Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, 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.
Program optimizationIn computer science, program optimization, code optimization, or software optimization, is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources. In general, a computer program may be optimized so that it executes more rapidly, or to make it capable of operating with less memory storage or other resources, or draw less power. Although the word "optimization" shares the same root as "optimal", it is rare for the process of optimization to produce a truly optimal system.
MachiningMachining is a process in which a material (often metal) is cut to a desired final shape and size by a controlled material-removal process. The methods that have this common theme are collectively called subtractive manufacturing, which utilizes machine tools, in contrast to additive manufacturing (3D printing), which uses controlled addition of material. Machining is a part of the manufacture of many metal products, but it can also be used on other materials such as wood, plastic, ceramic, and composite material.
Interprocedural optimizationInterprocedural optimization (IPO) is a collection of compiler techniques used in computer programming to improve performance in programs containing many frequently used functions of small or medium length. IPO differs from other compiler optimizations by analyzing the entire program as opposed to a single function or block of code. IPO seeks to reduce or eliminate duplicate calculations and inefficient use of memory and to simplify iterative sequences such as loops.
Combinatorial optimizationCombinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.
Ant colony optimization algorithmsIn computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. Artificial ants stand for multi-agent methods inspired by the behavior of real ants. The pheromone-based communication of biological ants is often the predominant paradigm used. Combinations of artificial ants and local search algorithms have become a method of choice for numerous optimization tasks involving some sort of graph, e.
Milling (machining)Milling is the process of machining using rotary cutters to remove material by advancing a cutter into a workpiece. This may be done by varying directions on one or several axes, cutter head speed, and pressure. Milling covers a wide variety of different operations and machines, on scales from small individual parts to large, heavy-duty gang milling operations. It is one of the most commonly used processes for machining custom parts to precise tolerances. Milling can be done with a wide range of machine tools.
Genetic algorithmIn computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, causal inference, etc.
Electrostatic dischargeElectrostatic discharge (ESD) is a sudden and momentary flow of electric current between two electrically charged objects caused by contact, an electrical short or dielectric breakdown. A buildup of static electricity can be caused by tribocharging or by electrostatic induction. The ESD occurs when differently-charged objects are brought close together or when the dielectric between them breaks down, often creating a visible spark.
Multi-objective optimizationMulti-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
Constrained optimizationIn mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized.
Partial dischargeIn electrical engineering, partial discharge (PD) is a localized dielectric breakdown (DB) (which does not completely bridge the space between the two conductors) of a small portion of a solid or fluid electrical insulation (EI) system under high voltage (HV) stress. While a corona discharge (CD) is usually revealed by a relatively steady glow or brush discharge (BD) in air, partial discharges within solid insulation system are not visible. PD can occur in a gaseous, liquid, or solid insulating medium.
Static single-assignment formIn compiler design, static single assignment form (often abbreviated as SSA form or simply SSA) is a property of an intermediate representation (IR) that requires each variable to be assigned exactly once and defined before it is used. Existing variables in the original IR are split into versions, new variables typically indicated by the original name with a subscript in textbooks, so that every definition gets its own version. In SSA form, use-def chains are explicit and each contains a single element.
AlgorithmIn mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.
Optimizing compilerIn computing, an optimizing compiler is a compiler that tries to minimize or maximize some attributes of an executable computer program. Common requirements are to minimize a program's execution time, memory footprint, storage size, and power consumption (the last three being popular for portable computers). Compiler optimization is generally implemented using a sequence of optimizing transformations, algorithms which take a program and transform it to produce a semantically equivalent output program that uses fewer resources or executes faster.
Dynamic programmingDynamic programming is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively.
Corona dischargeA corona discharge is an electrical discharge caused by the ionization of a fluid such as air surrounding a conductor carrying a high voltage. It represents a local region where the air (or other fluid) has undergone electrical breakdown and become conductive, allowing charge to continuously leak off the conductor into the air. A corona discharge occurs at locations where the strength of the electric field (potential gradient) around a conductor exceeds the dielectric strength of the air.
Electric dischargeIn electromagnetism, an electric discharge is the release and transmission of electricity in an applied electric field through a medium such as a gas (ie., an outgoing flow of electric current through a non-metal medium). The properties and effects of electric discharges are useful over a wide range of magnitudes. Tiny pulses of current are used to detect ionizing radiation in a Geiger–Müller tube. A low steady current can be used to illustrate the spectrum of gases in a gas-filled tube.
Machine toolA machine tool is a machine for handling or machining metal or other rigid materials, usually by cutting, boring, grinding, shearing, or other forms of deformations. Machine tools employ some sort of tool that does the cutting or shaping. All machine tools have some means of constraining the workpiece and provide a guided movement of the parts of the machine. Thus, the relative movement between the workpiece and the cutting tool (which is called the toolpath) is controlled or constrained by the machine to at least some extent, rather than being entirely "offhand" or "freehand".
Sorting algorithmIn computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output.
