Variant Of Simulated Annealing Research Articles

A landscape-based analysis of fixed temperature and simulated annealing

Since the introduction of Simulated Annealing (SA), researchers have considered variants that keep the same temperature value throughout the whole search and tried to determine whether this strategy can be more effective than the original cooling scheme. Several studied have tried to answer this question without a conclusive answer and without providing indications that could be useful for a practical implementation. In this work, we address this question following an experimental approach, relating the characteristics of the algorithms with the characteristics of the landscapes they encounter. We use problem-independent landscape features to study the algorithmic behaviour across different problems. We consider three different objective functions and various instance classes and determine the conditions under which the fixed-temperature variant of SA can outperform its original counterpart and when SA is instead a better choice.

Adaptive neighborhood simulated annealing for sustainability-oriented single machine scheduling with deterioration effect

This research considers the realistic phenomenon of cutting tool deterioration in the scheduling of jobs and tool replacement activities to ensure sustainable machining operations. Typically, each job has a basic processing time (independent of tool deterioration) and a tool age-dependent prolongation function. Nevertheless, such a strategy may replace the cutting tools before its useful lifespan to avoid longer processing time as it leads to higher energy consumption and likelihood of tardy jobs. Given the reduced tool operating duration, the prospect of exploiting its capability to limit the processing time prolongation is not considered by prior works. In this research, a single-machine scheduling approach that determines the job processing time based on tool age and operating duration (utilization) is studied. The problem is formulated as a mixed-integer linear program (MILP) with the objective of minimizing the weighted costs of energy consumption, tooling, and job tardiness. Due to its computational complexity, a new variant of simulated annealing (SA) algorithm is proposed to solve large instances, where an adaptive strategy is utilized to determine the neighborhood size for enhanced exploration and exploitation. Computational results for an exhaustive set of instances indicate the proposed scheduling strategy to always outperform the existing method, yielding up to a 43% reduction in total cost. Besides, the proposed variant of SA effectively solves the scheduling problem and consistently dominates the traditional SA method.

Smart Topology Optimization Using Adaptive Neighborhood Simulated Annealing

Topology optimization (TO) of engineering products is an important design task to maximize performance and efficiency, which can be divided into two main categories of gradient-based and non-gradient-based methods. In recent years, significant attention has been brought to the non-gradient-based methods, mainly because they do not demand access to the derivatives of the objective functions. This property makes them well compatible to the structure of knowledge in the digital design and simulation domains, particularly in Computer Aided Design and Engineering (CAD/CAE) environments. These methods allow for the generation and evaluation of new evolutionary solutions without using the sensitivity information. In this work, a new non-gradient TO methodology using a variation of Simulated Annealing (SA) is presented. This methodology adaptively adjusts newly-generated candidates based on the history of the current solutions and uses the crystallization heuristic to smartly control the convergence of the TO problem. If the changes in the previous solutions of an element and its neighborhood improve the results, the crystallization factor increases the changes in the newly random generated solutions. Otherwise, it decreases the value of changes in the recently generated solutions. This methodology wisely improves the random exploration and convergence of the solutions in TO. In order to study the role of the various parameters in the algorithm, a variety of experiments are conducted and results are analyzed. In multiple case studies, it is shown that the final results are well comparable to the results obtained from the classic gradient-based methods. As an additional feature, a density filter is added to the algorithm to remove discontinuities and gray areas in the final solution resulting in robust outcomes in adjustable resolutions.

Multi-objective Simulated Annealing Variants to Infer Gene Regulatory Network: A Comparative Study.

