Simulated annealing
•Download as PPTX, PDF•
2 likes•954 views
Simulated annealing is an optimization algorithm inspired by the physical annealing process. It mimics how a material is heated and slowly cooled to reach a uniform structure of minimum energy. The algorithm uses a cooling schedule that starts with a high "temperature" and lowers it gradually, accepting worse solutions with probability that decreases as cooling proceeds. Problem-specific decisions include the cost function, neighborhood definition, and performance evaluation. Sample problems that can be solved using simulated annealing include the traveling salesman problem, structural optimization, and network/graph problems. While results are generally good quality, simulated annealing may require significant computation time and results may vary between runs.
Report
Share
Report
Share
Recommended
Simulated annealing
Simulated annealing is an optimization technique inspired by annealing in metallurgy. It allows solutions to escape local minima by probabilistically accepting moves that increase the cost function. The method can solve mixed-integer, discrete, or continuous problems and is not influenced by the nature of the functions or constraints. It works by generating new solutions near the current one and accepting or rejecting them using the Metropolis criterion, which accepts worse solutions with a probability that decreases over iterations as the temperature cools. This continues until convergence within a set number of iterations or temperatures. Numerical examples demonstrate applying it to minimize functions.
Simulated Annealing - A Optimisation Technique
Simulated annealing is a global optimization technique inspired by the physical process of annealing in solids. It can find the global minimum of a cost function by slowly cooling the system. At each temperature, the algorithm accepts random moves to neighboring solutions with a probability based on the change in cost and current temperature. This allows occasionally moving to higher-cost solutions and avoids getting stuck in local minima. While slower than local search methods, simulated annealing is more likely to find the global optimum solution over multiple iterations as the temperature decreases.
Simulated Annealing
Simulated annealing is an algorithm that mimics the physical process of annealing in solids. It begins with an initial random solution in a high-energy state and gradually cools the system until reaching a low-energy ground state. At each temperature, the algorithm performs local searches and stochastically decides whether to accept worse solutions based on the temperature and difference in solution quality. This allows for a wide initial search of the solution space before converging to an optimal solution.
Simulated Annealing
SA is a global optimization technique.
It distinguishes between different local optima.
It is a memory less algorithm & the algorithm does not use any information gathered during the search.
SA is motivated by an analogy to annealing in solids.
& it is an iterative improvement algorithm.
Simulated annealing
This document describes the simulated annealing algorithm. It begins with an introduction that outlines the document. It then provides a formal definition of simulated annealing, explaining how it is analogous to the way metals cool and form crystalline structures. The core of the document describes the simulated annealing algorithm, including initializing a solution, evaluating solutions, making random changes, applying a criterion to accept or reject changes, and gradually lowering the temperature. It provides an example of applying the algorithm to the 40 queens puzzle. It also discusses tuning the algorithm by setting the initial and final temperatures. In conclusion, it covers the advantages, disadvantages, and applications of simulated annealing.
Thermodynamics kinetics
1) Thermodynamics describes how changes in temperature, pressure, and composition affect equilibrium in rock systems. It allows prediction of mineral stability and interpretation of mineral compositions.
2) Thermodynamic models use concepts like internal energy, enthalpy, entropy, and Gibbs free energy to describe equilibrium and the direction of spontaneous processes.
3) Phase diagrams visualize thermodynamic stability by showing pressure-temperature-composition conditions where minerals are stable. However, kinetic effects can cause disequilibrium.
Ch07a entropy
1. The document discusses entropy and the Clausius inequality which is a consequence of the second law of thermodynamics. It involves heat transfer (Q) to or from a system, absolute temperature (T) at the boundary, and a cyclic integral.
2. For a reversible heat engine or refrigeration cycle, the cyclic integral of Q/T is equal to zero, but it is always less than or greater than zero for irreversible cycles depending on whether it is a heat engine or refrigeration cycle.
3. Entropy change is calculated as the area under the T-S curve for a reversible process, but is always greater for an irreversible process between the same two states. Property diagrams like T-
Basic Thermodynamics.
- When two objects are in thermal equilibrium, they have the same temperature. The first law of thermodynamics states that energy is conserved and relates changes in internal energy to heat and work. The second law states that heat spontaneously flows from hot to cold objects. The third law states it is impossible to reach absolute zero temperature in a finite number of steps.
- Heat engines convert heat into work. Refrigerators and heat pumps use work to transfer heat from cold to warm regions against the natural direction of heat flow. The efficiency and coefficient of performance of these devices relate their input and output energies. Irreversible processes increase the total entropy of the universe, while reversible processes do not change it.
Recommended
Simulated annealing
Simulated annealing is an optimization technique inspired by annealing in metallurgy. It allows solutions to escape local minima by probabilistically accepting moves that increase the cost function. The method can solve mixed-integer, discrete, or continuous problems and is not influenced by the nature of the functions or constraints. It works by generating new solutions near the current one and accepting or rejecting them using the Metropolis criterion, which accepts worse solutions with a probability that decreases over iterations as the temperature cools. This continues until convergence within a set number of iterations or temperatures. Numerical examples demonstrate applying it to minimize functions.
Simulated Annealing - A Optimisation Technique
Simulated annealing is a global optimization technique inspired by the physical process of annealing in solids. It can find the global minimum of a cost function by slowly cooling the system. At each temperature, the algorithm accepts random moves to neighboring solutions with a probability based on the change in cost and current temperature. This allows occasionally moving to higher-cost solutions and avoids getting stuck in local minima. While slower than local search methods, simulated annealing is more likely to find the global optimum solution over multiple iterations as the temperature decreases.
