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Variable Specific Impulse Magnetoplasma Rocket

The Variable Specific Impulse Magnetoplasma Rocket (VASIMR) is an electrothermal thruster under development for possible use in spacecraft propulsion. It uses radio waves to ionize and heat an inert propellant, forming a plasma, then a magnetic field to confine and accelerate the expanding plasma, generating thrust. It is a plasma propulsion engine, one of several types of spacecraft electric propulsion systems.

The VASIMR method for heating plasma was originally developed during nuclear fusion research. VASIMR is intended to bridge the gap between high thrust, low specific impulse chemical rockets and low thrust, high specific impulse electric propulsion, but has not yet demonstrated high thrust. The VASIMR concept originated in 1977 with former NASA astronaut Franklin Chang Díaz, who has been developing the technology ever since.

Design and operation

VASIMR is a type of electrothermal plasma thruster/electrothermal magnetoplasma thruster. In these engines, a neutral, inert propellant is ionized and heated using radio waves. The resulting plasma is then accelerated with magnetic fields to generate thrust. Other related electrically powered spacecraft propulsion concepts are the electrodeless plasma thruster, the microwave arcjet rocket, and the pulsed inductive thruster.

The propellant, a neutral gas such as argon or xenon, is injected into a hollow cylinder surfaced with electromagnets. On entering the engine, the gas is first heated to a "cold plasma" by a helicon RF antenna/coupler that bombards the gas with electromagnetic energy, at a frequency of 10 to 50 MHz, stripping electrons off the propellant atoms and producing a plasma of ions and free electrons. By varying the amount of RF heating energy and plasma, VASIMR is claimed to be capable of generating either low-thrust, high–specific impulse exhaust or relatively high-thrust, low–specific impulse exhaust. The second phase of the engine is a strong solenoid-configuration electromagnet that channels the ionized plasma, acting as a convergent-divergent nozzle like the physical nozzle in conventional rocket engines.

A second coupler, known as the Ion Cyclotron Heating (ICH) section, emits electromagnetic waves in resonance with the orbits of ions and electrons as they travel through the engine. Resonance is achieved through a reduction of the magnetic field in this portion of the engine that slows the orbital motion of the plasma particles. This section further heats the plasma to greater than 1000000 K—about 173 times the temperature of the Sun's surface.

The path of ions and electrons through the engine approximates lines parallel to the engine walls; however, the particles actually orbit those lines while traveling linearly through the engine. The final, diverging, section of the engine contains an expanding magnetic field that ejects the ions and electrons from the engine at velocities as great as 50000 m/s.

Advantages
In contrast to the typical cyclotron resonance heating processes, VASIMR ions are immediately ejected from the magnetic nozzle before they achieve thermalized distribution. Based on novel theoretical work in 2004 by Alexey V. Arefiev and Boris N. Breizman of University of Texas at Austin, virtually all of the energy in the ion cyclotron wave is uniformly transferred to ionized plasma in a single-pass cyclotron absorption process. This allows for ions to leave the magnetic nozzle with a very narrow energy distribution, and for significantly simplified and compact magnet arrangement in the engine.

VASIMR does not use electrodes; instead, it magnetically shields plasma from most hardware parts, thus eliminating electrode erosion, a major source of wear in ion engines. Compared to traditional rocket engines with very complex plumbing, high performance valves, actuators and turbopumps, VASIMR has almost no moving parts (apart from minor ones, like gas valves), maximizing long term durability.

Disadvantages
According to Ad Astra as of 2015, the VX-200 engine requires 200 kW electrical power to produce 5 N of thrust, or 40 kW/N. In contrast, the conventional NEXT ion thruster produces 0.327 N with only 7.7 kW, or 24 kW/N. Electrically speaking, NEXT is almost twice as efficient, and successfully completed a 48,000 hours (5.5 years) test in December 2009.

New problems also emerge with VASIMR, such as interaction with strong magnetic fields and thermal management. The inefficiency with which VASIMR operates generates substantial waste heat that needs to be channeled away without creating thermal overload and thermal stress. The superconducting electromagnets necessary to contain hot plasma generate tesla-range magnetic fields that can cause problems with other onboard devices and produce unwanted torque by interaction with the magnetosphere. To counter this latter effect, two thruster units can be packaged with magnetic fields oriented in opposite directions, making a net zero-torque magnetic quadrupole.

Research and development
The first VASIMR experiment was conducted at Massachusetts Institute of Technology in 1983. Important refinements were introduced in the 1990s, including the use of the helicon plasma source, which replaced the plasma gun originally envisioned and its electrodes, adding to durability and long life.

As of 2010, Ad Astra Rocket Company (AARC) was responsible for VASIMR development, signing the first Space Act Agreement on 23 June 2005 to privatize VASIMR technology. Franklin Chang Díaz is Ad Astra's chairman and CEO, and the company had a testing facility in Liberia, Costa Rica on the campus of Earth University.

VX-10 to VX-50
In 1998, the first helicon plasma experiment was performed at the ASPL. VASIMR experiment 10 (VX-10) in 1998 achieved a helicon RF plasma discharge of up to 10 kW and VX-25 in 2002 of up to 25 kW. By 2005 progress at ASPL included full and efficient plasma production and acceleration of the plasma ions with the 50 kW, 0.5 N thrust VX-50. Published data on the 50 kW VX-50 showed the electrical efficiency to be 59% based on a 90% coupling efficiency and a 65% ion speed boosting efficiency.

VX-100
The 100 kilowatt VASIMR experiment was successfully running by 2007 and demonstrated efficient plasma production with an ionization cost below 100eV. VX-100 plasma output tripled the prior record of the VX-50.

The VX-100 was expected to have an ion speed boosting efficiency of 80%, but could not achieve this efficiency due to losses from the conversion of DC electric current to radio frequency power and the auxiliary equipment for the superconducting magnet. In contrast, 2009 state-of-the-art, proven ion engine designs such as NASA's High Power Electric Propulsion (HiPEP) operated at 80% total thruster/PPU energy efficiency.

VX-200
On 24 October 2008, the company announced in a press release that the helicon plasma generation component of the 200 kW VX-200 engine had reached operational status. The key enabling technology, solid-state DC-RF power-processing, reached 98% efficiency. The helicon discharge used 30 kW of radio waves to turn argon gas into plasma. The remaining 170 kW of power was allocated for acceleration of plasma in the second part of the engine, via ion cyclotron resonance heating.

Based on data from VX-100 testing, it was expected that, if room temperature superconductors are ever discovered, the VX-200 engine would have a system efficiency of 60–65% and a potential thrust level of 5 N. Optimal specific impulse appeared to be around 5,000 s using low cost argon propellant. One of the remaining untested issues was whether the hot plasma actually detached from the rocket. Another issue was waste heat management. About 60% of input energy became useful kinetic energy. Much of the remaining 40% is secondary ionizations from plasma crossing magnetic field lines and exhaust divergence. A significant portion of that 40% was waste heat (see energy conversion efficiency). Managing and rejecting that waste heat is critical.

Between April and September 2009, 200 kW tests were performed on the VX-200 prototype with 2 tesla superconducting magnets that are powered separately and not accounted for in any "efficiency" calculations. During November 2010, long duration, full power firing tests were performed, reaching steady state operation for 25 seconds and validating basic design characteristics.

Results presented in January 2011 confirmed that the design point for optimal efficiency on the VX-200 is 50 km/s exhaust velocity, or an I$sp$ of 5000s. The 200 kW VX-200 had executed more than 10,000 engine firings with argon propellant at full power by 2013, demonstrating greater than 70% thruster efficiency relative to RF power input.

VX-200SS
In March 2015, Ad Astra announced a $10 million award from NASA to advance the technology readiness of the next version of the VASIMR engine, the VX-200SS to meet the needs of deep space missions. The SS in the name stands for "steady state", as a goal of the long duration test is to demonstrate continuous operation at thermal steady state.

In August 2016, Ad Astra announced completion of the milestones for the first year of its 3-year contract with NASA. This allowed for first high-power plasma firings of the engines, with a stated goal to reach 100hr and 100 kW by mid-2018. In August 2017, the company reported completing its Year 2 milestones for the VASIMR electric plasma rocket engine. NASA gave approval for Ad Astra to proceed with Year 3 after reviewing completion of a 10-hour cumulative test of the VX-200SS engine at 100kW. It appears as though the planned 200 kW design is being run at 100 kW for reasons that are not mentioned in the press release. In August 2019, Ad Astra announced the successful completion of tests of a new generation radio-frequency (RF) Power Processing Unit (PPU) for the VASIMR engine, built by Aethera Technologies Ltd. of Canada. Ad Astra declared a power of 120 kW and >97% electrical-to-RF power efficiency, and that, at 52 kg, the new RF PPU is about 10x lighter than the PPUs of competing electric thrusters (power-to-weight ratio: 2.31 kW/kg)

In July 2021, Ad Astra announced the completion of a record-breaking test for the engine, running it for 28 hours at a power level of 82.5kW. A second test, conducted from July 12 to 16, successfully ran the engine for 88 hours at a power level of 80kW. Ad Astra anticipates conducting 100kW power level tests in 2023.

Potential applications
VASIMR has a comparatively poor thrust-to-weight ratio, and requires an ambient vacuum.

Proposed applications for VASIMR such as the rapid transportation of people to Mars would require a very high power, low mass energy source, ten times more efficient than a nuclear reactor (see nuclear electric rocket). In 2010 NASA Administrator Charles Bolden said that VASIMR technology could be the breakthrough technology that would reduce the travel time on a Mars mission from 2.5 years to 5 months. However this claim has not been repeated in the last decade.

In August 2008, Tim Glover, Ad Astra director of development, publicly stated that the first expected application of VASIMR engine is "hauling things [non-human cargo] from low-Earth orbit to low-lunar orbit" supporting NASA's return to Moon efforts.