Gene Regulatory Network (GRN) is formed due to mutual transcriptional regulation within a set of protein coding genes in cellular context of an organism. Computational inference of GRN is important to understand the behavior of each gene in terms of change in its protein production rate (expression level). As Recurrent Neural Network (RNN) is efficient in GRN modeling, a bi-objective RNN formulation has been applied here. Based on Archived Multi Objective Simulated Annealing (AMOSA), four algorithms, namely, AMOSA Revised (AMOSAR), Modified Freezing based AMOSA (AMOFSA), Tabu based AMOSA (AMOTSA) and Modified Freezing and Tabu based AMOSA (AMOFTSA) have been proposed and applied to RNN (treated as GRN) for parameter learning taking four gene expression time series datasets. Comparative studies on the performance of the algorithms (based on each dataset) have been made in terms of the number of GRNs obtained in the final non-dominated front and the performance metrics, namely, recall, precision and f1 score. Two proposed variants, namely, AMOFSA and AMOTSA have been found competitive in performance. Experimental observations and statistical analysis show that, modified algorithms are better than AMOSAR and the state-of-the-art algorithms in respect of the above-mentioned metrics.

Congestion Minimization of LTE Networks: A Deep Learning Approach

Reducing the number of users serviced by congested cellular towers given an offered load and a minimum level of acceptable user quality is a major challenge in the operation of LTE networks. In this paper, we utilize a supervised Deep Learning (DL) technique to predict the LTE and LTE-A loading of connected users and then dynamically predict the congestion threshold of each cellular tower under offered load. We then use the predicted congestion thresholds together with quality constraints to fine-tune cellular network operating parameters leading to minimizing overall network congestion. We propose two sets of optimization algorithms to solve our formulated congestion optimization problem. Those are, namely, a variant of Simulated Annealing (SA) algorithm to which we refer as Block Coordinated Descent Simulated Annealing (BCDSA) and Genetic Algorithm (GA). We first compare the performance of integrated DL-BCDSA and DL-GA algorithms and then show that our integrated DL-BCDSA can outperform existing state-of-the-art commercial self organizing tool already deployed in actual cellular networks.

Meta-heuristics for dynamic real time scheduling of diffusion furnace in semiconductor manufacturing industry

Most of the earlier research in dynamic scheduling (DS) of diffusion furnace (DF), considers only future arrival of jobs. However, in reality along with the future arrival of jobs, various unexpected real time events (RTE) related to jobs, and/or resources will occur. Hence, this study addresses the important real life characteristics of both future arrival jobs and the occurrence of a RTE while scheduling DF, called as dynamic real time scheduling (DRTS), with the scheduling objective of minimising total weighted tardiness (TWT). This study first explains the mathematical model for DS of single DF to minimise TWT. Then, this study proposes 12 variants of meta-heuristics (six variants of simulated annealing and six variants of tabu search) by considering six different initial solutions obtained from six variants of greedy heuristic algorithm for DRTS of DF. From empirical and statistical analyses on 270 problem instances, this study observed that one of the variants of simulated annealing consistently performing better.

Meta-heuristics for dynamic real time scheduling of diffusion furnace in semiconductor manufacturing industry

Most of the earlier research in dynamic scheduling (DS) of diffusion furnace (DF), considers only future arrival of jobs. However, in reality along with the future arrival of jobs, various unexpected real time events (RTE) related to jobs, and/or resources will occur. Hence, this study addresses the important real life characteristics of both future arrival jobs and the occurrence of a RTE while scheduling DF, called as dynamic real time scheduling (DRTS), with the scheduling objective of minimising total weighted tardiness (TWT). This study first explains the mathematical model for DS of single DF to minimise TWT. Then, this study proposes 12 variants of meta-heuristics (six variants of simulated annealing and six variants of tabu search) by considering six different initial solutions obtained from six variants of greedy heuristic algorithm for DRTS of DF. From empirical and statistical analyses on 270 problem instances, this study observed that one of the variants of simulated annealing consistently performing better.

A two-phase simulated annealing algorithm to minimise the completion time variance of jobs in flowshops

In this paper, simulated annealing (SA) algorithm is employed to solve the flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs. Four variants of the two-phase SA algorithm (SA-I to SA-IV) are proposed to solve flowshop scheduling problem with the objective of minimising the CTV of jobs without considering the right shifting of completion time of jobs on the last machine. The proposed SA algorithms have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed SA variants are compared with the best CTV of jobs reported in the literature, and the proposed SA-III is found to perform well in minimising the chosen performance measure (CTV) particularly in medium and large size problems.

