Optimization of a stochastically simulated gene network model via simulated annealing

By rearranging naturally occurring genetic components, gene networks can be created that display novel functions. When designing these networks, the kinetic parameters describing DNA/protein binding are of great importance, as these parameters strongly influence the behavior of the resulting gene network. This article presents an optimization method based on simulated annealing to locate combinations of kinetic parameters that produce a desired behavior in a genetic network. Since gene expression is an inherently stochastic process, the simulation component of simulated annealing optimization is conducted using an accurate multiscale simulation algorithm to calculate an ensemble of network trajectories at each iteration of the simulated annealing algorithm. Using the three-gene repressilator of Elowitz and Leibler as an example, we show that gene network optimizations can be conducted using a mechanistically realistic model integrated stochastically. The repressilator is optimized to give oscillations of an arbitrary specified period. These optimized designs may then provide a starting-point for the selection of genetic components needed to realize an in vivo system.     

Folding small proteins via annealing stochastic approximation Monte Carlo

Recently, the stochastic approximation Monte Carlo algorithm has been proposed by Liang et al. (2007) as a general-purpose stochastic optimization and simulation algorithm. An annealing version of this algorithm was developed for real small protein folding problems. The numerical results indicate that it outperforms simulated annealing and conventional Monte Carlo algorithms as a stochastic optimization algorithm. We also propose one method for the use of secondary structures in protein folding. The predicted protein structures are rather close to the true structures.     

Evaluation of a particle swarm algorithm for biomechanical optimization

Optimization is frequently employed in biomechanics research to solve system identification problems, predict human movement, or estimate muscle or other internal forces that cannot be measured directly. Unfortunately, biomechanical optimization problems often possess multiple local minima, making it difficult to find the best solution. Furthermore, convergence in gradient-based algorithms can be affected by scaling to account for design variables with different length scales or units. In this study we evaluate a recently-developed version of the particle swarm optimization (PSO) algorithm to address these problems. The algorithm's global search capabilities were investigated using a suite of difficult analytical test problems, while its scale-independent nature was proven mathematically and verified using a biomechanical test problem. For comparison, all test problems were also solved with three off-the-shelf optimization algorithms--a global genetic algorithm (GA) and multistart gradient-based sequential quadratic programming (SQP) and quasi-Newton (BFGS) algorithms. For the analytical test problems, only the PSO algorithm was successful on the majority of the problems. When compared to previously published results for the same problems, PSO was more robust than a global simulated annealing algorithm but less robust than a different, more complex genetic algorithm. For the biomechanical test problem, only the PSO algorithm was insensitive to design variable scaling, with the GA algorithm being mildly sensitive and the SQP and BFGS algorithms being highly sensitive. The proposed PSO algorithm provides a new off-the-shelf global optimization option for difficult biomechanical problems, especially those utilizing design variables with different length scales or units.     

A novel numerical optimization algorithm inspired from weed colonization

This paper introduces a novel numerical stochastic optimization algorithm inspired from colonizing weeds. Weeds are plants whose vigorous, invasive habits of growth pose a serious threat to desirable, cultivated plants making them a threat for agriculture. Weeds have shown to be very robust and adaptive to change in environment. Thus, capturing their properties would lead to a powerful optimization algorithm. It is tried to mimic robustness, adaptation and randomness of colonizing weeds in a simple but effective optimizing algorithm designated as Invasive Weed Optimization (IWO). The feasibility, the efficiency and the effectiveness of IWO are tested in details through a set of benchmark multi-dimensional functions, of which global and local minima are known. The reported results are compared with other recent evolutionary-based algorithms: genetic algorithms, memetic algorithms, particle swarm optimization, and shuffled frog leaping. The results are also compared with different versions of simulated annealing — a generic probabilistic meta-algorithm for the global optimization problem — which are simplex simulated annealing, and direct search simulated annealing. Additionally, IWO is employed for finding a solution for an engineering problem, which is optimization and tuning of a robust controller. The experimental results suggest that results from IWO are better than results from other methods. In conclusion, the performance of IWO has a reasonable performance for all the test functions.     

Multiple sequence alignment by parallel simulated annealing

We have developed simulated annealing algorithms to solve theproblem of multiple sequence alignment. The algorithm wns shownto give the optimal solution as confirmed by the rigorous dynamicprogramming algorithm for three-sequence alignment. To overcomelong execution times for simulated annealing, we utilized aparallel computer. A sequential algorithm, a simple parallelalgorithm and the temperature parallel algorithm were testedon a problem. The results were compared with the result obtainedby a conventional tree-based algorithm where alignments weremerged by two-' dynamic programming. Every annealing algorithmproduced a better energy value than the conventional algorithm.The best energy value, which probably represents the optimalsolution, wns reached within a reasonable time by both of theparallel annealing algorithms. We consider the temperature parallelalgorithm of simulated annealing to be the most suitable forfinding the optimal multiple sequence alignment because thealgorithm does not require any scheduling for optimization.The algorithm is also usefiui for refining multiple alignmentsobtained by other hewistic methods.     