Simulated Annealing
Simulated annealing is an algorithm that mimics the physical process of annealing in solids. It begins with an initial random solution in a high-energy state and gradually cools the system until reaching a low-energy ground state. At each temperature, the algorithm performs local searches and stochastically decides whether to accept worse solutions based on the temperature and difference in solution quality. This allows for a wide initial search of the solution space before converging to an optimal solution.
Simulated Annealing
SA is a global optimization technique.
It distinguishes between different local optima.
It is a memory less algorithm & the algorithm does not use any information gathered during the search.
SA is motivated by an analogy to annealing in solids.
& it is an iterative improvement algorithm.
Simulated annealing
This document describes the simulated annealing algorithm. It begins with an introduction that outlines the document. It then provides a formal definition of simulated annealing, explaining how it is analogous to the way metals cool and form crystalline structures. The core of the document describes the simulated annealing algorithm, including initializing a solution, evaluating solutions, making random changes, applying a criterion to accept or reject changes, and gradually lowering the temperature. It provides an example of applying the algorithm to the 40 queens puzzle. It also discusses tuning the algorithm by setting the initial and final temperatures. In conclusion, it covers the advantages, disadvantages, and applications of simulated annealing.
Thermodynamics kinetics
1) Thermodynamics describes how changes in temperature, pressure, and composition affect equilibrium in rock systems. It allows prediction of mineral stability and interpretation of mineral compositions.
2) Thermodynamic models use concepts like internal energy, enthalpy, entropy, and Gibbs free energy to describe equilibrium and the direction of spontaneous processes.
3) Phase diagrams visualize thermodynamic stability by showing pressure-temperature-composition conditions where minerals are stable. However, kinetic effects can cause disequilibrium.
Ch07a entropy
1. The document discusses entropy and the Clausius inequality which is a consequence of the second law of thermodynamics. It involves heat transfer (Q) to or from a system, absolute temperature (T) at the boundary, and a cyclic integral.
2. For a reversible heat engine or refrigeration cycle, the cyclic integral of Q/T is equal to zero, but it is always less than or greater than zero for irreversible cycles depending on whether it is a heat engine or refrigeration cycle.
3. Entropy change is calculated as the area under the T-S curve for a reversible process, but is always greater for an irreversible process between the same two states. Property diagrams like T-
Basic Thermodynamics.
- When two objects are in thermal equilibrium, they have the same temperature. The first law of thermodynamics states that energy is conserved and relates changes in internal energy to heat and work. The second law states that heat spontaneously flows from hot to cold objects. The third law states it is impossible to reach absolute zero temperature in a finite number of steps.
- Heat engines convert heat into work. Refrigerators and heat pumps use work to transfer heat from cold to warm regions against the natural direction of heat flow. The efficiency and coefficient of performance of these devices relate their input and output energies. Irreversible processes increase the total entropy of the universe, while reversible processes do not change it.
Entropy n process
1) Entropy is a measure of the disorder or randomness in a molecular system. It increases when a system changes from a solid to liquid or liquid to gas as the molecules gain more freedom of movement.
2) The mathematical expression for entropy is the ratio of the heat change (q) to the temperature (T) of a reversible cyclic process.
3) According to the second law of thermodynamics, entropy is related to unavailable energy - as heat is applied to a system, some energy is used for work but the remaining heat becomes unavailable, increasing the entropy. Entropy is also associated with increased randomness and more probable molecular states.
Thermodynamics-HEAT ENGINES
Thermodynamics deals with quantities like temperature, heat, work, pressure, and volume. Heat is the random motion of particles, and temperature is a measure of how fast particles are moving on average. Heat transfer occurs through conduction, convection, and radiation. The first law of thermodynamics states that energy is conserved, so heat added equals work done plus change in internal energy. Heat engines operate in cycles to convert heat into work. Engine efficiency is defined as the ratio of work output to heat input. The second law states no engine can reach 100% efficiency. The Carnot engine is theoretically the most efficient type.
Unit 1.1 thm
Thermodynamics is the science of energy and its transformations. The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. A system exchanges heat and work with its surroundings, and can be isolated, closed, or open depending on whether mass and/or energy can cross its boundary. A system's state is defined by properties like temperature, pressure, and volume, and a process occurs when a system changes state.
Entropy
This document discusses entropy and its relationship to the second law of thermodynamics. It defines entropy as a property that depends only on the end states of a reversible process between two states. The document proves that the entropy of a thermally isolated system never decreases, and instead either increases or remains constant, in accordance with the second law of thermodynamics. It also discusses how entropy is related to the disorder of a system on a microscopic scale, with irreversible processes increasing disorder and entropy.
Lecture 19 entropy
There are three key points about entropy and the second law of thermodynamics discussed in the document:
1) Entropy measures the dispersal or distribution of energy in a system. All spontaneous processes result in an increase in entropy, meaning a more even distribution of energy over time.
2) Entropy can be described on a microscopic level in terms of the number of possible microscopic configurations or "microstates" of a system. The higher the number of microstates, the higher the entropy and disorder.
3) The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. This means spontaneous processes are irreversible and move towards equilibrium, where energy is evenly dispersed.
Entropy
This presentation gives you information om Clausius Statement, its proof, Entropy change for Open System and reversible and irreversible processes with simple explanation and day to day examples.
available energy ,irreversibility,exchargy
The document discusses available energy, exergy, and irreversibility. It explains that:
1) According to the second law of thermodynamics, not all heat absorbed by a system can be converted to work. The maximum work that can be obtained from a heat source at temperature T is from a reversible Carnot engine.
