Genetic algorithms with filters for optimal control problems in fed-batch bioreactors

When using a genetic algorithm (GA) to solve optimal control problems that can arise in a fed-batch bioreactor, the most obvious direct approach is to rely on a finite dimensional discretization of the optimal control problem into a nonlinear programming problem. Usually only the control function is discretized, and the continuous control function is approximated by a series of piecewise constant functions. Even though the piecewise discretized controls that the GA produces for the optimal control problem may give good performances, the control policies often show very high activity and differ considerably from those obtained using a continuous optimization strategy. The present study introduces a few filters into a real-coded genetic algorithm as additional operators and investigates the smoothing capabilities of the filters employed. It is observed that inclusion of a filter significantly smoothens the optimal control profile and often encourages the convergence of the algorithm. The applicability of the technique is illustrated by solving two previously reported optimal control problems in fed-batch bioreactors that are known to have singular arcs.     

A genetic-algorithm-based approach to optimization of bioprocesses described by fuzzy rules

A new approach to optimization of bioprocesses described by fuzzy rules is introduced in the paper. It is based on genetic algorithms (GA) and allows to determine optimal values or profiles of control variables and to optimize fuzzy rules (parameters of membership functions). The process can be described by linguistic variables and fuzzy rules. An algorithm and related software was developed. The approach was applied to an industrial antibiotic fermentation. The optimal profile of a physical variable of the preculture was determined which leads to an increasing output product concentration in the main culture of about 5%.     

Evolutionary and swarm intelligence‐based approaches for optimization of lipase extraction from fermented broth

Evolutionary and swarm intelligence‐based optimization approaches, namely genetic algorithm (GA) and particle swarm optimization (PSO), were utilized to determine the optimal conditions for the lipase extraction process. The input space of the nonlinear response surface model of lipase extraction served as the objective function for both approaches. The optimization results indicate that the lipase activity was significantly improved, more than 20 U/g of dry substrate (U/gds), in both approaches. PSO (133.57 U/gds in the 27th generation) outperforms GA (132.24 U/gds in the 320th generation), slightly in terms of optimized lipase activity and highly in terms of convergence rate. The simple structure associated with the effective memory capability of PSO renders it superior over GA. The proposed GA and PSO approaches, based on a biological phenomenon, are considered as natural and thus may replace the traditional gradient‐based optimization approaches in the field of downstream processing of enzymes.     

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.     

Optimal Tracking Controller Design for a Small Scale Helicopter

A model helicopter is more difficult to control than its full scale counterpart. This is due to its greater sensitivity to control inputs and disturbances as well as higher bandwidth of dynamics. This work is focused on designing practical tracking controller for a small scale helicopter following predefined trajectories. A tracking controller based on optimal control theory is synthesized as a part of the development of an autonomous helicopter. Some issues with regards to control constraints are addressed.The weighting between state tracking performance and control power expenditure is analyzed. Overall performance of the control design is evaluated based on its time domain histories of trajectories as well as control inputs.     

Genetic algorithms and evolution

The genetic algorithm (GA) as developed by Holland (1975, Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press) is an optimization technique based on natural selection. We use a modified version of this technique to investigate which aspects of natural selection make it an efficient search procedure. Our main modification to Holland's GA is the subdividing of the population into semi-isolated demes. We consider two examples. One is a fitness landscape with many local optima. The other is a model of singing in birds that has been previously analysed using dynamic programming. Both examples have epistatic interactions. In the first example we show that the GA can find the global optimum and that its success is improved by subdividing the population. In the second example we show that GAs can evolve to the optimal policy found by dynamic programming.     

A parameter optimization approach for the optimal control of large-scale musculoskeletal systems.

This paper describes a computational method for solving optimal control problems involving large-scale, nonlinear, dynamical systems. Central to the approach is the idea that any optimal control problem can be converted into a standard nonlinear programming problem by parameterizing each control history using a set of nodal points, which then become the variables in the resulting parameter optimization problem. A key feature of the method is that it dispenses with the need to solve the two-point, boundary-value problem derived from the necessary conditions of optimal control theory. Gradient-based methods for solving such problems do not always converge due to computational errors introduced by the highly nonlinear characteristics of the costate variables. Instead, by converting the optimal control problem into a parameter optimization problem, any number of well-developed and proven nonlinear programming algorithms can be used to compute the near-optimal control trajectories. The utility of the parameter optimization approach for solving general optimal control problems for human movement is demonstrated by applying it to a detailed optimal control model for maximum-height human jumping. The validity of the near-optimal control solution is established by comparing it to a solution of the two-point, boundary-value problem derived on the basis of a bang-bang optimal control algorithm. Quantitative comparisons between model and experiment further show that the parameter optimization solution reproduces the major features of a maximum-height, countermovement jump (i.e., trajectories of body-segmental displacements, vertical and fore-aft ground reaction forces, displacement, velocity, and acceleration of the whole-body center of mass, pattern of lower-extremity muscular activity, jump height, and total ground contact time).     