Matching formulation of the Staff Transfer Problem: meta-heuristic approaches

In this paper, the Staff Transfer Problem (STP) in Human Resource Management is addressed as a stable matching problem. Earlier, formulation of this problem was of scheduling/allocation type. Here, the stable matching formulation is completely a new and more practical approach to the problem. This new formulation involves two preference lists: the first list contains the offices/locations preferred by the employees undergoing transfer and the second list contains the employees preferred by the employer of an office/location where those employees want to be transferred. The capacity of an office/location would act as a hard constraint. While matching these two lists, the objective is to maximize the number of transfers and at the same time to stabilize the matching, i.e., to minimize the number of blocking pairs. The resulting STP instance belongs to an instance of Maximum Size Minimum Blocking Pair Stable Matching with incomplete preference list (MAX SIZE MIN BP SMI) and has been proved in this paper to be NP-hard. As the problem is new in formulation, no previous work, method or result is available. There was no preference in selecting meta-heuristics. Among a large number of existing meta-heuristics, some most widely used meta-heuristics, namely, Simulated Annealing, Genetic Algorithms, Tabu Search and some variants of them have been chosen. Based on them four meta-heuristic approaches have been proposed, namely, btSA_match, gtSA_match, GA_match and TS_match. The variants btSA_match and gtSA_match are obtained from modifications made upon Simulated Annealing. EGA_match and TS_match are based on modified Genetic Algorithms and Tabu Search respectively. As there is no previous result in the existing literature, the performance has been compared among these four methods. It is observed that, variants of Simulated Annealing (SA) outperform others w.r.t. the performance metrics. The SA-variant with greedy nature, incorporated with a tabu list (gtSA_match) has shown that the best result on the basis of statistical analysis.

Coordinated optimization of equipment operations in a container terminal

Increasing international maritime transport drives the need for efficient container terminals. The speed at which containers can be processed through a terminal is an important performance indicator. In particular, the productivity of the quay cranes (QCs) determines the performance of a container terminal; hence QC scheduling has received considerable attention. This article develops a comprehensive model to represent the waterside operations of a container terminal. Waterside operations comprise single and twinlift handling of containers by QCs, automated guided vehicles and yard cranes. In common practice, an uncoordinated scheduling heuristic is used to dispatch the equipment operating on a terminal. Here, uncoordinated means that the different machines that operate in the container terminal seek optimal productivity solely considering their own respective stage. By contrast, our model provides a coordinated schedule in which operations of all terminal equipment can be considered at once to achieve productivity closer to the QC optimal. The model takes the form of a hybrid flow shop (HFS) with novel features for bi-directional flows and job pairing. The former enables jobs to move freely through the HFS in both directions; the latter constrains certain jobs to be performed simultaneously by a single machine. We solve the coordinated model by means of a tailored simulated annealing (SA) algorithm that balances solution quality and computational time. We empirically study time-bounded variants of SA and compare them with a branch-and-bound algorithm. We show that our approach can produce coordinated schedules for a terminal with up to eight QCs in near real time.

A Self Controlled Simulated Annealing Algorithm using Hidden Markov Model State Classification

The Simulated Annealing (SA) is a stochastic local search algorithm. Its efficiency involves the adaptation of the cooling law. In this paper, we integrate Hidden Markov Model (HMM) in SA to adapt the geometric cooling law at each iteration, based on the history of the search. This approach allows to controls the cooling of SA during the run, based on sequence of state generated from a set of rules. The HMM parameters are calculated and updated at each cooling step. The Viterbi algorithm is then used to classify the observed sequence as an exploration or exploitation or an escape from the local minimum. An experiments was performed on many benchmark functions and compared with others SA variants.