2) The difference between the maximum reversible work and the actual work of an irreversible process is called irreversibility. Irreversibility is always positive and represents the increase in entropy in the system and surroundings.
3) Exergy represents the maximum useful work possible during a process that brings a system into equilibrium with its surroundings. It provides an upper limit on the amount of
Thermodynamic, part 1
Thermodynamics is the study of heat, work, and energy. It describes macroscopic properties of systems in thermal equilibrium. A system is defined along with its surroundings and properties. Systems can be open, closed, or isolated. Thermodynamic properties include extensive properties that depend on system size and intensive properties that do not. The four laws of thermodynamics relate temperature, heat, work, and energy within a system. Heat transfer and phase changes involve latent heat in addition to specific heat.
Availability and irreversibility
(1) Availability analyses determine the maximum work possible from a device given a fuel amount. (2) Available energy is the maximum portion convertible to useful work by ideal processes reducing the system to equilibrium. The remainder is unavailable energy. (3) The theoretical maximum work from a system at state p1, T1 operating with a reservoir at p0, T0 is called availability. (4) Availability accounts for both work against resisting forces and the environment.
Simulated Annealing
Simulated annealing is a local search algorithm inspired by the metallurgical process of annealing. It starts with a random solution and neighbor selection at a high temperature, accepting worse solutions probabilistically based on temperature. The temperature gradually cools, and the process repeats until cooled, finding good but not necessarily optimal solutions. Key advantages are it can handle any system or cost function, is easy to implement, and generally finds good solutions.
Thermodynamic lecture
Thermodynamics deals with energy and its transformation between different forms. The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. A thermodynamic system exchanges energy in the form of heat or work with its surroundings. Closed systems exchange only energy, while open systems can exchange both energy and matter. Thermodynamic properties like pressure, temperature, and volume are used to describe different thermodynamic processes that occur at either constant values (isobaric, isochoric, isothermal) or with varying values.
equivalency and irreversibility
The document discusses the equivalence of the Kelvin-Planck and Clausius statements of the second law of thermodynamics. It shows that violating one statement necessarily leads to violating the other. It also examines two sources of irreversibility in thermodynamic processes: 1) lack of equilibrium during the process and 2) dissipative effects such as friction that degrade work into heat.
Thermodynamic
Here are the key steps to derive the expression for heat of reaction at constant pressure:
1) For a chemical reaction occurring at constant pressure, the enthalpy change (ΔH) is equal to the heat absorbed or released by the system (qP).
2) Enthalpy change (ΔH) is defined as the change in internal energy (ΔU) plus the product of pressure (P) and change in volume (ΔV).
ΔH = ΔU + PΔV
3) For a reaction at constant pressure, the volume change (ΔV) is small and pressure remains constant.
4) From the first law of thermodynamics, the change in internal energy (Δ
Thermodynamics
Thermodynamics deals with energy transformation between heat and work. A system is a specified region being studied, and can be open or closed to matter flow. The surroundings are outside the system boundary. A process is a change in a substance's state. A cycle occurs when the initial and final states are the same. The first law of thermodynamics states that energy cannot be created or destroyed, only converted between forms.
03 part3 availability irreversibility
This document discusses availability and irreversibility in transient and steady flow systems. It provides definitions for available energy, unavailable energy, dead state, and effectiveness. It examines availability in terms of the first and second laws of thermodynamics. Equations are given for calculating maximum work, availability, and irreversibility for various thermodynamic processes involving changes in temperature, pressure, and volume. Two sample problems are included and solved to demonstrate calculating work, availability change, and irreversibility for specified thermodynamic systems.
Chapter5
First Year in Dentistry First Semester
Al-Azhar University - Gaza
Lama El Banna
general chemistry
Work and heat
1) The document discusses different forms and modes of energy transfer including heat, work, internal energy, and kinetic and potential energy at both the macroscopic and microscopic levels.
2) Heat is defined as the random motion of particles and is identified as energy crossing system boundaries, while work involves a direct transfer of energy between a system and its surroundings.
3) The specific heat of a material is the amount of heat required to change its temperature by one degree, while heat of transformation (latent heat) is the energy required for phase changes like melting or vaporization.
Thermodynamics, part 8
The document discusses Gibbs free energy (G), which is a measure of the useful energy in a chemical reaction. A reaction will occur spontaneously if G decreases. G is defined as enthalpy (H) minus temperature (T) multiplied by entropy (S). The Gibbs free energy change (ΔG) for a reaction determines whether it is spontaneous or not. If ΔG is negative, the reaction proceeds spontaneously, and if ΔG is positive or zero, the reaction is at equilibrium or non-spontaneous. The Clapeyron equation relates the change in vapor pressure of a substance to temperature and can be used to calculate phase diagrams.
Heat & internal energy
Okay, let's solve this step-by-step:
* Jogger generates 8.0x105 J of heat in 0.5 hours = 3,600 seconds
* Jogger's mass is 65 kg
* Specific heat capacity of the human body is 3500 J/(kg°C)
* Use the heat equation: Q = cmΔT
* Plug in the values: 8.0x105 J = (65 kg) x (3500 J/(kg°C)) x ΔT
* Solve for ΔT: ΔT = 8.0x105 J / (65 kg x 3500 J/(kg°C)) = 1°C
Therefore, if the heat were
IB Chemistry Collision Theory, Arrhenius Equation and Maxwell Boltzmann Distr...