Mars in 39 days
In order to conduct an imagined crewed trip to Mars in 39 days, the VASIMR would require an electrical power level far beyond anything currently possible.

On top of that, any power generation technology will produce waste heat. The necessary 200 megawatt reactor "with a power-to-mass density of 1,000 watts per kilogram" would require extremely efficient radiators to avoid the need for "football-field sized radiators".


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Mongolian writing systems

Various Mongolian writing systems have been devised for the Mongolian language over the centuries, and from a variety of scripts. The oldest and native script, called simply the Mongolian script, has been the predominant script during most of Mongolian history, and is still in active use today in the Inner Mongolia region of China and has de facto use in Mongolia.

It has in turn spawned several alphabets, either as attempts to fix its perceived shortcomings, or to allow the notation of other languages, such as Chinese, Sanskrit and Tibetan. In the 20th century, Mongolia briefly switched to the Latin script, but then almost immediately replaced it with the Cyrillic script under the Mongolian People's Republic's for compatibility with the Soviet Union, as it was its satellite state. Nevertheless, Mongols living in Inner Mongolia as well as other parts of China continued to use alphabets based on the traditional Mongolian script.

In March 2020, the Government of Mongolia announced plans to use the traditional Mongolian script alongside the Cyrillic script in official documents (e.g. identity documents, academic certificates, birth certificates, marriage certificates, among others) as well as the State Great Khural by 2025, although the Cyrillic script could be used alone on an optional basis for less official writing.

Precursors
The Xianbei spoke a proto-Mongolic language and wrote down several pieces of literature in their language. They are believed to have used Chinese characters to phonetically represent Xianbei, like the Japanese system of Man'yōgana with Chinese, but all works written in Xianbei are now lost.

In 2019, with the emergence of new evidence through the analysis of the Brāhmī Bugut and Khüis Tolgoi, Rouran language was deciphered, and Rouran was spelled in Brahmi script.

The Khitan spoke another proto-Mongolic language and developed two scripts for writing it: Khitan large script and Khitan small script, logographic scripts derived from Chinese characters.

Traditional alphabet
At the very beginning of the Mongol Empire, around 1204, Genghis Khan defeated the Naimans and captured a Uyghur scribe called Tata-tonga, who then adapted the Uyghur alphabet—a descendant of the Syriac alphabet, via Sogdian—to write Mongol. With only minor modifications, it is used in Inner Mongolia to this day. Its most salient feature is its vertical direction; it is the only vertical script still in use that is written from left to right. (All other vertical writing systems are written right to left.) This is because the Uyghurs rotated their script 90 degrees anticlockwise to emulate the Chinese writing system.

As a variant of the traditional script there exists a vertical square script (Босоо дөрвөлжин), also called folded script, used e.g. on the Mongolian banknotes.

Galik alphabet
In 1587, the translator and scholar Ayuush Güüsh created the Galik alphabet, inspired by Sonam Gyatso, the third Dalai Lama. It primarily added extra letters to transcribe Tibetan and Sanskrit terms in religious texts, and later also from Chinese and Russian. Later some of these letters were officially merged into traditional alphabet as a group named "Galig usug" to transcribe foreign words in modern use.

Todo alphabet
In 1648, the Oirat Buddhist monk Zaya Pandita created this variation with the goal of bringing the written language closer to the actual Oirat pronunciation, and to make it easier to transcribe Tibetan and Sanskrit. The script was used by Kalmyks of Russia until 1924, when it was replaced by the Cyrillic alphabet. In Xinjiang, China, the Oirats still use it.

'Phags-pa script (Square script)
The traditional Mongolian alphabet is not a perfect fit for the Mongolian language, and it would be impractical to extend it to a language with a very different phonology like Chinese. Therefore, during the Yuan dynasty (c. 1269), Kublai Khan asked a Tibetan monk, Drogön Chögyal Phagpa, to design a new script for use by the whole empire. Phagpa extended his native Tibetan script to encompass Mongolian and Chinese; the result was known by several descriptive names, such as the Mongolian new script, but today is known as the 'Phags-pa script. The script did not receive wide acceptance and fell into disuse with the collapse of the Yuan dynasty in 1368. After this it was mainly used as a phonetic gloss for Mongols learning Chinese characters. However, scholars such as Gari Ledyard believe that in the meantime it was the source of some of the basic letters of the Korean hangul alphabet.

Soyombo script
The Soyombo script is an abugida created by the Mongolian monk and scholar Bogdo Zanabazar in the late 17th century, that can also be used to write Tibetan and Sanskrit. A special glyph in the script, the Soyombo symbol, became a national symbol of Mongolia, and has appeared on the national flag since 1921, and on the national coat of arms since 1992, as well as money, stamps, etc.

Zanabazar had created it for the translation of Buddhist texts from Sanskrit or Tibetan, and both he and his students used it extensively for that purpose. Aside from historical texts, it can usually be found in temple inscriptions. It also has some relevance to linguistic research, because it reflects certain developments in the Mongolian language, such as that of long vowels.

Horizontal square script
At around the same time, Zanabazar also developed the horizontal square script (Хэвтээ дөрвөлжин), which was only rediscovered in 1801. The script's applications during the period of its use are not known. It was also largely based on the Tibetan alphabet, read left to right, and employed vowel diacritics above and below the consonant letters. Additionally, a dot was used below consonants to show that they were syllable-final.

Horizontal square script is included in the Unicode Standard under the name "Zanabazar Square". The Zanabazar Square block, comprising 72 characters, was added as part of Unicode version 10.0 in June 2017.

Foreign scripts
Before the 13th century, foreign scripts such as the Uighur and the Tibetan scripts were used to write the Mongolian language. Even during the reign of the Mongol Empire, people in the conquered areas often wrote it in their local systems. In some cases it was transcribed phonetically using Chinese characters, as is the case with the only surviving copies of The Secret History of the Mongols. Subjects from the Middle East hired into administrative functions would also often use Perso-Arabic script to write their Mongolian language documents.

Latin script
On 1 February 1930, Mongolia officially adopted a Latin alphabet. On 25 March 1941, the decision was reversed. According to later official claims, the alphabet had turned out to have not been thought out well. It was said not to distinguish all the sounds of the Mongolian language, and was difficult to use. However, those seem to have been pretexts rather than the true reasons. Using "y" as feminine "u", with additional feminine "o" ("ө") and with additional consonants "ç" for "ch" , "ş" for "sh"  and ƶ for "zh" , it successfully served in printing books and newspapers. Many of the Latin letters (f, h, p, v) were even rarely used while q, w and x were completely excluded. The adoption of the Cyrillic script a short time later, almost simultaneously with most Soviet republics, suggests political reasons. In the advent of the Internet, people who use social networking services prefer typing in the Latin script for the ease of typing compared to the Cyrillic script, using the orthography introduced in 1939.

Cyrillic script
The most recent Mongolian alphabet is based on the Cyrillic script, more specifically the Russian alphabet plus the letters, Өө Öö and Үү Üü. It was introduced in the 1940s and has been in use as the official writing system of Mongolia ever since.

In March 2020, the Government of Mongolia announced plans to use the traditional Mongolian script alongside Cyrillic in official documents starting from 2025.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Mongolian writing systems


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Specific impulse

Specific impulse (usually abbreviated $I_{sp}$) is a measure of how efficiently a reaction mass engine, such as a rocket using propellant or a jet engine using fuel, generates thrust.

A propulsion system with a higher specific impulse uses the mass of the propellant more efficiently. In the case of a rocket, this means less propellant needed for a given delta-v, so that the vehicle attached to the engine can more efficiently gain altitude and velocity.

Propulsion systems
For engines like cold gas thrusters whose reaction mass is only the fuel they carry, specific impulse is exactly proportional to the effective exhaust gas velocity.

In atmosphere
In an atmospheric context, specific impulse can include the contribution to impulse provided by the mass of external air that is accelerated by the engine, such as by fuel combustion or by external propeller. Jet engines and turbofans breathe external air for both combustion and bypass, and therefore have a much higher specific impulse than rocket engines.

For air-breathing engines, only the fuel mass is counted, not the mass of air passing through the engine. Air resistance and the engine's inability to keep a high specific impulse at a fast burn rate are limiting factors to the propellant consumption rate. If it were not for air resistance and the reduction of propellant during flight, specific impulse would be a direct measure of the engine's effectiveness in converting propellant mass into forward momentum.

The specific impulse in terms of propellant mass spent has units of distance per time, which is a notional velocity called the effective exhaust velocity. This is higher than the actual exhaust velocity because the mass of the combustion air is not being accounted for. Actual and effective exhaust velocity are the same in rocket engines operating in a vacuum.

General considerations
The amount of propellant can be measured either in units of mass or weight. If mass is used, specific impulse is an impulse per unit of mass, which dimensional analysis shows to have units of speed, specifically the effective exhaust velocity. As the SI system is mass-based, this type of analysis is usually done in meters per second. If a force-based unit system is used, impulse is divided by propellant weight (weight is a measure of force), resulting in units of time (seconds). These two formulations differ from each other by the standard gravitational acceleration (g0) at the surface of the earth.

The rate of change of momentum of a rocket (including its propellant) per unit time is equal to the thrust. The higher the specific impulse, the less propellant is needed to produce a given thrust for a given time and the more efficient the propellant is. This should not be confused with the physics concept of energy efficiency, which can decrease as specific impulse increases, since propulsion systems that give high specific impulse require high energy to do so.

