scholarly journals Multiphase Simulated Annealing Based on Boltzmann and Bose-Einstein Distribution Applied to Protein Folding Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Juan Frausto-Solis ◽  
Ernesto Liñán-García ◽  
Juan Paulo Sánchez-Hernández ◽  
J. Javier González-Barbosa ◽  
Carlos González-Flores ◽  
...  
Keyword(s):  
Protein Folding ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Least Squares Method ◽  
Equilibrium Phase ◽  
Boltzmann Distribution ◽  
New Approach ◽  
Einstein Distribution ◽  
Problem Instances ◽  
Bose Einstein

A new hybrid Multiphase Simulated Annealing Algorithm using Boltzmann and Bose-Einstein distributions (MPSABBE) is proposed. MPSABBE was designed for solving the Protein Folding Problem (PFP) instances. This new approach has four phases: (i) Multiquenching Phase (MQP), (ii) Boltzmann Annealing Phase (BAP), (iii) Bose-Einstein Annealing Phase (BEAP), and (iv) Dynamical Equilibrium Phase (DEP). BAP and BEAP are simulated annealing searching procedures based on Boltzmann and Bose-Einstein distributions, respectively. DEP is also a simulated annealing search procedure, which is applied at the final temperature of the fourth phase, which can be seen as a second Bose-Einstein phase. MQP is a search process that ranges from extremely high to high temperatures, applying a very fast cooling process, and is not very restrictive to accept new solutions. However, BAP and BEAP range from high to low and from low to very low temperatures, respectively. They are more restrictive for accepting new solutions. DEP uses a particular heuristic to detect the stochastic equilibrium by applying a least squares method during its execution. MPSABBE parameters are tuned with an analytical method, which considers the maximal and minimal deterioration of problem instances. MPSABBE was tested with several instances of PFP, showing that the use of both distributions is better than using only the Boltzmann distribution on the classical SA.

scholarly journals Chaotic Multiquenching Annealing Applied to the Protein Folding Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Juan Frausto-Solis ◽  
Ernesto Liñan-García ◽  
Mishael Sánchez-Pérez ◽  
Juan Paulo Sánchez-Hernández
Keyword(s):  
Protein Folding ◽  
Simulated Annealing ◽  
Least Squares ◽  
Simulated Annealing Algorithm ◽  
Least Squares Method ◽  
Equilibrium Phase ◽  
Dynamical Equilibrium ◽  
Annealing Algorithm ◽  
Cooling Function ◽  
Very High

The Chaotic Multiquenching Annealing algorithm (CMQA) is proposed. CMQA is a new algorithm, which is applied to protein folding problem (PFP). This algorithm is divided into three phases: (i) multiquenching phase (MQP), (ii) annealing phase (AP), and (iii) dynamical equilibrium phase (DEP). MQP enforces several stages of quick quenching processes that include chaotic functions. The chaotic functions can increase the exploration potential of solutions space of PFP. AP phase implements a simulated annealing algorithm (SA) with an exponential cooling function. MQP and AP are delimited by different ranges of temperatures; MQP is applied for a range of temperatures which goes from extremely high values to very high values; AP searches for solutions in a range of temperatures from high values to extremely low values. DEP phase finds the equilibrium in a dynamic way by applying least squares method. CMQA is tested with several instances of PFP.

Solving Vehicle Routing Problem With Multi-Phases Simulated Annealing Algorithm

2018 ◽  
pp. 508-530
Author(s):  
Ernesto Liñán-García ◽  
Helue I. De la Barrera-Gómez ◽  
Ana Laura Vázquez-Esquivel ◽  
Jesús Aguirre-García ◽  
Andrea Isabel Cervantes-Payan ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Simulated Annealing Algorithm ◽  
Equilibrium Phase ◽  
Optimal Solution ◽  
Routing Problem ◽  
Stochastic Demands ◽  
Distribution Company ◽  
Bose Einstein

In this chapter, a new multi-phases meta-heuristic algorithm based on Simulated Annealing(SA) is proposed in order to solve the Capacitated Vehicle Routing Problem (CVRP) with stochastic demands. This algorithm is named Multi-Phases Simulated Annealing (MPSA), which has four phases of annealing, which are Fast Quenching Phase (FQP), the Annealing Boltzmann Phase (ABP), the Bose-Einstein Annealing Phase (BEAP), and the Dynamical Equilibrium Phase (DEP). These four phases are applied in different ranges of temperature in the Simulated Annealing. The proposed algorithm is applied to generate very close to optimal solution for a cleaning distribution company. Proposed approach is focused to the Vehicle Routing Problem with homogeneous capacities and stochastic demands to gain solutions where routes are the most economical, so based on this, the proposed algorithm is applied to solve the limited Capacity Vehicle Routing Problem (CVRP), trying to provide more effective and efficient metaheuristics.

scholarly journals On Boundedness of Entropy of Photon Gas in Noncommutative Spacetime

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Kazi Ashraful Alam ◽  
Mir Mehedi Faruk
Keyword(s):  
Black Holes ◽  
Distribution Function ◽  
Phase Space ◽  
Partition Function ◽  
Boltzmann Distribution ◽  
Einstein Distribution ◽  
Entropy Bound ◽  
Photon Gas ◽  
Noncommutative Spacetime ◽  
Bose Einstein

Entropy bound for the photon gas in a noncommutative (NC) spacetime where phase space is with compact spatial momentum space, previously studied by Nozari et al., has been reexamined with the correct distribution function. While Nozari et al. have employed Maxwell-Boltzmann distribution function to investigate thermodynamic properties of photon gas, we have employed the correct distribution function, that is, Bose-Einstein distribution function. No such entropy bound is observed if Bose-Einstein distribution is employed to solve the partition function. As a result, the reported analogy between thermodynamics of photon gas in such NC spacetime and Bekenstein-Hawking entropy of black holes should be disregarded.