This document provides a tutorial on collision theory, the Arrhenius equation, and the Maxwell-Boltzmann distribution curve. It explains that for a chemical reaction to occur, molecules must collide with the correct orientation and with energy greater than the activation energy. It also discusses how increasing the temperature or concentration of reactants increases the rate of reaction by increasing the frequency and energy of collisions. The Arrhenius equation quantitatively describes the relationship between reaction rate and temperature. The Maxwell-Boltzmann distribution curve illustrates how more molecules have energy above the activation energy at higher temperatures, explaining the temperature dependence of reaction rates.
Epitaxial growth of graphene on 6H-silicon carbide substrate by simulated an...
This document summarizes a talk given by Yoon Tiem Leong at the School of Physics, Universiti Sains Malaysia on January 24, 2014 about growing graphene epitaxially on a 6H-silicon carbide substrate using a simulated annealing method. The growth process was investigated using two empirical potentials: the Tersoff potential and its refined version called the TEA potential. Single layer graphene formation was achieved using the TEA potential at an annealing temperature of 1200K, agreeing with experimental observations. The formation of graphene was evaluated by calculating changes in the carbon-carbon bond length, binding energy, and distance between the graphene layer and underlying silicon atoms during the simulated annealing process.
spsann - optimization of sample patterns using spatial simulated annealing
Presentation at the European Geosciences Union General Assembly 2015 (EGU2015), Soil System Sciences section 11.3 - Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
More Related Content
What's hot
Entropy n process
1) Entropy is a measure of the disorder or randomness in a molecular system. It increases when a system changes from a solid to liquid or liquid to gas as the molecules gain more freedom of movement.
2) The mathematical expression for entropy is the ratio of the heat change (q) to the temperature (T) of a reversible cyclic process.
3) According to the second law of thermodynamics, entropy is related to unavailable energy - as heat is applied to a system, some energy is used for work but the remaining heat becomes unavailable, increasing the entropy. Entropy is also associated with increased randomness and more probable molecular states.
Thermodynamics-HEAT ENGINES
Thermodynamics deals with quantities like temperature, heat, work, pressure, and volume. Heat is the random motion of particles, and temperature is a measure of how fast particles are moving on average. Heat transfer occurs through conduction, convection, and radiation. The first law of thermodynamics states that energy is conserved, so heat added equals work done plus change in internal energy. Heat engines operate in cycles to convert heat into work. Engine efficiency is defined as the ratio of work output to heat input. The second law states no engine can reach 100% efficiency. The Carnot engine is theoretically the most efficient type.
Unit 1.1 thm
Thermodynamics is the science of energy and its transformations. The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. A system exchanges heat and work with its surroundings, and can be isolated, closed, or open depending on whether mass and/or energy can cross its boundary. A system's state is defined by properties like temperature, pressure, and volume, and a process occurs when a system changes state.
Entropy
This document discusses entropy and its relationship to the second law of thermodynamics. It defines entropy as a property that depends only on the end states of a reversible process between two states. The document proves that the entropy of a thermally isolated system never decreases, and instead either increases or remains constant, in accordance with the second law of thermodynamics. It also discusses how entropy is related to the disorder of a system on a microscopic scale, with irreversible processes increasing disorder and entropy.
Lecture 19 entropy
There are three key points about entropy and the second law of thermodynamics discussed in the document:
1) Entropy measures the dispersal or distribution of energy in a system. All spontaneous processes result in an increase in entropy, meaning a more even distribution of energy over time.
2) Entropy can be described on a microscopic level in terms of the number of possible microscopic configurations or "microstates" of a system. The higher the number of microstates, the higher the entropy and disorder.
3) The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. This means spontaneous processes are irreversible and move towards equilibrium, where energy is evenly dispersed.
Entropy
This presentation gives you information om Clausius Statement, its proof, Entropy change for Open System and reversible and irreversible processes with simple explanation and day to day examples.
available energy ,irreversibility,exchargy
The document discusses available energy, exergy, and irreversibility. It explains that:
1) According to the second law of thermodynamics, not all heat absorbed by a system can be converted to work. The maximum work that can be obtained from a heat source at temperature T is from a reversible Carnot engine.
2) The difference between the maximum reversible work and the actual work of an irreversible process is called irreversibility. Irreversibility is always positive and represents the increase in entropy in the system and surroundings.
3) Exergy represents the maximum useful work possible during a process that brings a system into equilibrium with its surroundings. It provides an upper limit on the amount of
Thermodynamic, part 1
Thermodynamics is the study of heat, work, and energy. It describes macroscopic properties of systems in thermal equilibrium. A system is defined along with its surroundings and properties. Systems can be open, closed, or isolated. Thermodynamic properties include extensive properties that depend on system size and intensive properties that do not. The four laws of thermodynamics relate temperature, heat, work, and energy within a system. Heat transfer and phase changes involve latent heat in addition to specific heat.
Availability and irreversibility
(1) Availability analyses determine the maximum work possible from a device given a fuel amount. (2) Available energy is the maximum portion convertible to useful work by ideal processes reducing the system to equilibrium. The remainder is unavailable energy. (3) The theoretical maximum work from a system at state p1, T1 operating with a reservoir at p0, T0 is called availability. (4) Availability accounts for both work against resisting forces and the environment.
Simulated Annealing
Simulated annealing is a local search algorithm inspired by the metallurgical process of annealing. It starts with a random solution and neighbor selection at a high temperature, accepting worse solutions probabilistically based on temperature. The temperature gradually cools, and the process repeats until cooled, finding good but not necessarily optimal solutions. Key advantages are it can handle any system or cost function, is easy to implement, and generally finds good solutions.