Thrust and specific impulse should not be confused. Thrust is the force supplied by the engine and depends on the amount of reaction mass flowing through the engine. Specific impulse measures the impulse produced per unit of propellant and is proportional to the exhaust velocity. Thrust and specific impulse are related by the design and propellants of the engine in question, but this relationship is tenuous. For example, LH2/LO$2$ bipropellant produces higher $I_{sp}$ but lower thrust than RP-1/LO$2$ due to the exhaust gases having a lower density and higher velocity (H2O vs CO2 and H2O). In many cases, propulsion systems with very high specific impulse—some ion thrusters reach 10,000 seconds—produce low thrust.

When calculating specific impulse, only propellant carried with the vehicle before use is counted. For a chemical rocket, the propellant mass therefore would include both fuel and oxidizer. In rocketry, a heavier engine with a higher specific impulse may not be as effective in gaining altitude, distance, or velocity as a lighter engine with a lower specific impulse, especially if the latter engine possesses a higher thrust-to-weight ratio. This is a significant reason for most rocket designs having multiple stages. The first stage is optimised for high thrust to boost the later stages with higher specific impulse into higher altitudes where they can perform more efficiently.

Units
The most common unit for specific impulse is the second, as values are identical regardless of whether the calculations are done in mks, imperial, or customary units. Nearly all manufacturers quote their engine performance in seconds, and the unit is also useful for specifying aircraft engine performance.

The use of metres per second to specify effective exhaust velocity is also reasonably common. The unit is intuitive when describing rocket engines, although the effective exhaust speed of the engines may be significantly different from the actual exhaust speed, especially in gas-generator cycle engines. For airbreathing jet engines, the effective exhaust velocity is not physically meaningful, although it can be used for comparison purposes.

Metres per second are numerically equivalent to newton-seconds per kg (N·s/kg), and mks measurements of specific impulse can be written in terms of either units interchangeably. This unit highlights the definition of specific impulse as impulse per unit mass of propellant.

Specific fuel consumption is inversely proportional to specific impulse and has units of g/(kN·s) or lb/(lbf·hr). Specific fuel consumption is used extensively for describing the performance of air-breathing jet engines.

Specific impulse in seconds
Specific impulse, measured in seconds, effectively means how many seconds a given propellant, when paired with a given engine, can accelerate its own initial mass at 1 g. The longer it can accelerate its own mass, the more delta-V it delivers to the whole system.

In other words, given a particular engine and a mass of a particular propellant, specific impulse measures for how long a time that engine can exert a continuous force (thrust) until fully burning that mass of propellant. A given mass of a more energy-dense propellant can burn for a longer duration than some less energy-dense propellant made to exert the same force while burning in an engine. Different engine designs burning the same propellant may not be equally efficient at directing their propellant's energy into effective thrust.

For all vehicles, specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by the following equation:

$$F_\text{thrust} = g_0 \cdot I_\text{sp} \cdot \dot m,$$

where:

 * $$F_\text{thrust}$$ is the thrust obtained from the engine (newtons or pounds force),
 * $$g_0$$ is the standard gravity, which is nominally the gravity at Earth's surface (m/s2 or ft/s2),
 * $$I_\text{sp}$$ is the specific impulse measured (seconds),
 * $$\dot m$$ is the mass flow rate of the expended propellant (kg/s or slugs/s)

The English unit pound mass is more commonly used than the slug, and when using pounds per second for mass flow rate, it is more convenient to express standard gravity as 1 pound-force per pound-mass. Note that this is equivalent to 32.17405 ft/s2, but expressed in more convenient units. This gives:

$$F_\text{thrust} = I_\text{sp} \cdot \dot m \cdot \left(1 \mathrm{\frac{lbf}{lbm}} \right).$$

Isp in seconds is the amount of time a rocket engine can generate thrust, given a quantity of propellant whose weight is equal to the engine's thrust.

The advantage of this formulation is that it may be used for rockets, where all the reaction mass is carried on board, as well as airplanes, where most of the reaction mass is taken from the atmosphere. In addition, it gives a result that is independent of units used (provided the unit of time used is the second).

Rocketry
In rocketry, the only reaction mass is the propellant, so the specific impulse is calculated using an alternative method, giving results with units of seconds. Specific impulse is defined as the thrust integrated over time per unit weight-on-Earth of the propellant:

$$I_\text{sp} = \frac{v_\text{e}}{g_0},$$

where

 * $$I_\text{sp}$$ is the specific impulse measured in seconds,
 * $$v_\text{e}$$ is the average exhaust speed along the axis of the engine (in m/s or ft/s),
 * $$g_0$$ is the standard gravity (in m/s2 or ft/s2).

In rockets, due to atmospheric effects, the specific impulse varies with altitude, reaching a maximum in a vacuum. This is because the exhaust velocity isn't simply a function of the chamber pressure, but is a function of the difference between the interior and exterior of the combustion chamber. Values are usually given for operation at sea level ("sl") or in a vacuum ("vac").

Specific impulse as effective exhaust velocity
Because of the geocentric factor of g0 in the equation for specific impulse, many prefer an alternative definition. The specific impulse of a rocket can be defined in terms of thrust per unit mass flow of propellant. This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, ve. "In actual rocket nozzles, the exhaust velocity is not really uniform over the entire exit cross section and such velocity profiles are difficult to measure accurately. A uniform axial velocity, v e, is assumed for all calculations which employ one-dimensional problem descriptions. This effective exhaust velocity represents an average or mass equivalent velocity at which propellant is being ejected from the rocket vehicle." The two definitions of specific impulse are proportional to one another, and related to each other by: $$v_\text{e} = g_0 \cdot I_\text{sp},$$ where
 * $$I_\text{sp}$$ is the specific impulse in seconds,
 * $$v_\text{e}$$ is the specific impulse measured in m/s, which is the same as the effective exhaust velocity measured in m/s (or ft/s if g is in ft/s2),
 * $$g_0$$ is the standard gravity, 9.80665 m/s2 (in United States customary units 32.174 ft/s2).

This equation is also valid for air-breathing jet engines, but is rarely used in practice.

(Note that different symbols are sometimes used; for example, c is also sometimes seen for exhaust velocity. While the symbol $$I_\text{sp}$$ might logically be used for specific impulse in units of (N·s$3$)/(m·kg); to avoid confusion, it is desirable to reserve this for specific impulse measured in seconds.)

It is related to the thrust, or forward force on the rocket by the equation: $$F_\text{thrust} = v_\text{e} \cdot \dot m,$$ where $$\dot m$$ is the propellant mass flow rate, which is the rate of decrease of the vehicle's mass.

A rocket must carry all its propellant with it, so the mass of the unburned propellant must be accelerated along with the rocket itself. Minimizing the mass of propellant required to achieve a given change in velocity is crucial to building effective rockets. The Tsiolkovsky rocket equation shows that for a rocket with a given empty mass and a given amount of propellant, the total change in velocity it can accomplish is proportional to the effective exhaust velocity.

A spacecraft without propulsion follows an orbit determined by its trajectory and any gravitational field. Deviations from the corresponding velocity pattern (these are called Δv) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change.

Actual exhaust speed versus effective exhaust speed
When an engine is run within the atmosphere, the exhaust velocity is reduced by atmospheric pressure, in turn reducing specific impulse. This is a reduction in the effective exhaust velocity, versus the actual exhaust velocity achieved in vacuum conditions. In the case of gas-generator cycle rocket engines, more than one exhaust gas stream is present as turbopump exhaust gas exits through a separate nozzle. Calculating the effective exhaust velocity requires averaging the two mass flows as well as accounting for any atmospheric pressure.

For air-breathing jet engines, particularly turbofans, the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This happens for several reasons. First, a good deal of additional momentum is obtained by using air as reaction mass, such that combustion products in the exhaust have more mass than the burned fuel. Next, inert gases in the atmosphere absorb heat from combustion, and through the resulting expansion provide additional thrust. Lastly, for turbofans and other designs there is even more thrust created by pushing against intake air which never sees combustion directly. These all combine to allow a better match between the airspeed and the exhaust speed, which saves energy/propellant and enormously increases the effective exhaust velocity while reducing the actual exhaust velocity. Again, this is because the mass of the air is not counted in the specific impulse calculation, thus attributing all of the thrust momentum to the mass of the fuel component of the exhaust, and omitting the reaction mass, inert gas, and effect of driven fans on overall engine efficiency from consideration.

Essentially, the momentum of engine exhaust includes a lot more than just fuel, but specific impulse calculation ignores everything but the fuel. Even though the effective exhaust velocity for an air-breathing engine seems nonsensical in the context of actual exhaust velocity, this is still useful for comparing absolute fuel efficiency of different engines.

Density specific impulse
A related measure, the density specific impulse, sometimes also referred to as Density Impulse and usually abbreviated as $x$ is the product of the average specific gravity of a given propellant mixture and the specific impulse. While less important than the specific impulse, it is an important measure in launch vehicle design, as a low specific impulse implies that bigger tanks will be required to store the propellant, which in turn will have a detrimental effect on the launch vehicle's mass ratio.

Specific fuel consumption
Specific impulse is inversely proportional to specific fuel consumption (SFC) by the relationship $x$ for SFC in kg/(N·s) and $x$ for SFC in lb/(lbf·hr).

Examples
An example of a specific impulse measured in time is 453 seconds, which is equivalent to an effective exhaust velocity of 4.440 km/s, for the RS-25 engines when operating in a vacuum. An air-breathing jet engine typically has a much larger specific impulse than a rocket; for example a turbofan jet engine may have a specific impulse of 6,000 seconds or more at sea level whereas a rocket would be between 200 and 400 seconds.

An air-breathing engine is thus much more propellant efficient than a rocket engine, because the air serves as reaction mass and oxidizer for combustion which does not have to be carried as propellant, and the actual exhaust speed is much lower, so the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust. While the actual exhaust velocity is lower for air-breathing engines, the effective exhaust velocity is very high for jet engines. This is because the effective exhaust velocity calculation assumes that the carried propellant is providing all the reaction mass and all the thrust. Hence effective exhaust velocity is not physically meaningful for air-breathing engines; nevertheless, it is useful for comparison with other types of engines.