Revisiting simulated annealing: A component-based analysis

Simulated Annealing (SA) is one of the oldest metaheuristics and has been adapted to solve many combinatorial optimization problems. Over the years, many authors have proposed both general and problem-specific improvements and variants of SA. We propose to accumulate this knowledge into automatically configurable, algorithmic frameworks so that for new applications that wealth of alternative algorithmic components is directly available for the algorithm designer without further manual intervention. Here, we describe SA as an ensemble of algorithmic components, and describe SA variants from the literature within these components. We show the advantages of our proposal by (i) implementing existing algorithmic components of variants of SA, (ii) studying SA algorithms proposed in the literature, (iii) improving SA performance by automatically designing new state-of-the-art SA implementations and (iv) studying the role and impact of the algorithmic components based on experimental data. Our experiments consider three common combinatorial optimization problems, the quadratic assignment problem and two variants of the permutation flow shop problem.

Optimal Sampling for Simulated Annealing Under Noise

This paper proposes a simulated annealing variant for optimization problems in which the solution quality can only be estimated by sampling from a random distribution. The aim is to find the solution with the best expected performance, as, e.g., is typical for problems where solutions are evaluated using a stochastic simulation. Assuming Gaussian noise with known standard deviation, we derive a fully sequential sampling procedure and decision rule. The procedure starts with a single sample of the value of a proposed move to a neighboring solution and then continues to draw more samples until it is able to make a decision to accept or reject the move. Under constraints of equilibrium detailed balance at each draw, we find a decoupling between the acceptance criterion and the choice of the rejection criterion. We derive a universally optimal acceptance criterion in the sense of maximizing the acceptance probability per sample and thus the efficiency of the optimization process. We show that the choice of the move rejection criterion depends on expectations of possible alternative moves and propose a simple and practical (albeit more empirical) solution that preserves detailed balance. An empirical evaluation shows that the resulting approach is indeed more efficient than several previously proposed simulated annealing variants.

Detecting Markov Chain Instability: A Monte Carlo Approach

We devise a Monte Carlo based method for detecting whether a non-negative Markov chain is stable for a given set of parameter values. More precisely, for a given subset of the parameter space, we develop an algorithm that is capable of deciding whether the set has a subset of positive Lebesgue measure for which the Markov chain is unstable. The approach is based on a variant of simulated annealing, and consequently only mild assumptions are needed to obtain performance guarantees. The theoretical underpinnings of our algorithm are based on a result stating that the stability of a set of parameters can be phrased in terms of the stability of a single Markov chain that searches the set for unstable parameters. Our framework leads to a procedure that is capable of performing statistically rigorous tests for instability, which has been extensively tested using several examples of standard and non-standard queueing networks.

Two-layer simulated annealing and tabu search heuristics for a vehicle routing problem with cross docks and split deliveries

Cross docking plays an increasingly important role in improving the efficiency of large-scale distribution networks. Unlike traditional warehouses, cross docks hold little or no inventory. Instead, goods from incoming trucks are unloaded and immediately transferred through the cross dock to outgoing trucks. Thus, cross docks serve to reduce inventory holding costs and shorten lead times from suppliers to retailers. However, to fully realize these benefits, trucks must be effectively coordinated at each cross dock. Such coordination brings a challenging extension to vehicle routing problems. In this paper a new vehicle routing problem with cross docks and split deliveries is proposed. A mixed-integer linear programming formulation is established for this problem, along with solution methodologies combining a constructive heuristic with two-layer simulated annealing and tabu search. The constructive heuristic creates a solution which is further improved by two-layer variants of simulated annealing or tabu search. The first layer optimizes the allocation of trucks to cross docks while the second layer optimizes the visitation order to suppliers and retailers for trucks assigned to each cross dock. Experimental results demonstrate that the proposed approach effectively solves large-size problems within a reasonable computational time.

