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Sanvicente–Sánchez, Héctor; Frausto–Solís, Juan; Imperial–Valenzuela, Froilán
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Since the apparition of Simulated Annealing algorithm (SA) it has shown to be an efficient method to solve combinatorial optimization problems. Due to this, new algorithms based on two looped cycles (temperatures and Markov chain) have emerged, one of them have been called Threshold Accepting (TA). Classical algorithms based on TA usually use the same Markov chain length for each temperature cycle, these methods spend a lot of time at high temperatures where the Markov chain length is supposed to be small. In this paper we propose a method based on the neighborhood structure to get the Markov chain length in a dynamic way for each temperature cycle. We implemented two TA algorithms (classical or TACM and proposed or TADM) for SAT. Experimentation shows that the proposed method is more efficient than the classical one since it obtain the same quality of the final solution with less processing time.
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RodriguezTello, Eduardo; Hao, JinKao; TorresJimenez, Jose
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This paper introduces a new evaluation function, called δ , for the Bandwidth Minimization Problem for Graphs (BMPG). Compared with the classical β evaluation function used, our δ function is much more discriminating and leads to smoother landscapes. The main characteristics of δ are analyzed and its practical usefulness is assessed within a Simulated Annealing algorithm. Experiments show that thanks to the use of the δ function, we are able to improve on some previous best results of a set of wellknown benchmarks.
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SanvicenteSánchez, Héctor; FraustoSolís, Juan
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2 Citations
The Methodology to Parallelize Simulated Annealing (MPSA) leads to massive parallelization by executing each temperature cycle of the Simulated Annealing (SA) algorithm in parallel. The initial solution for each internal cycle is set through a Monte Carlo random sampling to adjust the Boltzmann distribution at the cycle beginning. MPSA uses an asynchronous communication scheme and any implementation of MPSA leads to a parallel Simulated Annealing algorithm that is in general faster than its sequential implementation version while the precision is held. This paper illustrates the advantages of the MPSA scheme by parallelizing a SA algorithm for the Traveling Salesman Problem.
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SanvicenteSánchez, Héctor; FraustoSolís, Juan
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7 Citations
Since the publication of the seed paper of Simulated Annealing algorithm (SA) written by Kirkpatrich, several methods have been proposed to get the cooling scheme parameters. Although developed for SA, some of these methods can be extended to the algorithm known as Threshold Accepting (TA). SA and TA are quite similar and both are treated in this paper as a Simulated Annealing Like (SAL) algorithm. This paper presents a method to set the cooling scheme parameters in SAL algorithms; it establishes that both, the initial and the final temperatures are function of the maximum and minimum cost increment getting from the neighborhood structure. Experimentation with Traveling Salesman Problem and Hydraulic Network Design Problem shows that the cooling schemes getting through our method are more efficient than the previous ones.
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FraustoSolis, Juan; SoberonMainero, Xavier; LiñánGarcía, Ernesto
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3 Citations
This paper presents a new approach named MultiQuenching Annealing (MQA) for the Protein Folding Problem (PFP). MQA has two phases: Quenching Phase (QP) and Annealing Phase (AP). QP is applied at extremely high temperatures when the higher energy variations can occur. AP searches for the optimal solution at high and low temperatures when the energy variations are not very high. The temperature during the QP is decreased by an exponential function. Both QP and AP are divided in several subphases to decrease the temperature parameter until a dynamic equilibrium is detected by measuring its quality solution. In addition, an efficient analytical method to tune the algorithm parameters is used. Experimentation presented in the paper shows that MQA can obtain high quality of solution for PFP.
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FraustoSolis, Juan; MartinezRios, Felix
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1 Citations
Satisfiability (SAT) Problem is an NPComplete problem which means no deterministic algorithm is able to solve it in a polynomial time. Simulated Annealing (SA) can find very good solutions of SAT instances if its control parameters are correctly tuned. SA can be tuned experimentally or by using a Markov approach; the latter has been shown to be the most efficient one. Moreover Golden Ratio (GR) is an unconventional technique used to solve many problems. In this paper a new algorithm named Golden Ratio for Simulated Annealing (GRSA) is presented; it is tuned for three different cooling schemes. GRSA uses GR to dynamically decrease the SA temperature and a Markov Model to tune its parameters. Two SA tuned versions are compared in this paper: GRSA and a classical SA. Experimentation shows that the former is much more efficient than the latter.
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Richer, JeanMichel; RodriguezTello, Eduardo; VazquezOrtiz, Karla E.