The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was 542 isp with a tripropellant of lithium, fluorine, and hydrogen. However, this combination is impractical. Lithium and fluorine are both extremely corrosive, lithium ignites on contact with air, fluorine ignites on contact with most fuels, and hydrogen, while not hypergolic, is an explosive hazard. Fluorine and the hydrogen fluoride (HF) in the exhaust are very toxic, which damages the environment, makes work around the launch pad difficult, and makes getting a launch license that much more difficult. The rocket exhaust is also ionized, which would interfere with radio communication with the rocket.

Nuclear thermal rocket engines differ from conventional rocket engines in that energy is supplied to the propellants by an external nuclear heat source instead of the heat of combustion. The nuclear rocket typically operates by passing liquid hydrogen gas through an operating nuclear reactor. Testing in the 1960s yielded specific impulses of about 850 seconds (8,340 m/s), about twice that of the Space Shuttle engines.

A variety of other rocket propulsion methods, such as ion thrusters, give much higher specific impulse but with much lower thrust; for example the Hall-effect thruster on the SMART-1 satellite has a specific impulse of 1640 isp but a maximum thrust of only 68 mN. The variable specific impulse magnetoplasma rocket (VASIMR) engine currently in development will theoretically yield 20 to 300 km/s, and a maximum thrust of 5.7 N.

title: Specific impulse


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User:Pgdudda

Main areas of knowledge/competency are related to hearing impairment and linguistics.

I also forage a fair bit, and like to play "WikiRoulette" (called the Random Page link - *grin*).

Dramatis Temporae:

My father was born just outside of the town of Leipzig, Germany in 1940.

My mother was born in Königsberg, East Prussia (now Kaliningrad, Kaliningrad Oblast, Russia) in 1944.

My parents crossed paths in childhood during the WWII Allies' bombing of Dresden. My father was awakened by his parents to see the orange glow in the sky resulting from the bombing. My mother's family, her included, were on a train en route to Bavaria. That train stopped about an hour outside of Dresden, soon after which the bombing raid began. However, they did not actually meet until their late teens, after each of their families had moved to the area of Frankfurt am Main, Germany.

My brother (in 1969) and I (in 1974) were born in Frankfurt am Main. My partner was born in 1957, in Minneapolis, Minnesota, USA. We all live in the Twin Cities metropolitan area.

My father passed away unexpectedly in 1989, just weeks before the Berlin Wall fell.

I spent 1990 as an exchange student in Auckland, New Zealand.

I attended Grinnell college, starting in 1992. I received a Bachelor of Arts degree in Anthropology in December of 1995.

I now work in the Information Technology field for an insurance company.

My mother and I were in Germany on September 11, 2001.

In addition to the English language and German, I either speak or have studied American Sign Language, French, Mandarin Chinese, Modern Greek, plus smatterings of many other languages.

Grammatical and Orthographic Pet Peeves I have been known to edit an article simply for any one of these mistakes, particularly when they compromise clarity.

 * Confusing it’s and its. it’s = "it is", its = possessive form of "it".
 * Confusing who’s and whose. See above.
 * "It is I" is incorrect. The correct form is "It is me."  (After all, you'd never say "It's I!")  Compare with "It is him/her": Your choices are "I/He/She/It/You (verb) me/him/her/it/you."  See English grammar for a chart of all pronoun declensions.
 * And just to mark myself as a bad example, try to avoid confusing "who" and "whom". A quick test: replace who/whom with he/him.  Use "who" if "he" sounds natural, and use "whom" if "him" sounds right.
 * Affect is a cause, effect is a result. Also, insure : ensure :: protect : make sure.
 * Principal is the head of a school, or a noun meaning "chief, main, primary"; Principle is an ideal or a general rule.
 * The principal of the school was the principal advocate for the principle of fairness for all students.

 * Peeving right back at you: "It is I" is not incorrect, it's formal and/or archaic. "It is I, Arthur King of the Britons." "It is I, Big Billy Goat Gruff." While we're at it, "affect" is only a noun in a very limited and technical sense, and the "insure/ensure" stuff is partly UK/UK. Vicki Rosenzweig, Friday, July 5, 2002

 * Hi Vicki... Actually, I was referring to the use of "affect" and "effect" as verbs.  As a noun, "affect" is pronounced /} fEkt/, and is rarely misspelled.  As a verb, it's pronounced /@ fEkt/.  I pronounce "effect" /i fEkt/ or /E fEkt/, but I often hear /@ fEkt/.  Regardless, most people don't seem to realize that they are two distinct words with distinct meanings:  His behavior affected the effects of the law.  The problem is that the distinction is subtle enough that it's hard to encapsulate in a short "rule of thumb".
 * As for "It is I"... I wasn't aware of the formal/archaic use. I just thought it was wrong, based on the "incorrect" declension of the pronoun.  Though I've always been willing, based on common usage, to accept it as an emphatic form (grammatical deviation for emphasis).  Thanks for the correction/info!

 * I believe that the theory goes that, since the subject and the object of the verb to be are referring to the same thing, they take the same case (the nominative). If you use your own argument about who and whom, and use whom where him would go in the sentence it is him, then you come out with whom are you? which is unnatural at best and ear-grating at worst. :) thefamouseccles 23:17 GMT, 05-06-03

 * Yes, but isn't the Wh-word in your *whom are you example actually the subject of the verb? cf. "he is you", "they are you", therefore "who are you".  It's important to use the parallel construction!  In your example, the actual Wh-word replacement would be it is whom?  This is a case where many English speakers exhibit ergativity by using "it is who" and "it is he" instead of the more correct "it is whom" and "it is him".  :-) pgdudda 04:11 9 Jun 2003 (UTC)

 * You're right, my interpretation of the WH-question was incorrect. The construct it is whom? doesn't sound so bad to me as whom is it?. I'd just like to note, though, that the phenomenon in the sentence it is he might not be true ergativity, but what I call nominative equivalence (I haven't been able to find out whether there's alinguistic term for the phenomenon). Many languages (including Ubykh, my linguistic speciality) place the subject and the direct object of copular verbs, particularly to be, in the same case (in English, the nominative; in Ubykh, the absolutive) in order to demonstrate that the two noun phrases are equivalent. The fact that Ubykh itself is an ergative language makes the point even more interesting. It may be possible that languages with equivalence-based copular constructions use their default case in those constructs. What is the basic case of English nouns? thefamouseccles 05:35 29 Sep 2003 (UTC)

 * In my experience, speakers of English more often use who to start a question, regardless of which of who/whom is "correct", and when they do use whom, it is somewhat forced. I am inclined to group the who/whom rule together with "don't end a sentence with a preposition" and "don't use split infinitives": a stodgy 19th century prescriptive rule of grammar that did not reflect how English was spoken when it was written, much less today.  Most modern grammarians (that is, academics who study grammar within the field of linguistics, not authors of manuals of style) agree.  Now this is not to say that whom has no use in modern English or that speakers and writers should not be aware of the distinction, and I'm glad to see you can justify your opinion, but I would hope you would have restraint not to impose your grammar except where necessary for clarity. CyborgTosser 16:09, 25 Aug 2004 (UTC)
 * Of course not. Only when we're arguing about grammar. :) The fact is that people who use whom (like me) are in a very small minority, and it wouldn't surprise me if it dies out within a generation. I have no problem with that, and I wouldn't dream of pushing my way of speaking on another. That's beyond constructive criticism and into the realm of just plain rude. thefamouseccles 13:29, 20 Jan 2005 (UTC)

title: User:Pgdudda


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Rowrbrazzle

Rowrbrazzle is an Amateur Press Association magazine devoted to funny animal cartoon illustration.

History
Rowrbrazzle was founded in 1983 by Marc Schirmeister, who published the first issue in February 1984, and was editor for the first nineteen quarterly mailings. Fred Patten was then editor from January 1989 (Issue 20) through January 2005 until suffering a stroke and retiring after Issue 84. Edd Vick became Official Editor from April 2005 (Issue 85) to April 2007 (Issue 93), William Earl Haskell became Official Editor from Issue 94 (July 2007) to January 2016 (Issue 128) when he was forced to retire due to poor health, and Edd Vick became Official Editor again from April 2016 (Issue 129).

The first Rowrbrazzle was distributed to the association membership in February 1984.

Landmark issue number 150 was distributed in July 2021, in a continuing uninterrupted run of 37 1/2 years.

Significance
Fred Patten, onetime editor of Rowrbrazzle, had this view of Rowrbrazzle's significance:
 * "My thesis is that furry fandom coalesced out of sf fandom and comics fandom, blending elements from both of them and achieving its own critical mass in 1983/1984. The first clear signs of the independent furry fandom were the creation of its first APA, Rowrbrazzle, and the decision by some fans to self-publish furry comic books because there seemed to be enough fans of stories with talking animals to support them (as distinct from earlier attempts to self-publish comics which had to hope for sufficient sales from the public alone.)
 * "Rowrbrazzle started in February 1984. Since it was specifically an APA for writing and drawing funny animals as a genre and discussing the new fandom that was forming about them, it is a handy landmark to say that 'furry fandom existed at this time.'"
 * "Rowrbrazzle started in February 1984. Since it was specifically an APA for writing and drawing funny animals as a genre and discussing the new fandom that was forming about them, it is a handy landmark to say that 'furry fandom existed at this time.'"

title: Rowrbrazzle


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Precognition

Precognition (from the Latin prae- 'before', and cognitio 'acquiring knowledge') is the purported psychic phenomenon of seeing, or otherwise becoming directly aware of, events in the future.