Gene regulatory network modeling via global optimization of high-order dynamic Bayesian network

ABSTRACT: BACKGROUND: Dynamic Bayesian network (DBN) is among the mainstream approaches for modeling various biological networks, including the gene regulatory network (GRN). Most current methods for learning DBN employ either local search such as hill-climbing, or a meta stochastic global optimization framework such as genetic algorithm or simulated annealing, which are only able to locate sub-optimal solutions. Further, current DBN applications have essentially been limited to small sized networks. RESULTS: To overcome the above difficulties, we introduce here a deterministic global optimization based DBN approach for reverse engineering genetic networks from time course gene expression data. For such DBN models that consist only of inter time slice arcs, we show that there exists a polynomial time algorithm for learning the globally optimal network structure. The proposed approach, named GlobalMIT+, employs the recently proposed information theoretic scoring metric named mutual information test (MIT). GlobalMIT+ is able to learn high-order time delayed genetic interactions, which are common to most biological systems. Evaluation of the approach using both synthetic and real data sets, including a 733 cyanobacterial gene expression data set, shows significantly improved performance over other techniques. CONCLUSIONS: Our studies demonstrate that deterministic global optimization approaches can infer large scale genetic networks.     

Simulated parallel annealing within a neighborhood for optimization of biomechanical systems

Optimization problems for biomechanical systems have become extremely complex. Simulated annealing (SA) algorithms have performed well in a variety of test problems and biomechanical applications; however, despite advances in computer speed, convergence to optimal solutions for systems of even moderate complexity has remained prohibitive. The objective of this study was to develop a portable parallel version of a SA algorithm for solving optimization problems in biomechanics. The algorithm for simulated parallel annealing within a neighborhood (SPAN) was designed to minimize interprocessor communication time and closely retain the heuristics of the serial SA algorithm. The computational speed of the SPAN algorithm scaled linearly with the number of processors on different computer platforms for a simple quadratic test problem and for a more complex forward dynamic simulation of human pedaling.     

A comparison of physical mapping algorithms based on the maximum likelihood model

MOTIVATION: Physical mapping of chromosomes using the maximum likelihood (ML) model is a problem of high computational complexity entailing both discrete optimization to recover the optimal probe order as well as continuous optimization to recover the optimal inter-probe spacings. In this paper, two versions of the genetic algorithm (GA) are proposed, one with heuristic crossover and deterministic replacement and the other with heuristic crossover and stochastic replacement, for the physical mapping problem under the maximum likelihood model. The genetic algorithms are compared with two other discrete optimization approaches, namely simulated annealing (SA) and large-step Markov chains (LSMC), in terms of solution quality and runtime efficiency. RESULTS: The physical mapping algorithms based on the GA, SA and LSMC have been tested using synthetic datasets and real datasets derived from cosmid libraries of the fungus Neurospora crassa. The GA, especially the version with heuristic crossover and stochastic replacement, is shown to consistently outperform the SA-based and LSMC-based physical mapping algorithms in terms of runtime and final solution quality. Experimental results on real datasets and simulated datasets are presented. Further improvements to the GA in the context of physical mapping under the maximum likelihood model are proposed. AVAILABILITY: The software is available upon request from the first author.     

A parallel optimization approach for controlling allele diversity in conservation schemes

We propose a novel method to control allelic diversity in conservation schemes based on an optimization problem, characterized by a convex program subject to integer linear constraints. Departing from previous studies considering similar problems, we implement a parallel simulated annealing algorithm to minimize the number of alleles lost across generations. The proposed algorithm shows excellent timing and minimization performances. Execution time decreases linearly with the number of processors used, providing similar results in all cases.     

Parallel computation of a maximum-likelihood estimator of a physical map

Reconstructing a physical map of a chromosome from a genomic library presents a central computational problem in genetics. Physical map reconstruction in the presence of errors is a problem of high computational complexity that provides the motivation for parallel computing. Parallelization strategies for a maximum-likelihood estimation-based approach to physical map reconstruction are presented. The estimation procedure entails a gradient descent search for determining the optimal spacings between probes for a given probe ordering. The optimal probe ordering is determined using a stochastic optimization algorithm such as simulated annealing or microcanonical annealing. A two-level parallelization strategy is proposed wherein the gradient descent search is parallelized at the lower level and the stochastic optimization algorithm is simultaneously parallelized at the higher level. Implementation and experimental results on a distributed-memory multiprocessor cluster running the parallel virtual machine (PVM) environment are presented using simulated and real hybridization data.     