Improved local search approaches to solve the post enrolment course timetabling problem

In this work, we are addressing the post enrollment course timetabling (PE-CTT) problem. We combine different local search algorithms into an iterative two stage procedure. In the first stage, Tabu Search with Sampling and Perturbation (TSSP) is used to generate feasible solutions. In the second stage, we propose an improved variant of Simulated Annealing (SA), which we call Simulated Annealing with Reheating (SAR), to improve the solution quality of feasible solutions. SAR has three features: a novel neighborhood examination scheme, a new way of estimating local optima and a reheating scheme. SAR eliminates the need for extensive tuning as is often required in conventional SA. The proposed methodologies are tested on the three most studied datasets from the scientific literature. Our algorithms perform well and our results are competitive, if not better, compared to the benchmarks set by the state of the art methods. New best known results are provided for many instances.

Optimum design of steel lattice transmission line towers using simulated annealing and PLS-TOWER

This paper presents a new optimization tool for automated design of steel lattice transmission line towers in real-world engineering practice. This tool has been developed by integrating the simulated annealing (SA) optimization algorithm into the commercial PLS-TOWER software to optimize steel lattice towers for minimum weight according to ASCE 10-97 design specification using both size and layout design variables. In this context, a novel two-phase SA algorithm is specifically developed and compared with a typical SA formulation in three weight minimization problems of real-world steel lattice towers for high voltage overhead transmission lines between 110 and 400kV. The optimized designs and the CPU time required by the two SA variants are reported for each test problem and then compared with the currently available structural configurations resulting from a conventional design process in order to quantify material saving achieved through optimization.

Simulated Annealing, Its Variants and Engineering Applications

This paper presents a review of research reported on simulated annealing (SA). Different cooling/annealing schedules are summarized. Variants of SA are delineated. Recent applications of SA in engineering are reviewed.

Rayleigh wave inversion using heat-bath simulated annealing algorithm

The dispersion of Rayleigh waves can be used to obtain near-surface shear (S)-wave velocity profiles. This is performed mainly by inversion of the phase velocity dispersion curves, which has been proven to be a highly nonlinear and multimodal problem, and it is unsuitable to use local search methods (LSMs) as the inversion algorithm. In this study, a new strategy is proposed based on a variant of simulated annealing (SA) algorithm. SA, which simulates the annealing procedure of crystalline solids in nature, is one of the global search methods (GSMs). There are many variants of SA, most of which contain two steps: the perturbation of model and the Metropolis-criterion-based acceptance of the new model. In this paper we propose a one-step SA variant known as heat-bath SA. To test the performance of the heat-bath SA, two models are created. Both noise-free and noisy synthetic data are generated. Levenberg–Marquardt (LM) algorithm and a variant of SA, known as the fast simulated annealing (FSA) algorithm, are also adopted for comparison. The inverted results of the synthetic data show that the heat-bath SA algorithm is a reasonable choice for Rayleigh wave dispersion curve inversion. Finally, a real-world inversion example from a coal mine in northwestern China is shown, which proves that the scheme we propose is applicable.

Multi-armed bandits based on a variant of Simulated Annealing

A variant of Simulated Annealing termed Simulated Annealing with Multiplicative Weights (SAMW) has been proposed in the literature. However, convergence was dependent on a parameter β(T), which was calculated a-priori based on the total iterations T the algorithm would run for. We first show the convergence of SAMW even when a diminishing stepsize βk → 1 is used, where k is the index of iteration. Using this SAMW as a kernel, a stochastic multi-armed bandit (SMAB) algorithm called SOFTMIX can be improved to obtain the minimum-possible log regret, as compared to log2 regret of the original. Another modification of SOFTMIX is proposed which avoids the need for a parameter that is dependent on the reward distribution of the arms. Further, a variant of SOFTMIX that uses a comparison term drawn from another popular SMAB algorithm called UCB1 is then described. It is also shown why the proposed scheme is computationally more efficient over UCB1, and an alternative to this algorithm with simpler stepsizes is also proposed. Numerical simulations for all the proposed algorithms are then presented.