Modelling and optimization of environmental conditions for kefiran production by Lactobacillus kefiranofaciens

A mathematical model for kefiran production by Lactobacillus kefiranofaciens was established, in which the effects of pH, substrate and product on cell growth, exopolysaccharide formation and substrate assimilation were considered. The model gave a good representation both of the formation of exopolysaccharides (which are not only attached to cells but also released into the medium) and of the time courses of the production of galactose and glucose in the medium (which are produced and consumed by the cells). Since pH and both lactose and lactic acid concentrations differently affected production and growth activity, the model included the effects of pH and the concentrations of lactose and lactic acid. Based on the mathematical model, an optimal pH profile for the maximum production of kefiran in batch culture was obtained. In this study, a simplified optimization method was developed, in which the optimal pH profile was determined at a particular final fermentation time. This was based on the principle that, at a certain time, switching from the maximum specific growth rate to the critical one (which yields the maximum specific production rate) results in maximum production. Maximum kefiran production was obtained, which was 20% higher than that obtained in the constant-pH control fermentation. A genetic algorithm (GA) was also applied to obtain the optimal pH profile; and it was found that practically the same solution was obtained using the GA.     

Selecting a minimal number of relevant genes from microarray data to design accurate tissue classifiers

It is essential to select a minimal number of relevant genes from microarray data while maximizing classification accuracy for the development of inexpensive diagnostic tests. However, it is intractable to simultaneously optimize gene selection and classification accuracy that is a large parameter optimization problem. We propose an efficient evolutionary approach to gene selection from microarray data which can be combined with the optimal design of various multiclass classifiers. The proposed method (named GeneSelect) consists of three parts which are fully cooperated: an efficient encoding scheme of candidate solutions, a generalized fitness function, and an intelligent genetic algorithm (IGA). An existing hybrid approach based on genetic algorithm and maximum likelihood classification (GA/MLHD) is proposed to select a small number of relevant genes for accurate classification of samples. To evaluate the performance of GeneSelect, the gene selection is combined with the same maximum likelihood classification (named IGA/MLHD) for convenient comparisons. The performance of IGA/MLHD is applied to 11 cancer-related human gene expression datasets. The simulation results show that IGA/MLHD is superior to GA/MLHD in terms of the number of selected genes, classification accuracy, and robustness of selected genes and accuracy.     

Novel optimal temperature profile for acidification process of <Emphasis Type="Italic">Lactobacillus bulgaricus</Emphasis> and <Emphasis Type="Italic">Streptococcus thermophilus</Emphasis> in yoghurt fermentation using artificial neural network and genetic algorithm

The acidification behavior of Lactobacillus bulgaricus and Streptococcus thermophilus for yoghurt production was investigated along temperature profiles within the optimal window of 38–44 °C. For the optimal acidification temperature profile search, an optimization engine module built on a modular artificial neural network (ANN) and genetic algorithm (GA) was used. Fourteen batches of yoghurt fermentations were evaluated using different temperature profiles in order to train and validate the ANN sub-module. The ANN captured the nonlinear relationship between temperature profiles and acidification patterns on training data after 150 epochs. This served as an evaluation function for the GA. The acidification slope of the temperature profile was the performance index. The GA sub-module iteratively evolved better temperature profiles across generations using GA operations. The stopping criterion was met after 11 generations. The optimal profile showed an acidification slope of 0.06117 compared to an initial value of 0.0127 and at a set point sequence of 43, 38, 44, 43, and 39 °C. Laboratory evaluation of three replicates of the GA suggested optimum profile of 43, 38, 44, 43, and 39 °C gave an average slope of 0.04132. The optimization engine used (to be published elsewhere) could effectively search for optimal profiles of different physico-chemical parameters of fermentation processes.     