Time Varying Optimization for Monitoring Multiple Contaminants under Uncertain Hydrogeology

This study presents a method for identifying cost effective sampling designs for long-term monitoring of remediation of groundwater over multiple monitoring periods under uncertain flow conditions. A contaminant transport model is used to simulate plume migration under many equally likely stochastic hydraulic conductivity fields and provides representative samples of contaminant concentrations. Monitoring costs are minimized under a constraint to meet an acceptable level of error in the estimation of total mass for multiple contaminants simultaneously over many equiprobable realizations of hydraulic conductivity field. A new myopic heuristic algorithm (MS-ER) that combines a new error-reducing search neighborhood is developed to solve the optimization problem. A simulated annealing algorithm using the error-reducing neighborhood (SA-ER) and a genetic algorithm (GA) are also considered for solving the optimization problem. The method is applied to a hypothetical aquifer where enhanced anaerobic bioremediation of four toxic chlorinated ethene species is modeled using a complex contaminant transport model. The MS-ER algorithm consistently performed better in multiple trials of each algorithm when compared to SA-ER and GA. The best design of MS-ER algorithm produced a savings of nearly 25% in project cost over a conservative sampling plan that uses all possible locations and samples.     

Time Varying Optimization for Monitoring Multiple Contaminants under Uncertain Hydrogeology

This study presents a method for identifying cost effective sampling designs for long-term monitoring of remediation of groundwater over multiple monitoring periods under uncertain flow conditions. A contaminant transport model is used to simulate plume migration under many equally likely stochastic hydraulic conductivity fields and provides representative samples of contaminant concentrations. Monitoring costs are minimized under a constraint to meet an acceptable level of error in the estimation of total mass for multiple contaminants simultaneously over many equiprobable realizations of hydraulic conductivity field. A new myopic heuristic algorithm (MS-ER) that combines a new error-reducing search neighborhood is developed to solve the optimization problem. A simulated annealing algorithm using the error-reducing neighborhood (SA-ER) and a genetic algorithm (GA) are also considered for solving the optimization problem. The method is applied to a hypothetical aquifer where enhanced anaerobic bioremediation of four toxic chlorinated ethene species is modeled using a complex contaminant transport model. The MS-ER algorithm consistently performed better in multiple trials of each algorithm when compared to SA-ER and GA. The best design of MS-ER algorithm produced a savings of nearly 25% in project cost over a conservative sampling plan that uses all possible locations and samples.     

Optimal operating mode for enantioseparation of SB-553261 racemate based on simulated moving bed technology

The performance of the simulated moving bed (SMB) technology and its modification, the Varicol process, was optimized using an experimentally verified model for the enantioseparation of SB-553261 racemate. Single and multiobjective optimizations have been carried out for both existing as well as design stage and their efficiencies were compared. The optimization problem involves a relatively large number of decision variables, both continuous variables such as flow rates, switching time and length of the columns, as well as discrete variables like number and distribution of columns. A state-of-the-art new optimization technique based on a genetic algorithm (nondominated sorting genetic algorithm with jumping genes) was utilized which allows handling of these complex optimization problems. The optimization results showed that significant improvement could be made to the chiral drug separation process using both the SMB and the Varicol process. It was found that the performance of a Varicol process is superior to that of a SMB process in terms of treating more feed using less desorbent or increasing productivity while at the same time achieving better product quality. Optimum results were explained using equilibrium theory by locating them in the pure separation region.     

Optimal vaccination schedules using simulated annealing

SUMMARY: Since few years the problem of finding optimal solutions for drug or vaccine protocols have been tackled using system biology modeling. These approaches are usually computationally expensive. Our previous experiences in optimizing vaccine or drug protocols using genetic algorithms required the use of a high performance computing infrastructure for a couple of days. In the present article we show that by an appropriate use of a different optimization algorithm, the simulated annealing, we have been able to downsize the computational effort by a factor 10(2). The new algorithm requires computational effort that can be achieved by current generation personal computers. AVAILABILITY: Software and additional data can be found at http://www.immunomics.eu/SA/     

Optimization algorithm performance in determining optimal controls in human movement analyses

The objective of this study was to evaluate the performance of different multivariate optimization algorithms by solving a "tracking" problem using a forward dynamic model of pedaling. The tracking problem was defined as solving for the muscle controls (muscle stimulation onset, offset, and magnitude) that minimized the error between experimentally collected kinetic and kinematic data and the simulation results of pedaling at 90 rpm and 250 W. Three different algorithms were evaluated: a downhill simplex method, a gradient-based sequential quadratic programming algorithm, and a simulated annealing global optimization routine. The results showed that the simulated annealing algorithm performed for superior to the conventional routines by converging more rapidly and avoiding local minima.     

