1.
Simulated annealing
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Simulated annealing is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a search space. It is often used when the space is discrete. 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, both are attributes of the material that depend on its thermodynamic free energy. Heating and cooling the material both the temperature and the thermodynamic free energy. Khachaturyan, Svetlana V. Semenovskaya, Boris K. Vainshtein in 1979 and by Armen G. Khachaturyan, Svetlana V. Semenovskaya and these authors used computer simulation mimicking annealing and cooling of such a system to find its global minimum. This notion of slow cooling implemented in the Simulated Annealing algorithm is interpreted as a decrease in the probability of accepting worse solutions as the solution space is explored. The method is an adaptation of the Metropolis–Hastings algorithm, a Monte Carlo method to sample states of a thermodynamic system. Rosenbluth and published by N. Metropolis et al. in 1953, the state of some physical systems, and the function E to be minimized is analogous to the internal energy of the system in that state. The goal is to bring the system, from an initial state. At each step, the SA heuristic considers some neighbouring state s of the current state s and these probabilities ultimately lead the system to move to states of lower energy. Typically this step is repeated until the system reaches a state that is enough for the application. Optimization of a solution involves evaluating the neighbours of a state of the problem, the well-defined way in which the states are altered to produce neighbouring states is called a move, and different moves give different sets of neighbouring states. These moves usually result in alterations of the last state. States with a smaller energy are better than those with a greater energy, the probability function P must be positive even when e ′ is greater than e. This feature prevents the method from becoming stuck at a minimum that is worse than the global one. When T tends to zero, the probability P must tend to zero if e ′ > e, for sufficiently small values of T, the system will then increasingly favor moves that go downhill, and avoid those that go uphill. With T =0 the procedure reduces to the greedy algorithm, which makes only the downhill transitions

2.
Quantum annealing
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Quantum annealing is a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions, by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the space is discrete with many local minima. It was formulated in its present form by T. Kadowaki, sebenik and J. D. Doll, in Quantum annealing, A new method for minimizing multidimensional functions. Quantum annealing starts from a superposition of all possible states with equal weights. Then the system following the time-dependent Schrödinger equation, a natural quantum-mechanical evolution of physical systems. The amplitudes of all candidate states keep changing, realizing a quantum parallelism, according to the time-dependent strength of the transverse field, which causes quantum tunneling between states. If the rate of change of the transverse-field is slow enough, an experimental demonstration of the success of quantum annealing for random magnets was reported immediately after the initial theoretical proposal. Quantum annealing can be compared to simulated annealing, whose temperature parameter plays a role to QAs tunneling field strength. In simulated annealing, the temperature determines the probability of moving to a state of energy from a single current state. In quantum annealing, the strength of transverse field determines the probability to change the amplitudes of all states in parallel. Analytical and numerical evidence suggests that quantum annealing outperforms simulated annealing under certain conditions, the tunneling field is basically a kinetic energy term that does not commute with the classical potential energy part of the original glass. The whole process can be simulated in a computer using quantum Monte Carlo, then a suitable term consisting of non-commuting variable has to be introduced artificially in the Hamiltonian to play the role of the tunneling field. Then one may carry out the simulation with the quantum Hamiltonian thus constructed just as described above, here, there is a choice in selecting the non-commuting term and the efficiency of annealing may depend on that. If the barriers are thin enough, quantum fluctuations can surely bring the system out of the shallow local minima. For N -spin glasses, Δ is proportional to N, and with a linear annealing schedule for the transverse field and this O advantage in quantum search is well established. Moreover, it may be able to do this without the tight error controls needed to harness the quantum entanglement used in traditional quantum algorithms. In 2011, D-Wave Systems announced the first commercial quantum annealer on the market by the name D-Wave One, the company claims this system uses a 128 qubit processor chipset. On May 25,2011 D-Wave announced that Lockheed Martin Corporation entered into an agreement to purchase a D-Wave One system, on October 28,2011 USCs Information Sciences Institute took delivery of Lockheeds D-Wave One

3.
Annealing (metallurgy)
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It involves heating a material to above its recrystallization temperature, maintaining a suitable temperature, and then cooling. In annealing, atoms migrate in the lattice and the number of dislocations decreases, leading to the change in ductility. In the cases of copper, steel, silver, and brass, copper, silver and brass can be cooled slowly in air, or quickly by quenching in water, unlike ferrous metals, such as steel, which must be cooled slowly to anneal. In this fashion, the metal is softened and prepared for further work—such as shaping, stamping, annealing occurs by the diffusion of atoms within a solid material, so that the material progresses towards its equilibrium state. Heat increases the rate of diffusion by providing the energy needed to break bonds, the movement of atoms has the effect of redistributing and eradicating the dislocations in metals and in ceramics. This alteration to existing dislocations allows an object to deform more easily. The amount of process-initiating Gibbs free energy in a metal is also reduced by the annealing process. In practice and industry, this reduction of Gibbs free energy is termed stress relief, the relief of internal stresses is a thermodynamically spontaneous process, however, at room temperatures, it is a very slow process. The high temperatures at which annealing occurs serve to accelerate this process, the creation of lattice vacancies is governed by the Arrhenius equation, and the migration/diffusion of lattice vacancies are governed by Fick’s laws of diffusion. The three stages of the process that proceed as the temperature of the material is increased are, recovery, recrystallization. The first stage is recovery, and it results in softening of the metal through removal of primarily linear defects called dislocations, recovery occurs at the lower temperature stage of all annealing processes and before the appearance of new strain-free grains. The grain size and shape do not change, the second stage is recrystallization, where new strain-free grains nucleate and grow to replace those deformed by internal stresses. If annealing is allowed to continue once recrystallization has completed, then grain growth occurs, in grain growth, the microstructure starts to coarsen and may cause the metal to lose a substantial part of its original strength. This can however be regained with hardening, the high temperature of annealing may result in oxidation of the metal’s surface, resulting in scale. If scale must be avoided, annealing is carried out in a special atmosphere, annealing is also done in forming gas, a mixture of hydrogen and nitrogen. The magnetic properties of mu-metal are introduced by annealing the alloy in a hydrogen atmosphere, typically, large ovens are used for the annealing process. The inside of the oven is large enough to place the workpiece in a position to receive exposure to the circulating heated air. For high volume process annealing, gas fired conveyor furnaces are often used, for large workpieces or high quantity parts, car-bottom furnaces are used so workers can easily move the parts in and out