Thermodynamic lecture
Thermodynamics deals with energy and its transformation between different forms. The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. A thermodynamic system exchanges energy in the form of heat or work with its surroundings. Closed systems exchange only energy, while open systems can exchange both energy and matter. Thermodynamic properties like pressure, temperature, and volume are used to describe different thermodynamic processes that occur at either constant values (isobaric, isochoric, isothermal) or with varying values.
equivalency and irreversibility
The document discusses the equivalence of the Kelvin-Planck and Clausius statements of the second law of thermodynamics. It shows that violating one statement necessarily leads to violating the other. It also examines two sources of irreversibility in thermodynamic processes: 1) lack of equilibrium during the process and 2) dissipative effects such as friction that degrade work into heat.
Thermodynamic
Here are the key steps to derive the expression for heat of reaction at constant pressure:
1) For a chemical reaction occurring at constant pressure, the enthalpy change (ΔH) is equal to the heat absorbed or released by the system (qP).
2) Enthalpy change (ΔH) is defined as the change in internal energy (ΔU) plus the product of pressure (P) and change in volume (ΔV).
ΔH = ΔU + PΔV
3) For a reaction at constant pressure, the volume change (ΔV) is small and pressure remains constant.
4) From the first law of thermodynamics, the change in internal energy (Δ
Thermodynamics
Thermodynamics deals with energy transformation between heat and work. A system is a specified region being studied, and can be open or closed to matter flow. The surroundings are outside the system boundary. A process is a change in a substance's state. A cycle occurs when the initial and final states are the same. The first law of thermodynamics states that energy cannot be created or destroyed, only converted between forms.
03 part3 availability irreversibility
This document discusses availability and irreversibility in transient and steady flow systems. It provides definitions for available energy, unavailable energy, dead state, and effectiveness. It examines availability in terms of the first and second laws of thermodynamics. Equations are given for calculating maximum work, availability, and irreversibility for various thermodynamic processes involving changes in temperature, pressure, and volume. Two sample problems are included and solved to demonstrate calculating work, availability change, and irreversibility for specified thermodynamic systems.
Chapter5
First Year in Dentistry First Semester
Al-Azhar University - Gaza
Lama El Banna
general chemistry
Work and heat
1) The document discusses different forms and modes of energy transfer including heat, work, internal energy, and kinetic and potential energy at both the macroscopic and microscopic levels.
2) Heat is defined as the random motion of particles and is identified as energy crossing system boundaries, while work involves a direct transfer of energy between a system and its surroundings.
3) The specific heat of a material is the amount of heat required to change its temperature by one degree, while heat of transformation (latent heat) is the energy required for phase changes like melting or vaporization.
Thermodynamics, part 8
The document discusses Gibbs free energy (G), which is a measure of the useful energy in a chemical reaction. A reaction will occur spontaneously if G decreases. G is defined as enthalpy (H) minus temperature (T) multiplied by entropy (S). The Gibbs free energy change (ΔG) for a reaction determines whether it is spontaneous or not. If ΔG is negative, the reaction proceeds spontaneously, and if ΔG is positive or zero, the reaction is at equilibrium or non-spontaneous. The Clapeyron equation relates the change in vapor pressure of a substance to temperature and can be used to calculate phase diagrams.
Heat & internal energy
Okay, let's solve this step-by-step:
* Jogger generates 8.0x105 J of heat in 0.5 hours = 3,600 seconds
* Jogger's mass is 65 kg
* Specific heat capacity of the human body is 3500 J/(kg°C)
* Use the heat equation: Q = cmΔT
* Plug in the values: 8.0x105 J = (65 kg) x (3500 J/(kg°C)) x ΔT
* Solve for ΔT: ΔT = 8.0x105 J / (65 kg x 3500 J/(kg°C)) = 1°C
Therefore, if the heat were
IB Chemistry Collision Theory, Arrhenius Equation and Maxwell Boltzmann Distr...
This document provides a tutorial on collision theory, the Arrhenius equation, and the Maxwell-Boltzmann distribution curve. It explains that for a chemical reaction to occur, molecules must collide with the correct orientation and with energy greater than the activation energy. It also discusses how increasing the temperature or concentration of reactants increases the rate of reaction by increasing the frequency and energy of collisions. The Arrhenius equation quantitatively describes the relationship between reaction rate and temperature. The Maxwell-Boltzmann distribution curve illustrates how more molecules have energy above the activation energy at higher temperatures, explaining the temperature dependence of reaction rates.
What's hot (20)
IB Chemistry Collision Theory, Arrhenius Equation and Maxwell Boltzmann Distr...
IB Chemistry Collision Theory, Arrhenius Equation and Maxwell Boltzmann Distr...
Viewers also liked
Epitaxial growth of graphene on 6H-silicon carbide substrate by simulated an...
This document summarizes a talk given by Yoon Tiem Leong at the School of Physics, Universiti Sains Malaysia on January 24, 2014 about growing graphene epitaxially on a 6H-silicon carbide substrate using a simulated annealing method. The growth process was investigated using two empirical potentials: the Tersoff potential and its refined version called the TEA potential. Single layer graphene formation was achieved using the TEA potential at an annealing temperature of 1200K, agreeing with experimental observations. The formation of graphene was evaluated by calculating changes in the carbon-carbon bond length, binding energy, and distance between the graphene layer and underlying silicon atoms during the simulated annealing process.
spsann - optimization of sample patterns using spatial simulated annealing
Presentation at the European Geosciences Union General Assembly 2015 (EGU2015), Soil System Sciences section 11.3 - Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
MULTI OBJECTIVE SIMULATED ANNEALING-BASED CLUSTERING OF TISSUE SAMPLES FOR CA...