An intelligent two-stage evolutionary algorithm for dynamic pathway identification from gene expression profiles

From gene expression profiles, it is desirable to rebuild cellular dynamic regulation networks to discover more delicate and substantial functions in molecular biology, biochemistry, bioengineering and pharmaceutics. S-system model is suitable to characterize biochemical network systems and capable to analyze the regulatory system dynamics. However, inference of an S-system model of N-gene genetic networks has 2N(N+1) parameters in a set of non-linear differential equations to be optimized. This paper proposes an intelligent two-stage evolutionary algorithm (iTEA) to efficiently infer the S-system models of genetic networks from time-series data of gene expression. To cope with curse of dimensionality, the proposed algorithm consists of two stages where each uses a divide-and-conquer strategy. The optimization problem is first decomposed into N subproblems having 2(N+1) parameters each. At the first stage, each subproblem is solved using a novel intelligent genetic algorithm (IGA) with intelligent crossover based on orthogonal experimental design (OED). At the second stage, the obtained N solutions to the N subproblems are combined and refined using an OED-based simulated annealing algorithm for handling noisy gene expression profiles. The effectiveness of iTEA is evaluated using simulated expression patterns with and without noise running on a single-processor PC. It is shown that 1) IGA is efficient enough to solve subproblems; 2) IGA is significantly superior to the existing method SPXGA; and 3) iTEA performs well in inferring S-system models for dynamic pathway identification.     

Constrained global optimization for estimating molecular structure from atomic distances.

Finding optimal three-dimensional molecular configurations based on a limited amount of experimental and/or theoretical data requires efficient nonlinear optimization algorithms. Optimization methods must be able to find atomic configurations that are close to the absolute, or global, minimum error and also satisfy known physical constraints such as minimum separation distances between atoms (based on van der Waals interactions). The most difficult obstacles in these types of problems are that 1) using a limited amount of input data leads to many possible local optima and 2) introducing physical constraints, such as minimum separation distances, helps to limit the search space but often makes convergence to a global minimum more difficult. We introduce a constrained global optimization algorithm that is robust and efficient in yielding near-optimal three-dimensional configurations that are guaranteed to satisfy known separation constraints. The algorithm uses an atom-based approach that reduces the dimensionality and allows for tractable enforcement of constraints while maintaining good global convergence properties. We evaluate the new optimization algorithm using synthetic data from the yeast phenylalanine tRNA and several proteins, all with known crystal structure taken from the Protein Data Bank. We compare the results to commonly applied optimization methods, such as distance geometry, simulated annealing, continuation, and smoothing. We show that compared to other optimization approaches, our algorithm is able combine sparse input data with physical constraints in an efficient manner to yield structures with lower root mean squared deviation.     

遗传算法——进化论思想与遗传学原理在工程优化中的应用

优胜劣汰是自然界物种进化的法则,近年来,生物科学中的进化论思想与遗传学原理被成功地应用于工程中优化问题的计算,于是产生了一种不同于传统算法的优化算法———遗传算法（ＧＡ）。本文介绍遗传算法所采用的进化论思想和遗传学原理,遗传算法的基本操作、算法步骤、不同于传统算法的特点以及遗传算法的发展历史与应用情况等,并对遗传算法对生物科学的可能应用作了简单的展望。     

Calibration of a fuzzy cellular automata model of urban dynamics in Saudi Arabia

An urban cellular automata model has been designed, developed and tested for the city of Riyadh in Saudi Arabia as a research project. The model uses fuzzy set theory to capture the uncertainty associated with the transition rules and employs two automated methods of calibration: a genetic algorithm and simulated annealing. This paper describes the results of the calibration process for three time periods: 1987–1997, 1997–2005 and 1987–2005, which are characterised by different patterns of urban development. Nine different scenarios have been devised to capture the effect of different primary drivers to development including transport, urban agglomeration and topography and their interactions. The results showed that the genetic algorithm produces a better calibrated model than parallel simulated annealing. The model that contains all primary drivers and all interactions produced the best performing calibrated model overall.     

Constructing dense genetic linkage maps

This paper describes a novel combination of techniques for the construction of dense genetic linkage maps. The construction of such maps is hampered by the occurrence of even small proportions of typing errors. Simulated annealing is used to obtain the best map according to the optimality criterion: the likelihood or the total number of recombination events. Spatial sampling of markers is used to obtain a framework map. The construction of a framework map is essential if the steps used for simulated annealing are required to be simple. For missing-data imputation the Gibbs sampler is used. Map construction using simulated annealing and missing-data imputation are used in an iterative way. In order to obtain some measure of precision of the genetic linkage map obtained, the Metropolis-Hastings algorithm is used to obtain posterior intervals for the positions of markers. The process of map construction is embedded in a framework of pre-mapping and post-mapping diagnostics. The techniques described are illustrated using a practical application. Received: 1 June 2000 / Accepted: 21 September 2000