Dynamics or dynamic may refer to:
Metric or metrical may refer to:
Reliability, reliable, or unreliable may refer to:
Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Uncertainty or incertitude refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science.
In mathematical optimization and decision theory, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite, in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy.
Process engineering is the understanding and application of the fundamental principles and laws of nature that allow humans to transform raw material and energy into products that are useful to society, at an industrial level. By taking advantage of the driving forces of nature such as pressure, temperature and concentration gradients, as well as the law of conservation of mass, process engineers can develop methods to synthesize and purify large quantities of desired chemical products. Process engineering focuses on the design, operation, control, optimization and intensification of chemical, physical, and biological processes. Process engineering encompasses a vast range of industries, such as agriculture, automotive, biotechnical, chemical, food, material development, mining, nuclear, petrochemical, pharmaceutical, and software development. The application of systematic computer-based methods to process engineering is "process systems engineering".
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from a linear–quadratic regulator (LQR). Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry.
Automated planning and scheduling, sometimes denoted as simply AI planning, is a branch of artificial intelligence that concerns the realization of strategies or action sequences, typically for execution by intelligent agents, autonomous robots and unmanned vehicles. Unlike classical control and classification problems, the solutions are complex and must be discovered and optimized in multidimensional space. Planning is also related to decision theory.
In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modelling errors.
Info-gap decision theory seeks to optimize robustness to failure under severe uncertainty, in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the parameter of interest. It has some connections with Wald's maximin model; some authors distinguish them, others consider them instances of the same principle.
Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution. It is related to, but often distinguished from, probabilistic optimization methods such as chance-constrained optimization.
Robust decision-making (RDM) is an iterative decision analytics framework that aims to help identify potential robust strategies, characterize the vulnerabilities of such strategies, and evaluate the tradeoffs among them. RDM focuses on informing decisions under conditions of what is called "deep uncertainty", that is, conditions where the parties to a decision do not know or do not agree on the system models relating actions to consequences or the prior probability distributions for the key input parameters to those models.
OptiY is a design environment software that provides modern optimization strategies and state of the art probabilistic algorithms for uncertainty, reliability, robustness, sensitivity analysis, data-mining and meta-modeling.
AIMMS is a prescriptive analytics software company with offices in the Netherlands, United States and Singapore.
Robust fuzzy programming (ROFP) is a powerful mathematical optimization approach to deal with optimization problems under uncertainty. This approach is firstly introduced at 2012 by Pishvaee, Razmi & Torabi in the Journal of Fuzzy Sets and Systems. ROFP enables the decision makers to be benefited from the capabilities of both fuzzy mathematical programming and robust optimization approaches. At 2016 Pishvaee and Fazli put a significant step forward by extending the ROFP approach to handle flexibility of constraints and goals. ROFP is able to achieve a robust solution for an optimization problem under uncertainty.
Christine A. Shoemaker joined the Department of Industrial Systems Engineering & Management and the Department of Civil and Environmental Engineering as NUS Distinguished Professor on 31 August 2015. Prof Shoemaker obtained her Ph.D. in mathematics from the University of Southern California supervised by Richard Bellman in Dynamic Programming. Upon her graduation, she joined the School of Civil and Environmental Engineering and later the School of Operations Research and Information Engineering at Cornell University, Ithaca, NY, USA. She was promoted to full Professor in 1985. From 1985 to 1988, Professor Shoemaker was the Chair of the Department of Environmental Engineering at Cornell University. In 2002 Prof. Shoemaker was appointed the Joseph P. Ripley Professor of Engineering at Cornell University, USA. In 2015, Prof. Shoemaker became Distinguished Professor at National University of Singapore, in both Industrial Systems Engineering and Management Department and Civil and Environmental Engineering Department. While in Singapore she has worked with Singapore water agency to apply her global optimization algorithms to improve the selection of parameters for computationally expensive partial differential equation models for lake hydrodynamics and complex multi-species water quality elements. These results used her group's new parallel algorithms.
Aurelie or Aurélie Thiele is a French engineering and decision-making professor. She is an associate professor in the engineering management and information and systems department at the Lyle School of Engineering of Southern Methodist University.