This document describes a multi-objective simulated annealing (MOSA) based clustering method for cancer diagnosis and classification using gene expression data. The method uses MOSA to identify optimal clustering solutions based on multiple objectives like minimizing intra-cluster distances and maximizing inter-cluster distances. It is tested on three cancer gene expression datasets and able to accurately cluster samples and identify relevant gene markers for different cancer types. The method performs better than other algorithms like MOGASVM in terms of clustering accuracy and identifies clinically relevant gene markers for cancer subtypes.
Simulated annealing-global optimization algorithm
This document provides an overview of the simulated annealing algorithm for seismic inversion. It begins with an introduction to seismic inversion and how it aims to find the model with the minimum misfit between observed and synthetic data. It then explains that simulated annealing is a search algorithm that can help escape local minima traps by occasionally allowing search in unfavorable directions. The document outlines the simulated annealing process, which is inspired by annealing in thermodynamics, and provides details of the algorithm and how it uses a probabilistic approach and "temperature" parameter to help reach the global minimum over time. Finally, it discusses advantages like robustness and ability to approach optimality, and disadvantages like parameter tuning requirements.
Simulated annealing
Simulated annealing is an algorithm that mimics the physical process of annealing in solids to minimize an objective function. It works as follows:
1) Initialize with a random starting point and high temperature.
2) Make random moves and accept or reject them probabilistically based on the change in objective value and current temperature.
3) Gradually lower the temperature over time.
4) Repeat steps 2-3 until a freezing point is reached.
Lecture 27 simulated annealing
Simulated annealing is an algorithm that mimics the physical process of annealing to find the global minimum of a cost function. It works by randomly perturbing the current solution and accepting changes that increase the cost with a probability that decreases over time, allowing it to escape local minima. The algorithm includes a temperature parameter that controls the probability of accepting worse solutions, and lowering it slowly over iterations helps find better solutions than simple hill climbing.
Simulated Annealing
Simulated annealing is an algorithm for finding good solutions to optimization problems, such as the traveling salesman problem, where the goal is to find the shortest route between cities. It is inspired by annealing in metalworking, where heating and controlled cooling produces strong, defect-free metal. The algorithm starts with a random solution and finds neighboring solutions, accepting worse solutions with probability related to cost difference and iteration number, to avoid local optima. This allows big jumps early on, but the algorithm hones in on a local optimum over many iterations, usually finding a good enough solution. Parameters must be tuned correctly through trial and error. Overall, simulated annealing is considered effective for optimization problems.
Simulated annealing
This document discusses simulated annealing, a stochastic optimization algorithm inspired by the physical annealing process. It can help avoid getting stuck in local optima like hill climbing algorithms. It works by randomly exploring different solutions and probabilistically accepting moves that decrease fitness, controlled by a temperature parameter. The probability of accepting worse moves decreases over time, guiding the search toward better solutions like hill climbing, but also allowing some exploration to avoid local optima.
Stochastic Approximation and Simulated Annealing
AACIMP 2010 Summer School lecture by Leonidas Sakalauskas. "Applied Mathematics" stream. "Stochastic Programming and Applications" course. Part 8.
More info at http://summerschool.ssa.org.ua
Metaheurística Simulated Annealing
O documento descreve o algoritmo de Simulated Annealing, que é uma metaheurística inspirada no processo de resfriamento lento em metais. O algoritmo começa com uma alta temperatura e gera soluções aleatórias, aceitando também soluções de piora. Conforme a temperatura cai, diminui a probabilidade de aceitar soluções de piora até encontrar uma boa solução próxima do ótimo global.
Simulated annealing.ppt
This document discusses various concepts related to simulated annealing including the acceptance function, initial temperature, equilibrium state, cooling schedule, stopping condition, and handling constraints. It describes how the acceptance of non-improving moves is based on temperature and change in objective function. It also provides examples of different cooling schedules and discusses how to determine equilibrium state and stopping criteria. The document concludes with applying simulated annealing to solve the knapsack problem.
Simulated annealing
The document discusses simulated annealing, a metaheuristic technique inspired by the physical process of annealing in materials. It describes how simulated annealing works by generating random neighbor solutions at each iteration and probabilistically accepting worse solutions based on temperature to avoid local optima. The key concepts are explained, including the Boltzmann distribution used to determine acceptance probability. Parameters like initial temperature, cooling schedule, and stopping criteria are also covered. An example job scheduling problem demonstrates the algorithm. Finally, common applications of simulated annealing in areas like scheduling, routing, and optimization are listed.
15.simulated anneling
Simulated annealing is an optimization algorithm inspired by metallurgy. It combines Markov chain Monte Carlo and the Metropolis algorithm to find optimal solutions to problems by mimicking the physical process of annealing. The algorithm starts at a high temperature and progressively lowers it, simulating the cooling of metals in annealing. This allows the algorithm to avoid being trapped in local minima and find the global minimum, allowing for problems to be solved that cannot be solved using traditional optimization techniques alone.
Viewers also liked (13)
Epitaxial growth of graphene on 6H-silicon carbide substrate by simulated an...
Epitaxial growth of graphene on 6H-silicon carbide substrate by simulated an...
spsann - optimization of sample patterns using spatial simulated annealing
spsann - optimization of sample patterns using spatial simulated annealing
MULTI OBJECTIVE SIMULATED ANNEALING-BASED CLUSTERING OF TISSUE SAMPLES FOR CA...
MULTI OBJECTIVE SIMULATED ANNEALING-BASED CLUSTERING OF TISSUE SAMPLES FOR CA...
