Classical Simulated Annealing Algorithm Research Articles

A Novel Parallel Simulated Annealing Methodology to Solve the No-Wait Flow Shop Scheduling Problem with Earliness and Tardiness Objectives

In this paper, the no-wait flow shop problem with earliness and tardiness objectives is considered. The problem is proven to be NP-hard. Recent no-wait flow shop problem studies focused on familiar objectives, such as makespan, total flow time, and total completion time. However, the problem has limited studies with solution approaches covering the concomitant use of earliness and tardiness objectives. A novel methodology for the parallel simulated annealing algorithm is proposed to solve this problem in order to overcome the runtime drawback of classical simulated annealing and enhance its robustness. The well-known flow shop problem datasets in the literature are utilized for benchmarking the proposed algorithm, along with the classical simulated annealing, variants of tabu search, and particle swarm optimization algorithms. Statistical analyses were performed to compare the runtime and robustness of the algorithms. The results revealed the enhancement of the classical simulated annealing algorithm in terms of time consumption and solution robustness via parallelization. It is also concluded that the proposed algorithm could outperform the benchmark metaheuristics even when run in parallel. The proposed algorithm has a generic structure that can be easily adapted to many combinatorial optimization problems.

Continually reactivating iterative-projection method for instantiating microstructure from two-point statistics

Processing-structure (PS) linkages play a significant role in materials development. Nevertheless, currently there is a fascinating but of bottleneck task in terms of instantiating microstructure to understand and validate PS linkages. Its challenge lies on the lack of a robust method in computation efficiency and accuracy. Inspired from several advanced techniques such as hybrid input-output (HIO) algorithm, image processing operations and different-phase neighbors-based pixel swapping rule, we proposed a continually reactivating iterative-projection process (CRIP) method to address the challenge above. The output at each iteration in CRIP is continuously improved by eliminating and moving isolated or noise pixels towards an error-reduction direction to activate the iterative-projection process of the next iteration. The performance of the method was examined on two microstructure examples. It shows at least 99.86% improvement in convergence time compared with the classical simulated annealing algorithm and around 6.14 ×10−4 reduction in error compared with the traditional HIO algorithm. More importantly, CRIP is suitable for the task of instantiating microstructure from periodic two-point statistics predicted by PS linkage, which has been demonstrated by applying it to two experimental datasets of Ni-based superalloys and dual-phase steels. Our proposed method has the advantages of high efficiency, easy operation, reliable accuracy and remarkable generalization ability.

Quantum walk in a reinforced free-energy landscape: Quantum annealing with reinforcement

Providing an optimal path to a quantum annealing algorithm is key to finding good approximate solutions to computationally hard optimization problems. Reinforcement is one of the strategies that can be used to circumvent the exponentially small energy gaps of the system in the annealing process. Here a time-dependent reinforcement term is added to the Hamiltonian in order to give lower energies to the most probable states of the evolving system. In this study, we take a local entropy in the configuration space for the reinforcement and apply the algorithm to a number of easy and hard optimization problems. The reinforced algorithm performs better than the standard quantum annealing algorithm in the quantum search problem, where the optimal parameters behave very differently depending on the number of solutions. Moreover, the reinforcements can change the discontinuous phase transitions of the mean-field p-spin model ($p>2$) to a continuous transition. The algorithm's performance in the binary perceptron problem is also superior to that of the standard quantum annealing algorithm, which already works better than a classical simulated annealing algorithm.

Neutrosophic Simulated Annealing Algorithm and Its Application in Operation Optimization in Dangerous Goods Warehouse

In the classical simulated annealing algorithm (SAA), the iteration feasible solution is mainly based on a certain random probability. In the process of iteration, there is a lack of comparison between individuals and the whole population of feasible solutions, and the indicators to measure the change of state of individuals are too absolute to achieve the overall control of the algorithm. To deal with uncertain information that individuals encounter in iteration, this study introduces the idea of neutrosophic decision-making and establishes a kind of neutrosophic fuzzy set (NFS) to describe the time-varying iterative state of individuals according to the change of individual state, the change of population state, and the number of iteration. The biggest feature of this study is to propose a neutrosophic simulated annealing algorithm that combines the idea of NFS with simulated annealing. The biggest contribution of this study is to propose a novel entropy measurement method using the NFS and combine it with the simulated annealing algorithm to handle the optimization process. Finally, the effectiveness of the novel algorithm is verified by an example of warehouse optimization.

