Akman, Devin and Akman, Olcay and Schaefer, Elsa},
doi = {10.1155/2018/9160793},
issn = {16870042},
journal = {Journal of Applied Mathematics},
title = {{Parameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimization}},
volume = {2018},
year = {2018}
}
@article{Sengupta2018,
abstract = {Particle Swarm Optimization (PSO) is a metaheuristic global optimization paradigm that has gained prominence in the last two decades due to its ease of application in unsupervised, complex multidimensional problems that cannot be solved using traditional deterministic algorithms. The canonical particle swarm optimizer is based on the flocking behavior and social co-operation of birds and fish schools and draws heavily from the evolutionary behavior of these organisms. This paper serves to provide a thorough survey of the PSO algorithm with special emphasis on the development, deployment, and improvements of its most basic as well as some of the very recent state-of-the-art implementations. Concepts and directions on choosing the inertia weight, constriction factor, cognition and social weights and perspectives on convergence, parallelization, elitism, niching and discrete optimization as well as neighborhood topologies are outlined. Hybridization attempts with other evolutionary and swarm paradigms in selected applications are covered and an up-to-date review is put forward for the interested reader.},
archivePrefix = {arXiv},
arxivId = {1804.05319},
author = {Sengupta, Saptarshi and Basak, Sanchita and Peters, Richard},
doi = {10.3390/make1010010},
eprint = {1804.05319},
journal = {Machine Learning and Knowledge Extraction},
keywords = {agents,applications of pso,approximate algorithms,autonomous systems,evolutionary computation,heuristic search,hybrid algorithms,intelligent,optimization,particle swarm optimization,robotics and,swarm intelligence},
number = {1},
pages = {157--191},
title = {{Particle Swarm Optimization: A Survey of Historical and Recent Developments with Hybridization Perspectives}},
volume = {1},
year = {2018}
}