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4 Citations
The Maximum Parsimony (MP) problem aims at reconstructing a phylogenetic tree from DNA sequences while minimizing the total number of genetic transformations. In this paper we propose a carefully devised simulated annealing implementation, called SAMPARS (Simulated Annealing for Maximum PARSimony), for finding nearoptimal solutions for the MP problem. Different possibilities for its key components and input parameter values were carefully analyzed and tunned in order to find the combination of them offering the best quality solutions to the problem at a reasonable computational effort. Its performance is investigated through extensive experimentation over well known benchmark instances showing that our SAMPARS algorithm is able to improve some previous bestknown solutions.
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FraustoSolís, Juan; SanvicenteSánchez, Héctor; ImperialValenzuela, Froilán
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3 Citations
Because the efficiency and efficacy in Simulated Annealing (SA) algorithms is determined by their cooling scheme, several methods to set it have been proposed. In this paper an analytical method (ANDYMARK) to tune the parameters of the cooling scheme in SA for the Satisfiability (SAT) problem is presented. This method is based on a relation between the Markov chain’s length and the cooling scheme. We compared ANDYMARK versus a classical SA algorithm that uses the same constant Markov chain. Experimentation with SAT instances shows that SA using this method obtains similar quality solutions with less effort than the classical one.
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MartinezPena, Jorge; TorresJimenez, Jose; RangelValdez, Nelson; AvilaGeorge, Himer
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3 Citations
This paper presents a simulated annealing (SA) algorithm for the construction of ternary covering arrays (CAs) using a trinomial coefficient representation. A ternary CA, denoted by CA(t,k,3), is an N ×k array where each N ×t subarray contains each of the 3^{t} combinations of symbols at least once. The construction of optimal CAs is, in general, an NPcomplete problem. Many reported SA implementations use an N ×k matrix representation for the CA construction. Instead of this, we represent ternary CAs using trinomial coefficients in order to reduce the search space for the SA algorithm.
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Sanvicente Sánchez, Héctor; Frausto Solís, Juan
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Simulated Annealing (SA) is usually implemented in a sequential way. We propose a Methodology to Parallel the Simulated Annealing Algorithm (MPSA). This methodology carries out the parallelization of the cycle that controls the temperature in the algorithm. This approach lets a massive parallelization. The initial solution for each internal cycle may be set through a Monte Carlo random sampling to adjust the Boltzmann distribution at the cycle beginning. In MPSA the communication scheme and its implementation must be in an asynchronous way. Through a theoretical analysis we establish that any implementation of MPSA leads to a Simulated Annealing Parallel Algorithm (SAPA) that is in general more efficient than its sequential implementation version.
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FraustoSolis, Juan; Román, E. F.; Romero, David; Soberon, Xavier; LiñánGarcía, Ernesto
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3 Citations
In this paper a Simulated Annealing algorithm (SA) for solving the Protein Folding Problem (PFP) is presented. This algorithm has two phases: quenching and annealing. The first phase is applied at very high temperatures and the annealing phase is applied at high and low temperatures. The temperature during the quenching phase is decreased by an exponential function. We run through an efficient analytical method to tune the algorithm parameters. This method allows the change of the temperature in accordance with solution quality, which can save large amounts of execution time for PFP.
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TorresJimenez, Jose; RodriguezTello, Eduardo
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1 Citations
The Bandwidth Minimization Problem for Graphs (BMPG) can be defined as finding a labeling for the vertices of a graph, where the maximum absolute difference between labels of each pair of connected vertices is minimum. The most used measure for the BMPG algorithms isβ, that indicates only the maximum of all absolute differences.
After analyzing some drawbacks of β, a measure, calledγ, which uses a positional numerical system with variable base and takes into account all the absolute differences of a graph is given.
In order to test the performance of γ and β a stochastic search procedure based on a Simulated Annealing (SA) algorithm has been applied to solve the BMPG. The experiments show that the SA that uses γ has better results for many classes of graphs than the one that uses β.
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HerbertAcero, JoséFrancisco; FrancoAcevedo, JorgeRodolfo; ValenzuelaRendón, Manuel; ProbstOleszewski, Oliver
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3 Citations
The optimal positioning of wind turbines, even in one dimension, is a problem with no analytical solution. This article describes the application of computational intelligence techniques to solve this problem. A systematic analysis of the optimal positioning of wind turbines on a straight line, on flat terrain, and considering wake effects has been conducted using both simulated annealing and genetic algorithms. Free parameters were the number of wind turbines, the distances between wind turbines and wind turbine hub heights. Climate and terrain characteristics were varied, like incoming wind speed, wind direction, air density, and surface roughness length, producing different patterns of positioning. Analytical functions were used to model wake effects quantifying the reduction in speed after the wind passes through a wind turbine. Conclusions relevant to the placement of wind turbines for several cases are presented.