Specific PCR product primer design using memetic algorithm

To provide feasible primer sets for performing a polymerase chain reaction (PCR) experiment, many primer design methods have been proposed. However, the majority of these methods require a relatively long time to obtain an optimal solution since large quantities of template DNA need to be analyzed. Furthermore, the designed primer sets usually do not provide a specific PCR product size. In recent years, evolutionary computation has been applied to PCR primer design and yielded promising results. In this article, a memetic algorithm (MA) is proposed to solve primer design problems associated with providing a specific product size for PCR experiments. The MA is compared with a genetic algorithm (GA) using an accuracy formula to estimate the quality of the primer design and test the running time. Overall, 50 accession nucleotide sequences were sampled for the comparison of the accuracy of the GA and MA for primer design. Five hundred runs of the GA and MA primer design were performed with PCR product lengths of 150–300 bps and 500–800 bps, and two different methods of calculating T_m for each accession nucleotide sequence were tested. A comparison of the accuracy results for the GA and MA primer design showed that the MA primer design yielded better results than the GA primer design. The results further indicate that the proposed method finds optimal or near‐optimal primer sets and effective PCR products in a dry dock experiment. Related materials are available online at http://bio.kuas.edu.tw/ma‐pd/ . © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Baculovirus titration method based on MOI values for optimizing recombinant protein expression of the anti‐cancer vaccine candidate GA733‐Fc using Sf9 insect cells

The baculovirus expression system has been considered as a highly efficient tool for the production of recombinant biopharmaceutical proteins. The recombinant antigenic glycoprotein GA733 is a cell surface protein that is strongly expressed in human colorectal cancer. Efficient virus titration should be established to achieve optimal multiplicity of infection (MOI) conditions, which are in turn essential for strong expression of the recombinant GA733 fused to the human immunoglobulin IgG Fc fragment (GA733‐Fc) in the baculovirus‐insect system. In the present study, the Sf9 cell line was transfected with plasmid DNA containing the GA733‐Fc expression cassette under the control of the baculovirus polyhedron promoter. MOI values (0.05, 0.1, 0.5, 1, and 3) were calculated based on both microscope observations and results of titration assay and then used to determine the optimum recombinant expression and harvested sample [cell culture media (CM) or cell lysate (CL)]. The pFastBac dual vector carrying the GA733‐Fc gene was constructed to express GA733‐Fc and used to generate recombinant baculoviruses. Western blotting results showed that recombinant protein expression was dependent on the MOI. In addition, CM and CL showed significant differences in protein synthesis and protein secretion capacities. Our findings suggested that our proposed titration method can be used for reliable calculation of MOI values, which significantly influence recombinant GA733‐Fc protein expression in the baculovirus‐insect cell system.     

A hybrid genetic algorithm and expectation maximization method for global gene trajectory clustering

Clustering time-course gene expression data (gene trajectories) is an important step towards solving the complex problem of gene regulatory network modeling and discovery as it significantly reduces the dimensionality of the gene space required for analysis. Traditional clustering methods that perform hill-climbing from randomly initialized cluster centers are prone to produce inconsistent and sub-optimal cluster solutions over different runs. This paper introduces a novel method that hybridizes genetic algorithm (GA) and expectation maximization algorithms (EM) for clustering gene trajectories with the mixtures of multiple linear regression models (MLRs), with the objective of improving the global optimality and consistency of the clustering performance. The proposed method is applied to cluster the human fibroblasts and the yeast time-course gene expression data based on their trajectory similarities. It outperforms the standard EM method significantly in terms of both clustering accuracy and consistency. The biological implications of the improved clustering performance are demonstrated.     

Identification of biomarkers for risk stratification of cardiovascular events using genetic algorithm with recursive local floating search

Conventional biomarker discovery focuses mostly on the identification of single markers and thus often has limited success in disease diagnosis and prognosis. This study proposes a method to identify an optimized protein biomarker panel based on MS studies for predicting the risk of major adverse cardiac events (MACE) in patients. Since the simplicity and concision requirement for the development of immunoassays can only tolerate the complexity of the prediction model with a very few selected discriminative biomarkers, established optimization methods, such as conventional genetic algorithm (GA), thus fails in the high‐dimensional space. In this paper, we present a novel variant of GA that embeds the recursive local floating enhancement technique to discover a panel of protein biomarkers with far better prognostic value for prediction of MACE than existing methods, including the one approved recently by FDA (Food and Drug Administration). The new pragmatic method applies the constraints of MACE relevance and biomarker redundancy to shrink the local searching space in order to avoid heavy computation penalty resulted from the local floating optimization. The proposed method is compared with standard GA and other variable selection approaches based on the MACE prediction experiments. Two powerful classification techniques, partial least squares logistic regression (PLS‐LR) and support vector machine classifier (SVMC), are deployed as the MACE predictors owing to their ability in dealing with small scale and binary response data. New preprocessing algorithms, such as low‐level signal processing, duplicated spectra elimination, and outliner patient's samples removal, are also included in the proposed method. The experimental results show that an optimized panel of seven selected biomarkers can provide more than 77.1% MACE prediction accuracy using SVMC. The experimental results empirically demonstrate that the new GA algorithm with local floating enhancement (GA‐LFE) can achieve the better MACE prediction performance comparing with the existing techniques. The method has been applied to SELDI/MALDI MS datasets to discover an optimized panel of protein biomarkers to distinguish disease from control.     