Physical therapy scheduling of inpatients based on improved Genetic Algorithm

In recent years, the physical therapy has become more and more extensive. How to schedule corresponding treatments efficiently in rehabilitation hospitals has attracted the attention of many scholars. A typical physical therapy treatment can be divided into three stages, i.e., the beginning, the treating and the ending. Moreover, only the beginning and the ending stages require a therapist. The treating stage does not. In addition, a physical therapy treatment requires to occupy a bed and an instrument related simultaneously. In order to solve challenging scheduling problems, a genetic algorithm based on Waiting Time Priority Algorithm (WTPA) is designed. Finally, an instance from the rehabilitation department in a hospital is tested. By comparing with the classical simulated annealing algorithm (SA), it verifies the effectiveness and efficiency of the genetic algorithm designed.

A construction of MDS involutory matrices using MDS self-dual codes: a preliminary result

The Maximum Distance Separable (MDS) matrices have an important application in cryptography, for example see [1]. In order to reduce the implementation complexities, it is important to consider MDS matrices which are involutory. Some constructions of involutory MDS matrices can be found in [2, 3]. In this paper, we give some properties related to a construction of involutory MDS matrices using orthogonal matrices derived from Euclidean self-dual MDS codes. Then, we do a computer search to find involutory MDS matrices with small sizes using classical simulated annealing algorithm. The proposed construction is different compared to the ones in [2, 3].

Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications

This work proposes a novel optimization algorithm which can be used to solve a wide range of mathematical optimization problems where the global minimum or maximum is required. The new algorithm is based on random search and classical simulated annealing algorithm (it mimics the modern process of producing high-quality steel) and is designated dynamic differential annealed optimization (DDAO). The proposed algorithm was benchmarked for 51 test functions. The dynamic differential annealed optimization algorithm has been compared to a large number of highly cited optimization algorithms. Over numerical tests, DDAO has outperformed some of these algorithms in many cases and shown high performance. Constrained path planning and spring design problem were selected as a practical engineering optimization problem. DDAO converged to the global minimum of problems efficiently, and for spring design problem DDAO has found the best feasible solution than what is found by many algorithms.

Simulated Annealing Decoder for Linear Block Codes

In this study, we introduce a novel soft decoder, the first of its kind, for linear block codes, based on Simulated Annealing algorithm (SA). The main enhancement in our contribution which let our decoder over performs with large gain (about 3 dB at 710-4) the classical SA approach, is to take the most reliable information set of the received codeword as a start solution and also according to this reliability generate neighbor’s solutions. Besides, our algorithm performance is enhanced by reducing search space when we involve the code error correcting capability parameter. The performance of the designed algorithm is investigated through a parameter tuning process and then compared with other various decoding algorithms in terms of decoding performance and algorithmic complexity. Simulation results, show that our algorithm over performs its competitor decoders while keeping minimum computation cost. In fact, our algorithm has large gain over Chase-2 and GAMD, furthermore, it over performs the most efficient and up to date DDGA decoder by 2 dB at 10-5 for RS codes.

An Approach to Improve the Performance of Simulated Annealing Algorithm Utilizing the Variable Universe Adaptive Fuzzy Logic System

This paper focuses on improving the standard form of the classical simulated annealing algorithm (CSAA). A novel method of improving the performance of CSAA by the variable universe adaptive fuzzy logic system (VUAFLS) is studied. We develop the VUAFLS to adjust the annealing temperature, which is a very important parameter governing the performance of CSAA, and this algorithm is named VUAFLS-CSAA. The main innovations of VUAFLS-CSAA lie in the application of VUAFLS containing the fast cooling mechanism and reheating mechanism relative to the characteristic of the sustained temperature fall of CSAA. Compared with the conventional method for controlling annealing temperature, VUAFLS-CSAA can control the annealing temperature more effectively, leading to the high efficiency of CSAA. The performance of the proposed method is evaluated and compared with CSAA through two examples. One is the image restoration problem, and the other is the traveling salesman problem (TSP). The experimental result indicates that the new method proposed in this paper can improve the efficiency of CSAA by tremendously shortening the iteration optimization process. And at the same time, the successful application of the new method for tackling two different problems demonstrates the generality of this method. In addition, techniques that can further improve the performance of CSAA are discussed.