Similar to Simulated annealing
Undergraduate Research - Final presentation
This document summarizes Aevyrie Roessler's work over the summer continuing research on simulating the Selective Laser Sintering 3D printing process. The work focused on documenting existing code, improving the crystallization model, and modifying the simulation to handle complex part geometries. Future work includes converting to finite elements, enabling 3D simulations, optimizations for speed, and allowing the simulation to run in reverse to compute required part geometries.
Simulation of phase diagram and its advantages
This slide provides various aspects of the simulation of phase diagram using CALPHAD system and the future of it.
Simulation with Nonlinear Structural Materials
When the stress in a structure becomes sufficiently large, many materials display nonlinear behavior. Some materials may exhibit a nonlinear stress-strain response even at very low stress. Material models including elastoplastic, viscoplastic, creep, and hyperelastic require expressions more sophisticated than the linear Hooke’s law. This webinar presented applications of nonlinear materials modeling in COMSOL Multiphysics and demonstrated how user-defined materials can be incorporated into a simulation. The webinar concluded with a 15-minute Q&A session.
Watch the webinar to learn:
• which nonlinear material models are predefined in COMSOL
• how to simulate nonlinear material behavior
• how to combine different sources of material nonlinearity
Speaker: Mateusz Stec, Technical Product Manager, Fatigue, COMSOL
Bio: Mateusz works as the Technical Product Manager for the Fatigue Module. He studied Aerospace Engineering at the University of Michigan and Vehicle Engineering at the Royal Institute of Technology. In 2008, he completed his PhD in Solid Mechanics at the Royal Institute of Technology. Before joining COMSOL, he worked at SKF’s European Research Centre as a researcher and project leader.
Applications of Advanced Numerical Simulations and Analysis in Theoretical As...
This is a talk I gave at to the "Computational Research in Boston and Beyond" (http://math.mit.edu/crib/) group in October 2013 at MIT.
Unit I fdocuments.in_introduction-to-fea-and-applications.ppt
The document provides an introduction to finite element analysis (FEA) and its applications to engineering problems. It discusses that FEA is a numerical method used to solve problems that cannot be solved analytically due to complex geometry or materials. It involves discretizing a continuous structure into small, well-defined substructures called finite elements. The key steps in FEA include preprocessing such as defining geometry, meshing and material properties, solving the problem, and postprocessing results such as stresses and strains. The document also discusses various element types, assembly of elements, sources of error in FEA, and its advantages such as handling complex geometry, loading and materials.
Dma
Dynamic mechanical analysis (DMA) is a technique that applies a periodic force to a material and measures the storage and loss modulus to characterize the viscoelastic properties. It can detect glass transition temperatures and other secondary transitions. The main components of a DMA machine include a motor to apply dynamic stress, an LVDT to measure strain, and a furnace. Samples are clamped and heated while a sinusoidal force is applied. The storage and loss modulus are calculated from the stress and strain measurements and plotted against temperature or time. DMA can be used to characterize polymers and fibers, determine the effects of composition, crystallinity, and orientation on transitions, and identify defects.
HILL CLIMBING FOR ELECTRONICS AND COMMUNICATION ENG
HILL CLIMBING FOR ELECTRONICS AND COMMUNICATION ENG
Introduction to FEA and applications
The document provides an introduction to finite element analysis (FEA) including:
1) FEA involves discretizing a continuous structure into small substructures called finite elements connected at nodes. This process is called meshing.
2) The finite element method has three main phases - preprocessing (defining geometry, materials, mesh), solution (solving equations to obtain nodal results), and postprocessing (obtaining stresses, strains from nodal results).
3) FEA can model complex problems that cannot be solved analytically due to complicated geometry or materials, and is well-suited for solving problems in solid mechanics, heat transfer, and other fields on computers.
Program on Mathematical and Statistical Methods for Climate and the Earth Sys...
Program on Mathematical and Statistical Methods for Climate and the Earth Sys...The Statistical and Applied Mathematical Sciences Institute
Physical processes in the earth system are modeled with mathematical representations called parameterizations. This talk will describe some of the conceptual approaches and mathematics used do describe physical parameterizations focusing on cloud parameterizations. This includes tracing physical laws to discrete representations in coarse scale models. Clouds illustrate several of the complexities and techniques common to many physical parameterizations. This includes the problem of different scales, sub-grid scale variability. Discussions of mathematical methods for dealing with the sub-grid scale will be discussed. In-exactness or indeterminate problems for both weather and climate will be discussed, including the problems of indeterminate parameterizations, and inexact initial conditions. Different mathematical methods, including the use of stochastic methods, will be described and discussed, with examples from contemporary earth system models.Similar to Simulated annealing (9)
Applications of Advanced Numerical Simulations and Analysis in Theoretical As...
Applications of Advanced Numerical Simulations and Analysis in Theoretical As...
Unit I fdocuments.in_introduction-to-fea-and-applications.ppt
Unit I fdocuments.in_introduction-to-fea-and-applications.ppt
HILL CLIMBING FOR ELECTRONICS AND COMMUNICATION ENG
HILL CLIMBING FOR ELECTRONICS AND COMMUNICATION ENG
Program on Mathematical and Statistical Methods for Climate and the Earth Sys...
Program on Mathematical and Statistical Methods for Climate and the Earth Sys...
Recently uploaded
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
GraphSummit Singapore | Neo4j Product Vision & Roadmap - Q2 2024
Maruthi Prithivirajan, Head of ASEAN & IN Solution Architecture, Neo4j
Get an inside look at the latest Neo4j innovations that enable relationship-driven intelligence at scale. Learn more about the newest cloud integrations and product enhancements that make Neo4j an essential choice for developers building apps with interconnected data and generative AI.
