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Operations research

Operations research
Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.[1] It is often considered to be a sub-field of mathematics.[2] The terms management science and decision science are sometimes used as synonyms.[3] Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on human-technology interaction and because of its focus on practical applications, operations research has overlap with other disciplines, notably industrial engineering and operations management, and draws on psychology and organization science. Overview[edit] The major subdisciplines in modern operational research, as identified by the journal Operations Research,[6] are: History[edit] Historical origins[edit]

Constraint satisfaction problem Examples of simple problems that can be modeled as a constraint satisfaction problem Examples demonstrating the above are often provided with tutorials of ASP, boolean SAT and SMT solvers. In the general case, constraint problems can be much harder, and may not be expressible in some of these simpler systems. "Real life" examples include planning and resource allocation. Formal definition[edit] Formally, a constraint satisfaction problem is defined as a triple , where [1] is a set of variables, is a set of the respect domains of values, and is a set of constraints. Each variable can take on the values in the nonempty domain . is in turn a pair , where is a subset of variables and is an . . satisfies a constraint if the values assigned to the variables satisfies the relation An evaluation is consistent if it does not violate any of the constraints. Resolution of CSPs[edit] Constraint satisfaction problems on finite domains are typically solved using a form of search. Theoretical aspects of CSPs[edit]

Optical engineering Optical engineering metrology uses optical methods to measure either micro-vibrations with instruments like the laser speckle interferometer, or properties of masses with instruments that measure refraction[4] Nano-measuring and nano-positioning machines are devices designed by optical engineers. These machines, for example microphotolithographic steppers, have nanometer precision, and consequently are used in the fabrication of goods at this scale.[5] The optical system of the ELT showing the location of the mirrors.[6] See also[edit] References[edit]

Constraint optimization General form[edit] A general constrained minimization problem may be written as follows: where and Solution methods[edit] Many unconstrained optimization algorithms can be adapted to the constrained case, often via the use of a penalty method. Equality constraints[edit] If the constrained problem has only equality constraints, the method of Lagrange multipliers can be used to convert it into an unconstrained problem whose number of variables is the original number of variables plus the original number of equality constraints. Inequality constraints[edit] With inequality constraints, the problem can be characterized in terms of the Karush–Kuhn–Tucker conditions, in which simple problems may be solvable. Linear programming[edit] If the objective function and all of the hard constraints are linear, then the problem is a linear programming problem. Quadratic programming[edit] Constraint optimization problems[edit] Branch and bound[edit] First-choice bounding functions[edit] Russian doll search[edit]

Packaging engineering From Wikipedia, the free encyclopedia Broad topic ranging from design conceptualization to product placement Packaging engineering, also package engineering, packaging technology and packaging science, is a broad topic ranging from design conceptualization to product placement. All steps along the manufacturing process, and more, must be taken into account in the design of the package for any given product. Education[edit] Some packaging engineers have backgrounds in other science, engineering, or design disciplines while some have college degrees specializing in this field.[4] Formal packaging programs might be listed as package engineering, packaging science, packaging technology, etc. See also[edit] Notes[edit] Bibliography[edit]

Distributed constraint optimization Distributed constraint optimization (DCOP or DisCOP) is the distributed analogue to constraint optimization. A DCOP is a problem in which a group of agents must distributedly choose values for a set of variables such that the cost of a set of constraints over the variables is either minimized or maximized. Distributed Constraint Satisfaction is a framework for describing a problem in terms of constraints that are known and enforced by distinct participants (agents). Problems defined with this framework can be solved by any of the algorithms that are proposed for it. The framework was used under different names in the 1980s. Definitions[edit] DCOP[edit] A DCOP can be defined as a tuple , where: The objective of a DCOP is to have each agent assign values to its associated variables in order to either minimize or maximize for a given assignment of the variables. Context[edit] A Context is a variable assignment for a DCOP. implies that the agent has not yet assigned a value to variable function. . .

Nuclear engineering Applied science Nuclear engineering is the branch of engineering concerned with the application of breaking down atomic nuclei (fission) or of combining atomic nuclei (fusion), or with the application of other sub-atomic processes based on the principles of nuclear physics. In the sub-field of nuclear fission, it particularly includes the design, interaction, and maintenance of systems and components like reactors, power plants, or weaponry. The field also includes the study of medical and other applications of radiation, particularly Ionizing radiation, nuclear safety, heat/thermodynamics transport, nuclear fuel, or other related technology (e.g., radioactive waste disposal) and the problems of nuclear proliferation. This field also includes chemical engineering and electrical engineering.[1] Professional areas[edit] The United States currently generates about 20% of its electricity from nuclear power plants. B-61 thermonuclear weapon Nuclear medicine and medical physics[edit]

Combinatorial optimization In computer science and artificial intelligence, combinatorial search studies search algorithms for solving instances of problems that are believed to be hard in general, by efficiently exploring the usually large solution space of these instances. Combinatorial search algorithms achieve this efficiency by reducing the effective size of the search space or employing heuristics. Some algorithms are guaranteed to find the optimal solution, while others may only return the best solution found in the part of the state space that was explored. Classic combinatorial search problems include solving the eight queens puzzle or evaluating moves in games with a large game tree, such as reversi or chess. A study of computational complexity theory helps to motivate combinatorial search. Combinatorial search algorithms are typically concerned with problems that are NP-hard. Examples[edit] Common algorithms for solving combinatorial search problems include: Lookahead[edit] See also[edit] References[edit]

Naval architecture Engineering discipline dealing with the design and construction of marine vessels Reconstruction of a 19th-century naval architect's office, Aberdeen Maritime Museum General Course of Study leading to Naval Architecture degree Naval architecture, or naval engineering, is an engineering discipline incorporating elements of mechanical, electrical, electronic, software and safety engineering as applied to the engineering design process, shipbuilding, maintenance, and operation of marine vessels and structures.[1][2] Naval architecture involves basic and applied research, design, development, design evaluation (classification) and calculations during all stages of the life of a marine vehicle. Preliminary design of the vessel, its detailed design, construction, trials, operation and maintenance, launching and dry-docking are the main activities involved. The hull of a racing yacht being lifted from the water for maintenance Main subjects[edit] Hydrostatics[edit] Hydrodynamics[edit] [edit]

Backmarking In constraint satisfaction, backmarking is a variant of the backtracking algorithm. Backmarking works like backtracking by iteratively evaluating variables in a given order, for example, . It improves over backtracking by maintaining information about the last time a variable was instantiated to a value and information about what changed since then. An example, in which search has reached xi=d the first time. for each variable and value , the algorithm records information about the last time has been set to ; in particular, it stores the minimal index such that the assignment to was then inconsistent;for each variable , the algorithm stores some information relative to what changed since the last time it has evaluated ; in particular, it stores the minimal index of a variable that was changed since then. The first information is collected and stored every time the algorithm evaluates a variable to , and is done by simply checking consistency of the current assignments for , for , etc. with

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