There is no accepted scientific evidence that precognition is a real effect, and it is widely considered to be pseudoscience. Precognition violates the principle of causality, that an effect cannot occur before its cause.

Precognition has been widely believed in throughout history. Despite the lack of scientific evidence, many people believe it to be real; it is still widely reported and remains a topic of research and discussion within the parapsychology community.

Precognitive phenomena
Precognition is sometimes treated as an example of the wider phenomenon of prescience or foreknowledge, to understand by any means what is likely to happen in the future. It is distinct from premonition, which is a vaguer feeling of some impending disaster. Related activities such as predictive prophecy and fortune telling have been practised throughout history.

Precognitive dreams are the most widely reported occurrences of precognition. Usually, a dream or vision can only be identified as precognitive after the putative event has taken place. When such an event occurs after a dream, it is said to have "broken the dream".

In religion
In Judaism it is believed that dreams are mostly insignificant while others "have the potential to contain prophetic messages". Others hold that dreams have meaning, and bad dreams require amelioration. According to the Book of Genesis, God granted Joseph precognition through prophetic dreams and the ability to interpret the dreams of others.

Precognition has a role in Buddhism with dreams believed to be 'mind-created phenomena'. Those dreams which 'warn of impending danger or even prepare us for overwhelming good news" are considered the most important.

History
Throughout history it has been believed that certain individuals have precognitive abilities, or that certain practices can induce such experiences, and these visions have sometimes been associated with important historical events. Despite the lack of scientific evidence, many people still believe in precognition. A poll in 2005 showed 73% of Americans believe in at least one type of paranormal experience, with 41% believing in extrasensory perception.

Antiquity
Since ancient times precognition has been associated with dreams and trance states as well as waking premonitions, giving rise to acts of prophecy and fortune telling. Oracles, originally seen as sources of wisdom, became progressively associated with previsions of the future.

Such claims of seeing the future have never been without their sceptical critics. Aristotle carried out an inquiry into allegedly prophetic dreams in his On Divination in Sleep. He accepted that "it is quite conceivable that some dreams may be tokens and causes [of future events]" but also believed that "most [so-called prophetic] dreams are, however, to be classed as mere coincidences...". Where Democritus had suggested that emanations from future events could be sent back to the dreamer, Aristotle proposed that it was, rather, the dreamer's sense impressions which reached forward to the event.

17th–19th centuries
The term "precognition" first appeared in the 17th century but did not come into common use among investigators until much later.

An early investigation into claims of precognition was published by the missionary Fr. P. Boilat in 1883. He claimed to have put an unspoken question to an African witch-doctor whom he mistrusted. Contrary to his expectations, the witch-doctor gave him the correct answer without ever having heard the question.

Early 20th century
In the early 20th century J. W. Dunne, a British soldier and aeronautics engineer, experienced several dreams which he regarded as precognitive. He developed techniques to record and analyse them, identifying any correspondences between his future experiences and his recorded dreams. He reported his findings in his 1927 book An Experiment with Time. In it he alleges that 10% of his dreams appeared to include some element of future experience. He also persuaded some friends to try the experiment on themselves, with mixed results. He noted a strong cognitive bias in which subjects, including himself, were reluctant to ascribe their dream correspondences to precognition and determinedly sought alternative explanations. Dunne concluded that precognitive elements in dreams are common and that many people unknowingly have them. He suggested also that dream precognition did not reference future events of all kinds, but specifically the future experiences of the dreamer. He was led to this idea when he found that a dream of a volcanic eruption appeared to foresee not the disaster itself but his subsequent misreading of an inaccurate account in a newspaper.

Edith Lyttelton, who became President of the Society for Psychical Research (SPR), regarded his theory as consistent with her own idea of the superconscious. In 1932 he helped the SPR to conduct a more formal experiment, but he and the Society's lead researcher Theodore Besterman failed to agree on the significance of the results. Nevertheless, the Philosopher C. D. Broad remarked that, "The only theory known to me which seems worth consideration is that proposed by Mr. Dunne in his Experiment with Time." An Experiment with Time was widely read and "undoubtedly helped to form something of the imaginative climate of [the interwar] years", influencing many writers of both fact and fiction both then and since. According to Flieger, "Dunne's theory was so current and popular a topic that not to understand it was a mark of singularity." Major writers whose work was significantly influenced by his ideas on precognition in dreams and visions include H. G. Wells, J. B. Priestley and Olaf Stapledon. Vladimir Nabokov was also later influenced by Dunne.

In 1932 Charles Lindbergh's infant son was kidnapped, murdered and buried among trees. Psychologists Henry Murray and D. R. Wheeler used the event to test for dream precognition, by inviting the public to report any dreams of the child. A total of 1,300 dreams were reported. Only five per cent envisioned the child dead and only 4 of the 1,300 envisioned the location of the grave as amongst trees.

The first ongoing and organised research program on precognition was instituted by husband-and-wife team Joseph Banks Rhine and Louisa E. Rhine in the 1930s at Duke University's Parapsychology Laboratory. J. B. Rhine used a method of forced-choice matching in which participants guessed the order of a deck of 25 cards, each five of which bore one of five geometrical symbols. Although his results were positive and gained some academic acceptance, his methods were later shown to be badly flawed and subsequent researchers using more rigorous procedures were unable to reproduce his results. His mathematics was sometimes flawed, the experiments were not double-blinded or even necessarily single-blinded and some of the cards to be guessed were so thin that the symbol could be seen through the backing.

Samuel G. Soal, another leading member of the SPR, was described by Rhine as one of his harshest critics, running many similar experiments with wholly negative results. However, from around 1940 he ran forced-choice ESP experiments in which a subject attempted to identify which of five animal pictures a subject in another room was looking at. Their performance on this task was at chance, but when the scores were matched with the card that came after the target card, three of the thirteen subjects showed a very high hit rate; Rhine now described Soal's work as "a milestone in the field". However analyses of Soal's findings, conducted several years later, concluded that the positive results were more likely the result of deliberate fraud. The controversy continued for many years more. In 1978 the statistician and parapsychology researcher Betty Markwick, while seeking to vindicate Soal, discovered that he had tampered with his data. The untainted experimental results showed no evidence of precognition.

Late 20th century
As more modern technology became available, more automated techniques of experimentation were developed that did not rely on hand-scoring of equivalence between targets and guesses, and in which the targets could be more reliably and readily tested at random. In 1969 Helmut Schmidt introduced the use of high-speed random event generators (REG) for precognition testing, and experiments were also conducted at the Princeton Engineering Anomalies Research Lab. Once again, flaws were found in all of Schmidt's experiments, when the psychologist C. E. M. Hansel found that several necessary precautions were not taken.

SF writer Philip K Dick believed that he had precognitive experiences and used the idea in some of his novels, especially as a central plot element in his 1956 science fiction short story "The Minority Report" and in his 1956 novel The World Jones Made.

In 1963 the BBC television programme Monitor broadcast an appeal by the writer J.B. Priestley for experiences which challenged our understanding of Time. He received hundreds of letters in reply and believed that many of them described genuine precognitive dreams. In 2014 the BBC Radio 4 broadcaster Francis Spufford revisited Priestley's work and its relation to the ideas of J.W. Dunne.

In 1965 G. W. Lambert, a former Council member of the SPR, proposed five criteria that needed to be met before an account of a precognitive dream could be regarded as credible:
 * 1) The dream should be reported to a credible witness before the event.
 * 2) The time interval between the dream and the event should be short.
 * 3) The event should be unexpected at the time of the dream.
 * 4) The description should be of an event destined literally, and not symbolically, to happen.
 * 5) The details of dream and event should tally.

David Ryback, a psychologist in Atlanta, used a questionnaire survey approach to investigate precognitive dreaming in college students during the 1980s. His survey of over 433 participants showed that 290 or 66.9 per cent reported some form of paranormal dream. He rejected many of these reports, but claimed that 8.8 per cent of the population was having actual precognitive dreams.

21st century
In 2011 the psychologist Daryl Bem, a Professor Emeritus at Cornell University, published findings showing statistical evidence for precognition in the Journal of Personality and Social Psychology. The paper was heavily criticised, and the criticism widened to include the journal itself and the validity of the peer-review process. In 2012, an independent attempt to reproduce Bem's results was published, but it failed to do so. The widespread controversy led to calls for improvements in practice and for more research.

Scientific reception
Claims of precognition are, like any other claims, open to scientific criticism. However, the nature of the criticism must adapt to the nature of the claim.

Pseudoscience
Claims of precognition are criticised on three main grounds: Consequently, precognition is widely considered to be pseudoscience.
 * There is no known scientific mechanism which would allow precognition. It breaks temporal causality, in that the precognised event causes an effect in the subject prior to the event itself.
 * The large body of experimental work has produced no accepted scientific evidence that precognition exists.
 * The large body of anecdotal evidence can be explained by alternative psychological mechanisms.

Violation of causality
Precognition would violate the principle of antecedence (causality); that is, that an effect does not happen before its cause. Information passing backwards in time (retrocausality) would need to be carried by physical particles doing the same. Experimental evidence from high-energy physics suggests that this cannot happen. There is therefore no direct justification for precognition from a physics-based approach.

Precognition would also contradict "most of the neuroscience and psychology literature, from electrophysiology and neuroimaging to temporal effects found in psychophysical research."

Lack of evidence
A great deal of evidence for precognition has been put forward, both as witnessed anecdotes and as experimental results, but none has been accepted as rigorous scientific proof of the phenomenon. Even the most prominent pieces of evidence have been repeatedly rejected due to errors in those experiments as well as follow-on studies contradicting the original evidence. This suggests that the evidence was not valid in the first place.