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Mugica, Francisco; Nebot, Angela
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The main goal of this research is to study the usefulness of the Simulated Annealing (SA) approach, developed in the context of the Fuzzy Inductive Reasoning (FIR) methodology, for the automatic identification of fuzzy partitions in the human Central Nervous System (CNS) modeling problem. The SA algorithm can be viewed as a preprocess of the FIR methodology that allows the modeler to use it in a more efficient way. Two different SA algorithm cost functions have been studied and evaluated in this paper. The new approach is applied to obtain accurate models for the five controllers that compose the CNS. The results are compared and discussed with those obtained by other inductive methodologies for the same problem.
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Andrade, Miguel Ángel Gutiérrez; García, Eric Alfredo Rincón
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1 Citations
The design of electoral zones is a complex problem in which democracy of the electoral processes is promoted by some constraints such as population balance, contiguity and compactness. In fact, the computational complexity of zone design problems has been shown to be NPHard. This paper propose the use of a new measure of compactness, which uses a mesh formed with square cells to measure the quality of the electoral zones. Finally, a practical real case was chosen, which topographical settings causes some traditional measures of compactness to give very poor quality results, and was designed an algorithm based on simulated annealing that realizes a search in the space of feasible solutions. The results show that the new measure favors the creation of zones with straight forms and avoids twisted or dispersed figures, without an important effect to the population balance, which are considered zones of high quality.
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LiñánGarcía, Ernesto; Cruz Villegas, Linda Crystal; Montes Dorantes, Pascual; Méndez, Gerardo Maximiliano
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In this paper, a metaheuristic hybridized for solving the Capacity Vehicle Routing Problem (CVRP) is proposed. The classical simulated annealing is combined with Saving’s Algorithm (ClarkeWright Algorithm) in order to obtain solution of CVRP with stochastic demand. This approach was tested with different solomon’s instances of CVRP. Simulated Annealing is a simulation of heating and cooling of a metal to solve an optimization problem. Saving’s algorithm is a deterministic heuristic for solving the Capacity Vehicle Routing Problem. In order to generate high quality solution of CVRP, our approach applies Saving’s algorithm into Metropolis Cycle of Simulated Annealing. Initial solution of Simulated Annealing is also generated by Saving’s Algorithm. This new approach has lead to increase the quality of the solution to CVRP with respect to the classical Simulated Annealing algorithm and classical Saving’s Algorithm.
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RangelValdez, Nelson; JassoLuna, Jorge Omar; RodriguezChavez, Mario Humberto; BujanoGuzman, Gustavo
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The CurriculumBased Course Timetabling (CBCTT) problem involves the task of scheduling lectures of courses to classrooms, considering teacher availability, a specified curricula, and a set of constraints. In the Polytechnic University of Victoria (PUV), Mexico, the CBCTT problem occurs with the additional constraints that the courses must be assigned to teachers and that a teacher cannot teach more than one course in the same curriculum. This document proposes a methodology to solve this special case CBCTT problem. The main contributions derived from the research are: (a) the solution of the special case of the CBCTT problem; (b) the use of a Simulated Annealing based methodology, which relaxes the problem into three simpler subproblems (the assignment, distribution, and scheduling of courses), to reduce the search space and speed up the construction of a solution; and (c) the solution of a real world instance using the proposed methodology. The results show that the approach can construct solutions for the problem in the PUV in a few minutes, and of a similar quality to those manually constructed in a couple of weeks.
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FraustoSolís, Juan; SánchezPérez, Mishael; LińanGarcía, Ernesto; SánchezHernández, Juan Paulo
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2 Citations
In this paper, Threshold Temperature Simulated Annealing algorithm (TTSA) is presented. TTSA is an algorithm based on the classical Simulated Annealing Algorithm (SA) and a reheat technique. This algorithm was devised for the problem known as Protein Folding Problem (PFP) in small peptides. A quality threshold temperature is introduced in the paper; the new temperature is a restarting phase of the algorithm, which depends on the maximum and minimum deterioration of the energy function. The Threshold Temperature is obtained by applying analytical and experimental tuning techniques. The performance of the quality of the solutions for PFP in small peptides is discussed in the paper.
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