Threshold temperature tuning Simulated Annealing for Protein Folding Problem in small peptides

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.

Simulated Annealing with Previous Solutions Applied to DNA Sequence Alignment

A new algorithm for solving sequence alignment problem is proposed, which is named SAPS (Simulated Annealing with Previous Solutions). This algorithm is based on the classical Simulated Annealing (SA). SAPS is implemented in order to obtain results of pair and multiple sequence alignment. SA is a simulation of heating and cooling of a metal to solve an optimization problem. In order to select randomly a current solution, SAPS algorithm chooses a solution from solutions that have been previously generated within the Metropolis Cycle. This simple change has led to increase the quality of the solution to the problem of aligning genomic sequences with respect to the classical Simulated Annealing algorithm. The parameters of SAPS, for certain instances, are tuned by an analytical method, and some parameters have experimentally been tuned. SAPS has generated high-quality results in comparison with the classical SA. The instances used are specific genes of the AIDS virus.

Part I — CRS stack: Global optimization of the 2D CRS-attributes

Abstract The common-reflection-surface (CRS) stacking method simulates zero-offset (ZO) seismic traces by means of summing the amplitudes of seismic reflection events of multi-coverage data by using a stacking operator defined for the midpoint and half-offset coordinates. For two-dimensional media, this operator depends on three kinematic attributes, also referred to as CRS attributes. The main problem in using the CRS stacking method is the determination of the three CRS attributes from multi-coverage seismic data for each sample point in the simulated ZO section. Usually, the CRS attributes are determined in several steps, through searching individual attributes on the prestack seismic gathers and on post-stack sections. This multi-step solution may accumulate errors or inaccuracies in the CRS attributes, which can compromise the quality of the ZO stacked section and affects their successful application to other processes. In this study, the optimization problem of the CRS method is solved by means of multidimensional global optimization, which uses an objective function based on a coherence measure (semblance) of the traces in the multi-coverage data. The simultaneous determination of the three CRS attributes is performed by applying the Simulated Annealing (SA), Modified Simulated Annealing (MSA) and Very Fast Simulated Annealing (VFSA) global optimization algorithms. These algorithms were compared in terms of their effectiveness, efficiency and robustness. The results show that the VFSA and MSA algorithms are more suitable for determining the CRS attributes and generate high signal-to-noise ratio ZO stacked sections. Both algorithms are highly effective, but VFSA is more efficient than MSA. The classical SA algorithm has a low efficiency and effectiveness for determining the CRS attributes. In our proposed single-step global optimization strategy to search CRS attributes, we use the stacking velocity model derived from conventional velocity analysis to determine the lower and upper limits of the optimization search space for RNIP‐ We use real data with low fold and high noise level to illustrate the proposed optimization strategy and show that its result is of higher quality than that obtained with CRS stack based on the well-known extended-pragmatic search strategy.

A simulated annealing algorithm for balancing the assembly line type II problem with sequence-dependent setup times between tasks

This paper addresses the general assembly line balancing problem where the simple version is enriched by considering sequence-dependent setup times between tasks. Recently, Andres et al. (Andres, C., Miralles, C., and Pastor, R., 2008. Balancing and scheduling tasks in assembly lines with sequence-dependent setup times. European Journal of Operational Research, 187, (3), 1212–1223.) proposed the type I general assembly line balancing problem with setups (GALBPS-I) and developed a mathematical model and several algorithms for solving the problem. In a similar vein, we scrutinised the GALBPS type II problem where the challenge is to find the minimum cycle time for a predefined number of work stations. To solve the problem, we develop a mathematical model and a novel simulated annealing (SA) algorithm to solve such an NP-hard problem. We then employed the Taguchi method as an optimisation technique to extensively tune different parameters of our algorithm and make the classical SA algorithm more efficient in terms of running time and solution quality. Computational results reflected the high efficiency of the SA algorithm in both aspects.