Alternative explanations
Various known psychological processes have been put forward to explain experiences of apparent precognition. These include:

 * Coincidence, where apparent instances of precognition in fact arise from the law of large numbers.
 * Self-fulfilling prophecy and unconscious enactment, where people unconsciously bring about events which they have previously imagined.
 * Unconscious perception, where people unconsciously infer, from data they have unconsciously learned, that a certain event will probably happen in a certain context. When the event occurs, the former knowledge appears to have been acquired without the aid of recognised channels of information.
 * Retrofitting, which involves the false interpretation of a past record of a dream or vision, in order to match it to a recent event. Retrofitting provides an explanation for the supposed accuracy of Nostradamus's vague predictions. For example, quatrain I:60 states "A ruler born near Italy...He's less a prince than a butcher." The phrase "near Italy" can be construed as covering a very broad range of geography, while no details are provided by Nostradamus regarding the era when this ruler will live.   Because of this vagueness, and the flexibility of retrofitting, this quatrain has been interpreted by some as referring to Napoleon, but by others as referring to the Holy Roman Emperor Ferdinand II, and by others still as a reference to Hitler.
 * False memories, such as identifying paramnesia and memory biases, where the memory of a non-existent precognitive event is formed after the real event has occurred. Where subjects in a dream experiment have been asked to write down their dreams in a diary, this can prevent selective memory effects such that the dreams no longer seem accurate about the future.
 * Déjà vu, where people experience a false feeling that an identical event has occurred previously. Some recent authors have suggested that déjà vu and identifying paramnesia are the same thing. This view is not universally held, with others instead treating them as distinct phenomena.

Psychological explanations have also been proposed for belief in precognition. Psychologists have conducted experiments which are claimed to show that people who feel loss of control in their lives will turn to belief in precognition, because it gives them a sense of regaining control.

title: Precognition


text:
Genetic algorithm

In 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.

Optimization problems
In a genetic algorithm, a population of candidate solutions (called individuals, creatures, organisms, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible.

The evolution usually starts from a population of randomly generated individuals, and is an iterative process, with the population in each iteration called a generation. In each generation, the fitness of every individual in the population is evaluated; the fitness is usually the value of the objective function in the optimization problem being solved. The more fit individuals are stochastically selected from the current population, and each individual's genome is modified (recombined and possibly randomly mutated) to form a new generation. The new generation of candidate solutions is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population.

A typical genetic algorithm requires:

 * 1) a genetic representation of the solution domain,
 * 2) a fitness function to evaluate the solution domain.

A standard representation of each candidate solution is as an array of bits (also called bit set or bit string). Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size, which facilitates simple crossover operations. Variable length representations may also be used, but crossover implementation is more complex in this case. Tree-like representations are explored in genetic programming and graph-form representations are explored in evolutionary programming; a mix of both linear chromosomes and trees is explored in gene expression programming.

Once the genetic representation and the fitness function are defined, a GA proceeds to initialize a population of solutions and then to improve it through repetitive application of the mutation, crossover, inversion and selection operators.

Initialization
The population size depends on the nature of the problem, but typically contains several hundreds or thousands of possible solutions. Often, the initial population is generated randomly, allowing the entire range of possible solutions (the search space). Occasionally, the solutions may be "seeded" in areas where optimal solutions are likely to be found or the distribution of the sampling probability tuned to focus in those areas of greater interest.

Selection
During each successive generation, a portion of the existing population is selected to reproduce for a new generation. Individual solutions are selected through a fitness-based process, where fitter solutions (as measured by a fitness function) are typically more likely to be selected. Certain selection methods rate the fitness of each solution and preferentially select the best solutions. Other methods rate only a random sample of the population, as the former process may be very time-consuming.

The fitness function is defined over the genetic representation and measures the quality of the represented solution. The fitness function is always problem-dependent. For instance, in the knapsack problem one wants to maximize the total value of objects that can be put in a knapsack of some fixed capacity. A representation of a solution might be an array of bits, where each bit represents a different object, and the value of the bit (0 or 1) represents whether or not the object is in the knapsack. Not every such representation is valid, as the size of objects may exceed the capacity of the knapsack. The fitness of the solution is the sum of values of all objects in the knapsack if the representation is valid, or 0 otherwise.

In some problems, it is hard or even impossible to define the fitness expression; in these cases, a simulation may be used to determine the fitness function value of a phenotype (e.g. computational fluid dynamics is used to determine the air resistance of a vehicle whose shape is encoded as the phenotype), or even interactive genetic algorithms are used.

Genetic operators
The next step is to generate a second generation population of solutions from those selected, through a combination of genetic operators: crossover (also called recombination), and mutation.

For each new solution to be produced, a pair of "parent" solutions is selected for breeding from the pool selected previously. By producing a "child" solution using the above methods of crossover and mutation, a new solution is created which typically shares many of the characteristics of its "parents". New parents are selected for each new child, and the process continues until a new population of solutions of appropriate size is generated. Although reproduction methods that are based on the use of two parents are more "biology inspired", some research suggests that more than two "parents" generate higher quality chromosomes.

These processes ultimately result in the next generation population of chromosomes that is different from the initial generation. Generally, the average fitness will have increased by this procedure for the population, since only the best organisms from the first generation are selected for breeding, along with a small proportion of less fit solutions. These less fit solutions ensure genetic diversity within the genetic pool of the parents and therefore ensure the genetic diversity of the subsequent generation of children.

Opinion is divided over the importance of crossover versus mutation. There are many references in Fogel (2006) that support the importance of mutation-based search.

Although crossover and mutation are known as the main genetic operators, it is possible to use other operators such as regrouping, colonization-extinction, or migration in genetic algorithms.

It is worth tuning parameters such as the mutation probability, crossover probability and population size to find reasonable settings for the problem class being worked on. A very small mutation rate may lead to genetic drift (which is non-ergodic in nature). A recombination rate that is too high may lead to premature convergence of the genetic algorithm. A mutation rate that is too high may lead to loss of good solutions, unless elitist selection is employed. An adequate population size ensures sufficient genetic diversity for the problem at hand, but can lead to a waste of computational resources if set to a value larger than required.

Heuristics
In addition to the main operators above, other heuristics may be employed to make the calculation faster or more robust. The speciation heuristic penalizes crossover between candidate solutions that are too similar; this encourages population diversity and helps prevent premature convergence to a less optimal solution.

Termination
This generational process is repeated until a termination condition has been reached. Common terminating conditions are:

 * A solution is found that satisfies minimum criteria
 * Fixed number of generations reached
 * Allocated budget (computation time/money) reached
 * The highest ranking solution's fitness is reaching or has reached a plateau such that successive iterations no longer produce better results
 * Manual inspection
 * Combinations of the above

The building block hypothesis
Genetic algorithms are simple to implement, but their behavior is difficult to understand. In particular, it is difficult to understand why these algorithms frequently succeed at generating solutions of high fitness when applied to practical problems. The building block hypothesis (BBH) consists of:

 * 1) A description of a heuristic that performs adaptation by identifying and recombining "building blocks", i.e. low order, low defining-length schemata with above average fitness.
 * 2) A hypothesis that a genetic algorithm performs adaptation by implicitly and efficiently implementing this heuristic.

Goldberg describes the heuristic as follows:

 * "Short, low order, and highly fit schemata are sampled, recombined [crossed over], and resampled to form strings of potentially higher fitness. In a way, by working with these particular schemata [the building blocks], we have reduced the complexity of our problem; instead of building high-performance strings by trying every conceivable combination, we construct better and better strings from the best partial solutions of past samplings.

 * "Because highly fit schemata of low defining length and low order play such an important role in the action of genetic algorithms, we have already given them a special name: building blocks. Just as a child creates magnificent fortresses through the arrangement of simple blocks of wood, so does a genetic algorithm seek near optimal performance through the juxtaposition of short, low-order, high-performance schemata, or building blocks."

Despite the lack of consensus regarding the validity of the building-block hypothesis, it has been consistently evaluated and used as reference throughout the years. Many estimation of distribution algorithms, for example, have been proposed in an attempt to provide an environment in which the hypothesis would hold. Although good results have been reported for some classes of problems, skepticism concerning the generality and/or practicality of the building-block hypothesis as an explanation for GAs' efficiency still remains. Indeed, there is a reasonable amount of work that attempts to understand its limitations from the perspective of estimation of distribution algorithms.

Limitations
The practical use of a genetic algorithm has limitations, especially as compared to alternative optimization algorithms:

 * Repeated fitness function evaluation for complex problems is often the most prohibitive and limiting segment of artificial evolutionary algorithms. Finding the optimal solution to complex high-dimensional, multimodal problems often requires very expensive fitness function evaluations. In real world problems such as structural optimization problems, a single function evaluation may require several hours to several days of complete simulation. Typical optimization methods cannot deal with such types of problem. In this case, it may be necessary to forgo an exact evaluation and use an approximated fitness that is computationally efficient. It is apparent that amalgamation of approximate models may be one of the most promising approaches to convincingly use GA to solve complex real life problems.
 * Genetic algorithms do not scale well with complexity. That is, where the number of elements which are exposed to mutation is large there is often an exponential increase in search space size. This makes it extremely difficult to use the technique on problems such as designing an engine, a house or a plane . In order to make such problems tractable to evolutionary search, they must be broken down into the simplest representation possible. Hence we typically see evolutionary algorithms encoding designs for fan blades instead of engines, building shapes instead of detailed construction plans, and airfoils instead of whole aircraft designs. The second problem of complexity is the issue of how to protect parts that have evolved to represent good solutions from further destructive mutation, particularly when their fitness assessment requires them to combine well with other parts.
 * The "better" solution is only in comparison to other solutions. As a result, the stopping criterion is not clear in every problem.
 * In many problems, GAs have a tendency to converge towards local optima or even arbitrary points rather than the global optimum of the problem. This means that it does not "know how" to sacrifice short-term fitness to gain longer-term fitness. The likelihood of this occurring depends on the shape of the fitness landscape: certain problems may provide an easy ascent towards a global optimum, others may make it easier for the function to find the local optima. This problem may be alleviated by using a different fitness function, increasing the rate of mutation, or by using selection techniques that maintain a diverse population of solutions, although the No Free Lunch theorem proves that there is no general solution to this problem. A common technique to maintain diversity is to impose a "niche penalty", wherein, any group of individuals of sufficient similarity (niche radius) have a penalty added, which will reduce the representation of that group in subsequent generations, permitting other (less similar) individuals to be maintained in the population. This trick, however, may not be effective, depending on the landscape of the problem. Another possible technique would be to simply replace part of the population with randomly generated individuals, when most of the population is too similar to each other. Diversity is important in genetic algorithms (and genetic programming) because crossing over a homogeneous population does not yield new solutions. In evolution strategies and evolutionary programming, diversity is not essential because of a greater reliance on mutation.
 * Operating on dynamic data sets is difficult, as genomes begin to converge early on towards solutions which may no longer be valid for later data. Several methods have been proposed to remedy this by increasing genetic diversity somehow and preventing early convergence, either by increasing the probability of mutation when the solution quality drops (called triggered hypermutation), or by occasionally introducing entirely new, randomly generated elements into the gene pool (called random immigrants). Again, evolution strategies and evolutionary programming can be implemented with a so-called "comma strategy" in which parents are not maintained and new parents are selected only from offspring. This can be more effective on dynamic problems.
 * GAs cannot effectively solve problems in which the only fitness measure is a binary pass/fail outcome (like decision problems), as there is no way to converge on the solution (no hill to climb). In these cases, a random search may find a solution as quickly as a GA. However, if the situation allows the success/failure trial to be repeated giving (possibly) different results, then the ratio of successes to failures provides a suitable fitness measure.
 * For specific optimization problems and problem instances, other optimization algorithms may be more efficient than genetic algorithms in terms of speed of convergence. Alternative and complementary algorithms include evolution strategies, evolutionary programming, simulated annealing, Gaussian adaptation, hill climbing, and swarm intelligence (e.g.: ant colony optimization, particle swarm optimization) and methods based on integer linear programming. The suitability of genetic algorithms is dependent on the amount of knowledge of the problem; well known problems often have better, more specialized approaches.

Chromosome representation
The simplest algorithm represents each chromosome as a bit string. Typically, numeric parameters can be represented by integers, though it is possible to use floating point representations. The floating point representation is natural to evolution strategies and evolutionary programming. The notion of real-valued genetic algorithms has been offered but is really a misnomer because it does not really represent the building block theory that was proposed by John Henry Holland in the 1970s. This theory is not without support though, based on theoretical and experimental results (see below). The basic algorithm performs crossover and mutation at the bit level. Other variants treat the chromosome as a list of numbers which are indexes into an instruction table, nodes in a linked list, hashes, objects, or any other imaginable data structure. Crossover and mutation are performed so as to respect data element boundaries. For most data types, specific variation operators can be designed. Different chromosomal data types seem to work better or worse for different specific problem domains.

When bit-string representations of integers are used, Gray coding is often employed. In this way, small changes in the integer can be readily affected through mutations or crossovers. This has been found to help prevent premature convergence at so-called Hamming walls, in which too many simultaneous mutations (or crossover events) must occur in order to change the chromosome to a better solution.

Other approaches involve using arrays of real-valued numbers instead of bit strings to represent chromosomes. Results from the theory of schemata suggest that in general the smaller the alphabet, the better the performance, but it was initially surprising to researchers that good results were obtained from using real-valued chromosomes. This was explained as the set of real values in a finite population of chromosomes as forming a virtual alphabet (when selection and recombination are dominant) with a much lower cardinality than would be expected from a floating point representation.

An expansion of the Genetic Algorithm accessible problem domain can be obtained through more complex encoding of the solution pools by concatenating several types of heterogenously encoded genes into one chromosome. This particular approach allows for solving optimization problems that require vastly disparate definition domains for the problem parameters. For instance, in problems of cascaded controller tuning, the internal loop controller structure can belong to a conventional regulator of three parameters, whereas the external loop could implement a linguistic controller (such as a fuzzy system) which has an inherently different description. This particular form of encoding requires a specialized crossover mechanism that recombines the chromosome by section, and it is a useful tool for the modelling and simulation of complex adaptive systems, especially evolution processes.

Elitism
A practical variant of the general process of constructing a new population is to allow the best organism(s) from the current generation to carry over to the next, unaltered. This strategy is known as elitist selection and guarantees that the solution quality obtained by the GA will not decrease from one generation to the next.

Parallel implementations
Parallel implementations of genetic algorithms come in two flavors. Coarse-grained parallel genetic algorithms assume a population on each of the computer nodes and migration of individuals among the nodes. Fine-grained parallel genetic algorithms assume an individual on each processor node which acts with neighboring individuals for selection and reproduction. Other variants, like genetic algorithms for online optimization problems, introduce time-dependence or noise in the fitness function.

Adaptive GAs
Genetic algorithms with adaptive parameters (adaptive genetic algorithms, AGAs) is another significant and promising variant of genetic algorithms. The probabilities of crossover (pc) and mutation (pm) greatly determine the degree of solution accuracy and the convergence speed that genetic algorithms can obtain. Researchers have analyzed GA convergence analytically.

Instead of using fixed values of pc and pm, AGAs utilize the population information in each generation and adaptively adjust the pc and pm in order to maintain the population diversity as well as to sustain the convergence capacity. In AGA (adaptive genetic algorithm), the adjustment of pc and pm depends on the fitness values of the solutions. There are more examples of AGA variants: Successive zooming method is an early example of improving convergence. In CAGA (clustering-based adaptive genetic algorithm), through the use of clustering analysis to judge the optimization states of the population, the adjustment of pc and pm depends on these optimization states. Recent approaches use more abstract variables for deciding pc and pm. Examples are dominance & co-dominance principles and LIGA (levelized interpolative genetic algorithm), which combines a flexible GA with modified A* search to tackle search space anisotropicity.

It can be quite effective to combine GA with other optimization methods. A GA tends to be quite good at finding generally good global solutions, but quite inefficient at finding the last few mutations to find the absolute optimum. Other techniques (such as simple hill climbing) are quite efficient at finding absolute optimum in a limited region. Alternating GA and hill climbing can improve the efficiency of GA while overcoming the lack of robustness of hill climbing.

This means that the rules of genetic variation may have a different meaning in the natural case. For instance – provided that steps are stored in consecutive order – crossing over may sum a number of steps from maternal DNA adding a number of steps from paternal DNA and so on. This is like adding vectors that more probably may follow a ridge in the phenotypic landscape. Thus, the efficiency of the process may be increased by many orders of magnitude. Moreover, the inversion operator has the opportunity to place steps in consecutive order or any other suitable order in favour of survival or efficiency.

A variation, where the population as a whole is evolved rather than its individual members, is known as gene pool recombination.

A number of variations have been developed to attempt to improve performance of GAs on problems with a high degree of fitness epistasis, i.e. where the fitness of a solution consists of interacting subsets of its variables. Such algorithms aim to learn (before exploiting) these beneficial phenotypic interactions. As such, they are aligned with the Building Block Hypothesis in adaptively reducing disruptive recombination. Prominent examples of this approach include the mGA, GEMGA and LLGA.

Problem domains
Problems which appear to be particularly appropriate for solution by genetic algorithms include timetabling and scheduling problems, and many scheduling software packages are based on GAs. GAs have also been applied to engineering. Genetic algorithms are often applied as an approach to solve global optimization problems.

As a general rule of thumb genetic algorithms might be useful in problem domains that have a complex fitness landscape as mixing, i.e., mutation in combination with crossover, is designed to move the population away from local optima that a traditional hill climbing algorithm might get stuck in. Observe that commonly used crossover operators cannot change any uniform population. Mutation alone can provide ergodicity of the overall genetic algorithm process (seen as a Markov chain).

Examples of problems solved by genetic algorithms include: mirrors designed to funnel sunlight to a solar collector, antennae designed to pick up radio signals in space, walking methods for computer figures, optimal design of aerodynamic bodies in complex flowfields

In his Algorithm Design Manual, Skiena advises against genetic algorithms for any task:

"[I]t is quite unnatural to model applications in terms of genetic operators like mutation and crossover on bit strings. The pseudobiology adds another level of complexity between you and your problem. Second, genetic algorithms take a very long time on nontrivial problems. [...] [T]he analogy with evolution—where significant progress require [sic] millions of years—can be quite appropriate. [...] I have never encountered any problem where genetic algorithms seemed to me the right way to attack it. Further, I have never seen any computational results reported using genetic algorithms that have favorably impressed me. Stick to simulated annealing for your heuristic search voodoo needs."

History
In 1950, Alan Turing proposed a "learning machine" which would parallel the principles of evolution. Computer simulation of evolution started as early as in 1954 with the work of Nils Aall Barricelli, who was using the computer at the Institute for Advanced Study in Princeton, New Jersey. His 1954 publication was not widely noticed. Starting in 1957, the Australian quantitative geneticist Alex Fraser published a series of papers on simulation of artificial selection of organisms with multiple loci controlling a measurable trait. From these beginnings, computer simulation of evolution by biologists became more common in the early 1960s, and the methods were described in books by Fraser and Burnell (1970) and Crosby (1973). Fraser's simulations included all of the essential elements of modern genetic algorithms. In addition, Hans-Joachim Bremermann published a series of papers in the 1960s that also adopted a population of solution to optimization problems, undergoing recombination, mutation, and selection. Bremermann's research also included the elements of modern genetic algorithms. Other noteworthy early pioneers include Richard Friedberg, George Friedman, and Michael Conrad. Many early papers are reprinted by Fogel (1998).

