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Abdelrahman Ogail

Simulated annealing - Wikipedia, the free encyclopedia - 1 views

  • Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of applied mathematics, namely locating a good approximation to the global minimum of a given function in a large search space. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For certain problems, simulated annealing may be more effective than exhaustive enumeration — provided that the goal is merely to find an acceptably good solution in a fixed amount of time, rather than the best possible solution. The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one. By analogy with this physical process, each step of the SA algorithm replaces the current solution by a random "nearby" solution, chosen with a probability that depends on the difference between the corresponding function values and on a global parameter T (called the temperature), that is gradually decreased during the process. The dependency is such that the current solution changes almost randomly when T is large, but increasingly "downhill" as T goes to zero. The allowance for "uphill" moves saves the method from becoming stuck at local minima—which are the bane of greedier methods. The method was independently described by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi in 1983 [1], and by V. Černý in 1985 [2]. The method is an adaptation of the Metropolis-Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, invented by N. Metropolis et al. in 1953 [3].
  • Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of applied mathematics, namely locating a good approximation to the global minimum of a given function in a large search space. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For certain problems, simulated annealing may be more effective than exhaustive enumeration — provided that the goal is merely to find an acceptably good solution in a fixed amount of time, rather than the best possible solution. The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one. By analogy with this physical process, each step of the SA algorithm replaces the current solution by a random "nearby" solution, chosen with a probability that depends on the difference between the corresponding function values and on a global parameter T (called the temperature), that is gradually decreased during the process. The dependency is such that the current solution changes almost randomly when T is large, but increasingly "downhill" as T goes to zero. The allowance for "uphill" moves saves the method from becoming stuck at local minima—which are the bane of greedier methods. The method was independently described by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi in 1983 [1], and by V. Černý in 1985 [2]. The method is an adaptation of the Metropolis-Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, invented by N. Metropolis et al. in 1953 [3].
  • Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of applied mathematics, namely locating a good approximation to the global minimum of a given function in a large search space. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For certain problems, simulated annealing may be more effective than exhaustive enumeration — provided that the goal is merely to find an acceptably good solution in a fixed amount of time, rather than the best possible solution. The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one. By analogy with this physical process, each step of the SA algorithm replaces the current solution by a random "nearby" solution, chosen with a probability that depends on the difference between the corresponding function values and on a global parameter T (called the temperature), that is gradually decreased during the process. The dependency is such that the current solution changes almost randomly when T is large, but increasingly "downhill" as T goes to zero. The allowance for "uphill" moves saves the method from becoming stuck at local minima—which are the bane of greedier methods. The method was independently described by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi in 1983 [1], and by V. Černý in 1985 [2]. The method is an adaptation of the Metropolis-Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, invented by N. Metropolis et al. in 1953 [3].
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  • Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of applied mathematics, namely locating a good approximation to the global minimum of a given function in a large search space. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For certain problems, simulated annealing may be more effective than exhaustive enumeration — provided that the goal is merely to find an acceptably good solution in a fixed amount of time, rather than the best possible solution. The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one. By analogy with this physical process, each step of the SA algorithm replaces the current solution by a random "nearby" solution, chosen with a probability that depends on the difference between the corresponding function values and on a global parameter T (called the temperature), that is gradually decreased during the process. The dependency is such that the current solution changes almost randomly when T is large, but increasingly "downhill" as T goes to zero. The allowance for "uphill" moves saves the method from becoming stuck at local minima—which are the bane of greedier methods. The method was independently described by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi in 1983 [1], and by V. Černý in 1985 [2]. The method is an adaptation of the Metropolis-Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, invented by N. Metropolis et al. in 1953 [3].
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    Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of applied mathematics, namely locating a good approximation to the global minimum of a given function in a large search space. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For certain problems, simulated annealing may be more effective than exhaustive enumeration - provided that the goal is merely to find an acceptably good solution in a fixed amount of time, rather than the best possible solution. The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one. By analogy with this physical process, each step of the SA algorithm replaces the current solution by a random "nearby" solution, chosen with a probability that depends on the difference between the corresponding function values and on a global parameter T (called the temperature), that is gradually decreased during the process. The dependency is such that the current solution changes almost randomly when T is large, but increasingly "downhill" as T goes to zero. The allowance for "uphill" moves saves the method from becoming stuck at local minima-which are the bane of greedier methods. The method was independently described by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi in 1983 [1], and by V. Černý in 1985 [2]. The method is an adaptation of the Metropolis-Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, invented by N. Metropolis et al. in 1953 [3].
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    A natural AI approach
Janos Haits

Higher Education | BoodleBox - 0 views

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    "Collaborative AI for College Classrooms GenAI that helps faculty and students prepare for class efficiently, teach & learn responsible AI collaboratively, and assess assignments accurately to enhance learning outcomes."
Janos Haits

AI Learning Library - BoodleBox - 0 views

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    "Explore the many ways professors and students from across the globe are teaching and learning with AI."
Islam TeCNo

Design pattern - Wikipedia, the free encyclopedia - 0 views

  • A pattern must explain why a particular situation causes problems, and why the proposed solution is considered a good one. Christopher Alexander describes common design problems as arising from "conflicting forces" -- such as the conflict between wanting a room to be sunny and wanting it not to overheat on summer afternoons. A pattern would not tell the designer how many windows to put in the room; instead, it would propose a set of values to guide the designer toward a decision that is best for their particular application. Alexander, for example, suggests that enough windows should be included to direct light all around the room. He considers this a good solution because he believes it increases the enjoyment of the room by its occupants. Other authors might come to different conclusions, if they place higher value on heating costs, or material costs. These values, used by the pattern's author to determine which solution is "best", must also be documented within the pattern. A pattern must also explain when it is applicable. Since two houses may be very different from one another, a design pattern for houses must be broad enough to apply to both of them, but not so vague that it doesn't help the designer make decisions. The range of situations in which a pattern can be used is called its context. Some examples might be "all houses", "all two-story houses", or "all places where people spend time." The context must be documented within the pattern. For instance, in Christopher Alexander's work, bus stops and waiting rooms in a surgery are both part of the context for the pattern "A PLACE TO WAIT."
    • Islam TeCNo
       
      This is Not a CS related articile ....check this link !! http://en.wikipedia.org/wiki/Design_pattern_(computer_science)
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    Design Patterns
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    Design Patterns
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