Golden Ratio Simulated Annealing for Protein Folding Problem

2015 ◽  
Vol 12 (06) ◽  
pp. 1550037 ◽  
Author(s):  
Juan Frausto-Solis ◽  
Juan Paulo Sánchez-Hernández ◽  
Mishael Sánchez-Pérez ◽  
Ernesto Liñán García
Keyword(s):  
Protein Folding ◽  
Simulated Annealing ◽  
Thermal Equilibrium ◽  
Experimental Approach ◽  
Least Squares Method ◽  
Golden Ratio ◽  
Search Space ◽  
Threshold Temperature ◽  
Local Optima ◽  
Heuristic Technique

In this paper, Golden Ratio Simulated Annealing (GRSA) for Protein Folding Problem (PFP) is presented. GRSA is similar to Multiquenching Annealing (MQA) and Threshold Temperature Simulated Annealing (TTSA) algorithms. In contrast to MQA and TTSA, GRSA uses several strategies in order to reduce the execution time for finding the best solution of PFP. Firstly, temperature parameters are tuned with an analytical-experimental approach; secondly, a heuristic technique for dividing the search space is implemented. GRSA has a special phase which detects the thermal equilibrium by a least squares method. In addition, a reheat strategy to escape from local optima is applied.

scholarly journals Maxwell–Boltzmann type Hawking radiation

2017 ◽  
Vol 32 (12) ◽  
pp. 1750071 ◽  
Author(s):  
Youngsub Yoon
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Radiation Spectrum ◽  
Boltzmann Distribution ◽  
Black Hole Horizon ◽  
Not Given ◽  
Horizon Area ◽  
Einstein Distribution ◽  
Bose Einstein

Twenty years ago, Rovelli proposed that the degeneracy of black hole (i.e. the exponential of the Bekenstein–Hawking entropy) is given by the number of ways the black hole horizon area can be expressed as a sum of unit areas. However, when counting the sum, one should treat the area quanta on the black hole horizon as distinguishable. This distinguishability of area quanta is noted in Rovelli’s paper. Building on this idea, we derive that the Hawking radiation spectrum is not given by Planck radiation spectrum (i.e. Bose–Einstein distribution) but given by Maxwell–Boltzmann distribution.

scholarly journals Application of simulated annealing algorithm for 3D coordinate transformation problem solution

2020 ◽  
Vol 12 (1) ◽  
pp. 491-502 ◽  
Author(s):  
Waldemar Odziemczyk
Keyword(s):  
Simulated Annealing ◽  
Geographical Information Systems ◽  
Simulated Annealing Algorithm ◽  
Least Squares Method ◽  
Initial Approximation ◽  
Initial Step ◽  
Geographical Information ◽  
Problem Solution ◽  
Annealing Algorithm ◽  
Transformation Parameters

AbstractTransformation of spatial coordinates (3D) is a common computational task in photogrammetry, engineering geodesy, geographical information systems or computer vision. In the most frequently used variant, transformation of point coordinates requires knowledge of seven transformation parameters, of which three determine translation, another three rotation and one change in scale. As these parameters are commonly determined through iterative methods, it is essential to know their initial approximation. While determining approximate values of the parameters describing translation or scale change is relatively easy, determination of rotation requires more advanced methods. This study proposes an original, two-step procedure of estimating transformation parameters. In the initial step, a modified version of simulated annealing algorithm is used for identifying the approximate value of the rotation parameter. In the second stage, traditional least squares method is applied to obtain the most probable values of transformation parameters. The way the algorithm works was checked on two numerical examples. The computational experiments proved that proposed algorithm is efficient even in cases characterised by very disadvantageous configuration of common points.

An evaluation of the simulated annealing algorithm for solving the area-restricted harvest-scheduling model against optimal benchmarks

2005 ◽  
Vol 35 (10) ◽  
pp. 2500-2509 ◽  
Author(s):  
Kevin A Crowe ◽  
J D Nelson
Keyword(s):  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Computing Time ◽  
Multiple Time ◽  
Harvest Scheduling ◽  
Problem Size ◽  
Solution Quality ◽  
Annealing Algorithm ◽  
Objective Function Values ◽  
Problem Instances

A common approach for incorporating opening constraints into harvest scheduling is through the area-restricted model. This model is used to select which stands to include in each opening while simultaneously determining an optimal harvest schedule over multiple time periods. In this paper we use optimal benchmarks from a range of harvest scheduling problem instances to test a metaheuristic algorithm, simulated annealing, that is commonly used to solve these problems. Performance of the simulated annealing algorithm was assessed over a range of problem attributes such as the number of forest polygons, age-class distribution, and opening size. In total, 29 problem instances were used, ranging in size from 1269 to 36 270 binary decision variables. Overall, the mean objective function values found with simulated annealing ranged from approximately 87% to 99% of the optima after 30 min of computing time, and a moderate downward trend of the relationship between problem size and solution quality was observed.

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