Although Barricelli, in work he reported in 1963, had simulated the evolution of ability to play a simple game, artificial evolution only became a widely recognized optimization method as a result of the work of Ingo Rechenberg and Hans-Paul Schwefel in the 1960s and early 1970s – Rechenberg's group was able to solve complex engineering problems through evolution strategies. Another approach was the evolutionary programming technique of Lawrence J. Fogel, which was proposed for generating artificial intelligence. Evolutionary programming originally used finite state machines for predicting environments, and used variation and selection to optimize the predictive logics. Genetic algorithms in particular became popular through the work of John Holland in the early 1970s, and particularly his book Adaptation in Natural and Artificial Systems (1975). His work originated with studies of cellular automata, conducted by Holland and his students at the University of Michigan. Holland introduced a formalized framework for predicting the quality of the next generation, known as Holland's Schema Theorem. Research in GAs remained largely theoretical until the mid-1980s, when The First International Conference on Genetic Algorithms was held in Pittsburgh, Pennsylvania.

Commercial products
In the late 1980s, General Electric started selling the world's first genetic algorithm product, a mainframe-based toolkit designed for industrial processes. In 1989, Axcelis, Inc. released Evolver, the world's first commercial GA product for desktop computers. The New York Times technology writer John Markoff wrote about Evolver in 1990, and it remained the only interactive commercial genetic algorithm until 1995. Evolver was sold to Palisade in 1997, translated into several languages, and is currently in its 6th version. Since the 1990s, MATLAB has built in three derivative-free optimization heuristic algorithms (simulated annealing, particle swarm optimization, genetic algorithm) and two direct search algorithms (simplex search, pattern search).

Parent fields
Genetic algorithms are a sub-field:
 * Evolutionary algorithms
 * Evolutionary computing
 * Metaheuristics
 * Stochastic optimization
 * Optimization

Evolutionary algorithms
Evolutionary algorithms is a sub-field of evolutionary computing.

 * Evolution strategies (ES, see Rechenberg, 1994) evolve individuals by means of mutation and intermediate or discrete recombination. ES algorithms are designed particularly to solve problems in the real-value domain. They use self-adaptation to adjust control parameters of the search. De-randomization of self-adaptation has led to the contemporary Covariance Matrix Adaptation Evolution Strategy (CMA-ES).
 * Evolutionary programming (EP) involves populations of solutions with primarily mutation and selection and arbitrary representations. They use self-adaptation to adjust parameters, and can include other variation operations such as combining information from multiple parents.
 * Estimation of Distribution Algorithm (EDA) substitutes traditional reproduction operators by model-guided operators. Such models are learned from the population by employing machine learning techniques and represented as Probabilistic Graphical Models, from which new solutions can be sampled or generated from guided-crossover.
 * Genetic programming (GP) is a related technique popularized by John Koza in which computer programs, rather than function parameters, are optimized. Genetic programming often uses tree-based internal data structures to represent the computer programs for adaptation instead of the list structures typical of genetic algorithms. There are many variants of Genetic Programming, including Cartesian genetic programming, Gene expression programming, grammatical evolution, Linear genetic programming, Multi expression programming etc.
 * Grouping genetic algorithm (GGA) is an evolution of the GA where the focus is shifted from individual items, like in classical GAs, to groups or subset of items. The idea behind this GA evolution proposed by Emanuel Falkenauer is that solving some complex problems, a.k.a. clustering or partitioning problems where a set of items must be split into disjoint group of items in an optimal way, would better be achieved by making characteristics of the groups of items equivalent to genes. These kind of problems include bin packing, line balancing, clustering with respect to a distance measure, equal piles, etc., on which classic GAs proved to perform poorly. Making genes equivalent to groups implies chromosomes that are in general of variable length, and special genetic operators that manipulate whole groups of items. For bin packing in particular, a GGA hybridized with the Dominance Criterion of Martello and Toth, is arguably the best technique to date.
 * Interactive evolutionary algorithms are evolutionary algorithms that use human evaluation. They are usually applied to domains where it is hard to design a computational fitness function, for example, evolving images, music, artistic designs and forms to fit users' aesthetic preference.

Swarm intelligence
Swarm intelligence is a sub-field of evolutionary computing.

 * Ant colony optimization (ACO) uses many ants (or agents) equipped with a pheromone model to traverse the solution space and find locally productive areas.
 * Although considered an Estimation of distribution algorithm, Particle swarm optimization (PSO) is a computational method for multi-parameter optimization which also uses population-based approach. A population (swarm) of candidate solutions (particles) moves in the search space, and the movement of the particles is influenced both by their own best known position and swarm's global best known position. Like genetic algorithms, the PSO method depends on information sharing among population members. In some problems the PSO is often more computationally efficient than the GAs, especially in unconstrained problems with continuous variables.

Other evolutionary computing algorithms
Evolutionary computation is a sub-field of the metaheuristic methods.

 * Memetic algorithm (MA), often called hybrid genetic algorithm among others, is a population-based method in which solutions are also subject to local improvement phases. The idea of memetic algorithms comes from memes, which unlike genes, can adapt themselves. In some problem areas they are shown to be more efficient than traditional evolutionary algorithms.
 * Bacteriologic algorithms (BA) inspired by evolutionary ecology and, more particularly, bacteriologic adaptation. Evolutionary ecology is the study of living organisms in the context of their environment, with the aim of discovering how they adapt. Its basic concept is that in a heterogeneous environment, there is not one individual that fits the whole environment. So, one needs to reason at the population level. It is also believed BAs could be successfully applied to complex positioning problems (antennas for cell phones, urban planning, and so on) or data mining.
 * Cultural algorithm (CA) consists of the population component almost identical to that of the genetic algorithm and, in addition, a knowledge component called the belief space.
 * Differential evolution (DE) inspired by migration of superorganisms.
 * Gaussian adaptation (normal or natural adaptation, abbreviated NA to avoid confusion with GA) is intended for the maximisation of manufacturing yield of signal processing systems. It may also be used for ordinary parametric optimisation. It relies on a certain theorem valid for all regions of acceptability and all Gaussian distributions. The efficiency of NA relies on information theory and a certain theorem of efficiency. Its efficiency is defined as information divided by the work needed to get the information. Because NA maximises mean fitness rather than the fitness of the individual, the landscape is smoothed such that valleys between peaks may disappear. Therefore it has a certain "ambition" to avoid local peaks in the fitness landscape. NA is also good at climbing sharp crests by adaptation of the moment matrix, because NA may maximise the disorder (average information) of the Gaussian simultaneously keeping the mean fitness constant.

Other metaheuristic methods
Metaheuristic methods broadly fall within stochastic optimisation methods.

 * Simulated annealing (SA) is a related global optimization technique that traverses the search space by testing random mutations on an individual solution. A mutation that increases fitness is always accepted. A mutation that lowers fitness is accepted probabilistically based on the difference in fitness and a decreasing temperature parameter. In SA parlance, one speaks of seeking the lowest energy instead of the maximum fitness. SA can also be used within a standard GA algorithm by starting with a relatively high rate of mutation and decreasing it over time along a given schedule.
 * Tabu search (TS) is similar to simulated annealing in that both traverse the solution space by testing mutations of an individual solution. While simulated annealing generates only one mutated solution, tabu search generates many mutated solutions and moves to the solution with the lowest energy of those generated. In order to prevent cycling and encourage greater movement through the solution space, a tabu list is maintained of partial or complete solutions. It is forbidden to move to a solution that contains elements of the tabu list, which is updated as the solution traverses the solution space.
 * Extremal optimization (EO) Unlike GAs, which work with a population of candidate solutions, EO evolves a single solution and makes local modifications to the worst components. This requires that a suitable representation be selected which permits individual solution components to be assigned a quality measure ("fitness"). The governing principle behind this algorithm is that of emergent improvement through selectively removing low-quality components and replacing them with a randomly selected component. This is decidedly at odds with a GA that selects good solutions in an attempt to make better solutions.

Other stochastic optimisation methods

 * The cross-entropy (CE) method generates candidate solutions via a parameterized probability distribution. The parameters are updated via cross-entropy minimization, so as to generate better samples in the next iteration.
 * Reactive search optimization (RSO) advocates the integration of sub-symbolic machine learning techniques into search heuristics for solving complex optimization problems. The word reactive hints at a ready response to events during the search through an internal online feedback loop for the self-tuning of critical parameters. Methodologies of interest for Reactive Search include machine learning and statistics, in particular reinforcement learning, active or query learning, neural networks, and metaheuristics.

Resources

 * Provides a list of resources in the genetic algorithms field
 * An Overview of the History and Flavors of Evolutionary Algorithms

Tutorials

 * Genetic Algorithms - Computer programs that "evolve" in ways that resemble natural selection can solve complex problems even their creators do not fully understand An excellent introduction to GA by John Holland and with an application to the Prisoner's Dilemma
 * An online interactive Genetic Algorithm tutorial for a reader to practise or learn how a GA works: Learn step by step or watch global convergence in batch, change the population size, crossover rates/bounds, mutation rates/bounds and selection mechanisms, and add constraints.
 * A Genetic Algorithm Tutorial by Darrell Whitley Computer Science Department Colorado State University An excellent tutorial with much theory
 * "Essentials of Metaheuristics", 2009 (225 p). Free open text by Sean Luke.
 * Global Optimization Algorithms – Theory and Application
 * Genetic Algorithms in Python Tutorial with the intuition behind GAs and Python implementation.
 * Genetic Algorithms evolves to solve the prisoner's dilemma. Written by Robert Axelrod.

Genetisk programmering

title: Genetic algorithm