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
Sudheer Mechineni, Head of Application Frameworks, Standard Chartered Bank
Discover how Standard Chartered Bank harnessed the power of Neo4j to transform complex data access challenges into a dynamic, scalable graph database solution. This keynote will cover their journey from initial adoption to deploying a fully automated, enterprise-grade causal cluster, highlighting key strategies for modelling organisational changes and ensuring robust disaster recovery. Learn how these innovations have not only enhanced Standard Chartered Bank’s data infrastructure but also positioned them as pioneers in the banking sector’s adoption of graph technology.
Essentials of Automations: The Art of Triggers and Actions in FME
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
Mind map of terminologies used in context of Generative AI
Mind map of common terms used in context of Generative AI.
Best 20 SEO Techniques To Improve Website Visibility In SERP
Boost your website's visibility with proven SEO techniques! Our latest blog dives into essential strategies to enhance your online presence, increase traffic, and rank higher on search engines. From keyword optimization to quality content creation, learn how to make your site stand out in the crowded digital landscape. Discover actionable tips and expert insights to elevate your SEO game.
20240607 QFM018 Elixir Reading List May 2024
Everything I found interesting about the Elixir programming ecosystem in May 2024
TrustArc Webinar - 2024 Global Privacy Survey
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
Communications Mining Series - Zero to Hero - Session 1
This session provides introduction to UiPath Communication Mining, importance and platform overview. You will acquire a good understand of the phases in Communication Mining as we go over the platform with you. Topics covered:
• Communication Mining Overview
• Why is it important?
• How can it help today’s business and the benefits
• Phases in Communication Mining
• Demo on Platform overview
• Q/A
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Discover the seamless integration of RPA (Robotic Process Automation), COMPOSER, and APM with AWS IDP enhanced with Slack notifications. Explore how these technologies converge to streamline workflows, optimize performance, and ensure secure access, all while leveraging the power of AWS IDP and real-time communication via Slack notifications.
Removing Uninteresting Bytes in Software Fuzzing
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
Infrastructure Challenges in Scaling RAG with Custom AI models
Building Retrieval-Augmented Generation (RAG) systems with open-source and custom AI models is a complex task. This talk explores the challenges in productionizing RAG systems, including retrieval performance, response synthesis, and evaluation. We’ll discuss how to leverage open-source models like text embeddings, language models, and custom fine-tuned models to enhance RAG performance. Additionally, we’ll cover how BentoML can help orchestrate and scale these AI components efficiently, ensuring seamless deployment and management of RAG systems in the cloud.
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
Video Streaming: Then, Now, and in the Future
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
Leonard Jayamohan, Partner & Generative AI Lead, Deloitte
This keynote will reveal how Deloitte leverages Neo4j’s graph power for groundbreaking digital twin solutions, achieving a staggering 100x performance boost. Discover the essential role knowledge graphs play in successful generative AI implementations. Plus, get an exclusive look at an innovative Neo4j + Generative AI solution Deloitte is developing in-house.
Recently uploaded (20)
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for Life Science to increase LLM accuracy
GraphSummit Singapore | Neo4j Product Vision & Roadmap - Q2 2024
GraphSummit Singapore | Neo4j Product Vision & Roadmap - Q2 2024
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
GraphSummit Singapore | Graphing Success: Revolutionising Organisational Stru...
Essentials of Automations: The Art of Triggers and Actions in FME
Essentials of Automations: The Art of Triggers and Actions in FME
Mind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AI
Best 20 SEO Techniques To Improve Website Visibility In SERP
Best 20 SEO Techniques To Improve Website Visibility In SERP
Communications Mining Series - Zero to Hero - Session 1
Communications Mining Series - Zero to Hero - Session 1
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Infrastructure Challenges in Scaling RAG with Custom AI models
Infrastructure Challenges in Scaling RAG with Custom AI models
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...
Simulated annealing
- 1. Simulated Annealing Bladimir Lenis Gil University of Puerto Rico, Mayaguez Campus Physics Graduate Seminar Nov. 18 2010 Dr. Angel Lopez Professor
- 2. Simulated Annealing Contents 1. Introduction 2. S.A. Cooling Schedule 3. Exponential Cooling 4. Problem Specific Decisions 5. S.A. Block Diagram 6. Sample Problems by S.A. 7. Summary
- 3. Introduction • Others names: – MonteCarlo Annealing – Statistical Cooling – Probabilistic Hill Climbing – Stochastic Relaxation – Probabilistic Exchange Algorithm • Motivated by the physical annealing process
- 4. Introduction • Material is heat and slowly cooled into a uniform structure • Simulated annealing mimic this process • The first S.A. algorithm was developed in 1953 (Metropolis)
- 5. S.A. Cooling Schedule • Starting Temperature • Final Temperature • Temperature Decrement • Iterations at each temperature
- 6. Exponential Cooling • Can also do linear or step- wise cooling • But exponential cooling often work best.
- 7. Problem Specific Decisions • Cost Function • Neighbourhood • Performance
- 9. Sample Problems by S.A. • Matlab “Peaks” Function • “Peaks” Convergence • Traveling Salesman Problem • Structural Optimization • Networks and Graphs Problems • Telescope Array Optimization
- 10. Summary • SA is a general solution method that is easily applicable to a large number of problems • Generally the quality of the results of SA is good, although it can take a lot of time • Results are generally not reproducible: another run can give a different result • Proven to find the optimum under certain conditions; one of these conditions is that you must run forever
- 11. Thanks!!!