Linear programming (LP), also called linear optimization, is a method to achieve the best outcome in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming.
Science education is the teaching and learning of science to school children, college students, or adults within the general public. The field of science education includes work in science content, science process, some social science, and some teaching pedagogy. The standards for science education provide expectations for the development of understanding for students through the entire course of their K-12 education and beyond. The traditional subjects included in the standards are physical, life, earth, space, and human sciences.
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.
In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, tune, or select a heuristic that may provide a sufficiently good solution to an optimization problem or a machine learning problem, especially with incomplete or imperfect information or limited computation capacity. Metaheuristics sample a subset of solutions which is otherwise too large to be completely enumerated or otherwise explored. Metaheuristics may make relatively few assumptions about the optimization problem being solved and so may be usable for a variety of problems.
Educational technology is the combined use of computer hardware, software, and educational theory and practice to facilitate learning. When referred to with its abbreviation, "EdTech", it often refers to the industry of companies that create educational technology. In EdTech Inc.: Selling, Automating and Globalizing Higher Education in the Digital Age, Tanner Mirrlees and Shahid Alvi (2019) argue "EdTech is no exception to industry ownership and market rules" and "define the EdTech industries as all the privately owned companies currently involved in the financing, production and distribution of commercial hardware, software, cultural goods, services and platforms for the educational market with the goal of turning a profit. Many of these companies are US-based and rapidly expanding into educational markets across North America, and increasingly growing all over the world."
An intelligent tutoring system (ITS) is a computer system that imitates human tutors and aims to provide immediate and customized instruction or feedback to learners, usually without requiring intervention from a human teacher. ITSs have the common goal of enabling learning in a meaningful and effective manner by using a variety of computing technologies. There are many examples of ITSs being used in both formal education and professional settings in which they have demonstrated their capabilities and limitations. There is a close relationship between intelligent tutoring, cognitive learning theories and design; and there is ongoing research to improve the effectiveness of ITS. An ITS typically aims to replicate the demonstrated benefits of one-to-one, personalized tutoring, in contexts where students would otherwise have access to one-to-many instruction from a single teacher, or no teacher at all. ITSs are often designed with the goal of providing access to high quality education to each and every student.
A memetic algorithm (MA) in computer science and operations research, is an extension of the traditional genetic algorithm (GA) or more general evolutionary algorithm (EA). It may provide a sufficiently good solution to an optimization problem. It uses a suitable heuristic or local search technique to improve the quality of solutions generated by the EA and to reduce the likelihood of premature convergence.
A schedule or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are intended to take place. The process of creating a schedule — deciding how to order these tasks and how to commit resources between the variety of possible tasks — is called scheduling, and a person responsible for making a particular schedule may be called a scheduler. Making and following schedules is an ancient human activity.
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?" It generalises the travelling salesman problem (TSP). It first appeared in a paper by George Dantzig and John Ramser in 1959, in which the first algorithmic approach was written and was applied to petrol deliveries. Often, the context is that of delivering goods located at a central depot to customers who have placed orders for such goods. The objective of the VRP is to minimize the total route cost. In 1964, Clarke and Wright improved on Dantzig and Ramser's approach using an effective greedy algorithm called the savings algorithm.
Inquiry-based learning is a form of active learning that starts by posing questions, problems or scenarios. It contrasts with traditional education, which generally relies on the teacher presenting facts and their knowledge about the subject. Inquiry-based learning is often assisted by a facilitator rather than a lecturer. Inquirers will identify and research issues and questions to develop knowledge or solutions. Inquiry-based learning includes problem-based learning, and is generally used in small-scale investigations and projects, as well as research. The inquiry-based instruction is principally very closely related to the development and practice of thinking and problem-solving skills.
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem. On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such values of x and y. In this case, the formula is satisfiable when x is true, so the solver should return "satisfiable". Since the introduction of algorithms for SAT in the 1960s, modern SAT solvers have grown into complex software artifacts involving a large number of heuristics and program optimizations to work efficiently.
Ravindra K. Ahuja is an Indian-born American computer scientist and entrepreneur. He is currently Professor of Industrial and Systems Engineering at the University of Florida in Gainesville, Florida, and CEO of the automation and optimization solutions provider Optym, which he founded in 2000 as Innovative Scheduling, Inc.
A flipped classroom is an instructional strategy and a type of blended learning. It aims to increase student engagement and learning by having pupils complete readings at home, and work on live problem-solving during class time. This pedagogical style moves activities, including those that may have traditionally been considered homework, into the classroom. With a flipped classroom, students watch online lectures, collaborate in online discussions, or carry out research at home, while actively engaging concepts in the classroom with a mentor's guidance.
The nurse scheduling problem (NSP), also called the nurse rostering problem (NRP), is the operations research problem of finding an optimal way to assign nurses to shifts, typically with a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative quality of valid solutions. Solutions to the nurse scheduling problem can be applied to constrained scheduling problems in other fields.
Google OR-Tools is a free and open-source software suite developed by Google for solving linear programming (LP), mixed integer programming (MIP), constraint programming (CP), vehicle routing (VRP), and related optimization problems.
In discrete mathematics, the social golfer problem (SGP) is a combinatorial-design problem derived from a question posted in the usenet newsgroup sci.op-research in May 1998. The problem is as follows: 32 golfers play golf once a week in groups of 4. Schedule these golfers to play for as many weeks as possible without any two golfers playing together in a group more than once.
Course allocation is the problem of allocating seats in university courses among students. Many universities impose an upper bound on the number of students allowed to register to each course, in order to ensure that the teachers can give sufficient attention to each individual student. Since the demand for some courses is higher than the upper bound, a natural question is which students should be allowed to register to each course.
A large-scale capacitated arc routing problem (LSCARP) is a variant of the capacitated arc routing problem that covers 300 or more edges to model complex arc routing problems at large scales.
Optimal kidney exchange (OKE) is an optimization problem faced by programs for kidney paired donations (also called Kidney Exchange Programs). Such programs have large databases of patient-donor pairs, where the donor is willing to donate a kidney in order to help the patient, but cannot do so due to medical incompatibility. The centers try to arrange exchanges between such pairs. For example, the donor in pair A donates to the patient in pair B, the donor in pair B donates to the patient in pair C, and the donor in pair C donates to the patient in pair A.
Fractional job scheduling is a variant of optimal job scheduling in which it is allowed to break jobs into parts and process each part separately on the same or a different machine. Breaking jobs into parts may allow for improving the overall performance, for example, decreasing the makespan. Moreover, the computational problem of finding an optimal schedule may become easier, as some of the optimization variables become continuous. On the other hand, breaking jobs apart might be costly.