Combination of MRF model and particle swarm optimization algorithm for texture segmentation of remote sensing images

Markov Random Field ( MRF) model is a classical image texture analysis method, which has been widely used in image texture simulation and segmentation. However, when the classical simulated annealing algorithm is used to compute a global optimal solution, it cannot satisfy the performance requirements of texture analysis and processing due to less efficiency. A fitness function which could determine texture class was designed, and the use of Particle Swarm Optimization ( PSO) was proposed to calculate the optimal solution of it. Based on the proposed method, texture segmentation of remote sensing images was carried out. Compared with the simulated annealing algorithm, the experimental results show that PSO algorithm can reduce the computational complexity and it is a more effectively optimal method of image segmentation.

Heuristic optimization of the scanning path of particle therapy beams

Quasidiscrete scanning is a delivery strategy for proton and ion beam therapy in which the beam is turned off when a slice is finished and a new energy must be set but not during the scanning between consecutive spots. Different scanning paths lead to different dose distributions due to the contribution of the unintended transit dose between spots. In this work an algorithm to optimize the scanning path for quasidiscrete scanned beams is presented. The classical simulated annealing algorithm is used. It is a heuristic algorithm frequently used in combinatorial optimization problems, which allows us to obtain nearly optimal solutions in acceptable running times. A study focused on the best choice of operational parameters on which the algorithm performance depends is presented. The convergence properties of the algorithm have been further improved by using the next-neighbor algorithm to generate the starting paths. Scanning paths for two clinical treatments have been optimized. The optimized paths are found to be shorter than the back-and-forth, top-to-bottom (zigzag) paths generally provided by the treatment planning systems. The gamma method has been applied to quantify the improvement achieved on the dose distribution. Results show a reduction of the transit dose when the optimized paths are used. The benefit is clear especially when the fluence per spot is low, as in the case of repainting. The minimization of the transit dose can potentially allow the use of higher beam intensities, thus decreasing the treatment time. The algorithm implemented for this work can optimize efficiently the scanning path of quasidiscrete scanned particle beams. Optimized scanning paths decrease the transit dose and lead to better dose distributions.

Stochastic optimization of spin-glasses on cellular neural/nonlinear network based processors

Nowadays, Cellular Neural/Nonlinear Networks (CNN) are practically implemented in parallel, analog computers, showing a fast developing trend. It is important also for physicists to be aware that such computers are appropriate for implementing in an elegant manner practically important algorithms, which are extremely slow on the classical digital architecture. Here, CNN is used for optimization of spin-glass systems. We prove, that a CNN in which the parameters of all cells can be separately controlled, is the analog correspondent of a two-dimensional Ising type spin-glass system. Using the properties of CNN we show that one single operation on the CNN chip would yield a local minimum of the spin-glass energy function. By using this property a fast optimization method, similar to simulated annealing, can be built. After estimating the simulation time needed for this algorithm on CNN based computers, and comparing it with the time needed on normal digital computers using the classical simulated annealing algorithm, the results look promising: a speed-up of the order 10 12 is expected already at 50×50 lattice sizes. Hardwares realized nowadays are of 128×128 size. Also, there seem to be no technical difficulties adapting CNN chips for such problems and the needed local control of the parameters could be fully developed in the near future.

Learning associations between natural groups of input and output with a neurofuzzy structure

A new modeling approach that finds the associations between natural groups of input and output is proposed. In the new method, input and output are clustered separately by means of Fuzzy C-Means (FCM) algorithm. Then, the learning algorithm identifies the fuzzy rules by relating the resulting fuzzy sets in input and output spaces by using a neurofuzzy architecture. A modified version of classical simulated annealing algorithm is used in order to identify the relative weights of system input variables. The proposed approach is applied to a highly nonlinear function and successful result is achieved.

A Parallel Simulated Annealing Algorithm for the Placement of Macro-Cells

A modification of the classical Simulated Annealing algorithm for the macro-cell placement problem is proposed for implementation on multiprocessor systems. The algorithm has been implemented on the Sequent Balance 8000, a multiprocessor system with a shared-memory architecture. Experimental results show that the new algorithm obtains results comparable in quality to those of the single processor version; processor utilization is greater than 80 percent using up to eight processors.