Expectation-Maximization Binary Clustering for Behavioural Annotation

The growing capacity to process and store animal tracks has spurred the development of new methods to segment animal trajectories into elementary units of movement. Key challenges for movement trajectory segmentation are to (i) minimize the need of supervision, (ii) reduce computational costs, (iii) minimize the need of prior assumptions (e.g. simple parametrizations), and (iv) capture biologically meaningful semantics, useful across a broad range of species. We introduce the Expectation-Maximization binary Clustering (EMbC), a general purpose, unsupervised approach to multivariate data clustering. The EMbC is a variant of the Expectation-Maximization Clustering (EMC), a clustering algorithm based on the maximum likelihood estimation of a Gaussian mixture model. This is an iterative algorithm with a closed form step solution and hence a reasonable computational cost. The method looks for a good compromise between statistical soundness and ease and generality of use (by minimizing prior assumptions and favouring the semantic interpretation of the final clustering). Here we focus on the suitability of the EMbC algorithm for behavioural annotation of movement data. We show and discuss the EMbC outputs in both simulated trajectories and empirical movement trajectories including different species and different tracking methodologies. We use synthetic trajectories to assess the performance of EMbC compared to classic EMC and Hidden Markov Models. Empirical trajectories allow us to explore the robustness of the EMbC to data loss and data inaccuracies, and assess the relationship between EMbC output and expert label assignments. Additionally, we suggest a smoothing procedure to account for temporal correlations among labels, and a proper visualization of the output for movement trajectories. Our algorithm is available as an R-package with a set of complementary functions to ease the analysis.     

Inferring gene regulatory networks with time delays using a genetic algorithm

Recently a state-space model with time delays for inferring gene regulatory networks was proposed. It was assumed that each regulation between two internal state variables had multiple time delays. This assumption caused underestimation of the model with many current gene expression datasets. In biological reality, one regulatory relationship may have just a single time delay, and not multiple time delays. This study employs Boolean variables to capture the existence of the time-delayed regulatory relationships in gene regulatory networks in terms of the state-space model. As the solution space of time delayed relationships is too large for an exhaustive search, a genetic algorithm (GA) is proposed to determine the optimal Boolean variables (the optimal time-delayed regulatory relationships). Coupled with the proposed GA, Bayesian information criterion (BIC) and probabilistic principle component analysis (PPCA) are employed to infer gene regulatory networks with time delays. Computational experiments are performed on two real gene expression datasets. The results show that the GA is effective at finding time-delayed regulatory relationships. Moreover, the inferred gene regulatory networks with time delays from the datasets improve the prediction accuracy and possess more of the expected properties of a real network, compared to a gene regulatory network without time delays.     

Study of the genetic code adaptability by means of a genetic algorithm

We used simulated evolution to study the adaptability level of the canonical genetic code. An adapted genetic algorithm (GA) searches for optimal hypothetical codes. Adaptability is measured as the average variation of the hydrophobicity that the encoded amino acids undergo when errors or mutations are present in the codons of the hypothetical codes. Different types of mutations and point mutation rates that depend on codon base number are considered in this study. Previous works have used statistical approaches based on randomly generated alternative codes or have used local search techniques to determine an optimum value. In this work, we emphasize what can be concluded from the use of simulated evolution considering the results of previous works. The GA provides more information about the difficulty of the evolution of codes, without contradicting previous studies using statistical or engineering approaches. The GA also shows that, within the coevolution theory, the third base clearly improves the adaptability of the current genetic code.     

Optimization of HAART with genetic algorithms and agent-based models of HIV infection

MOTIVATION: Highly Active AntiRetroviral Therapies (HAART) can prolong life significantly to people infected by HIV since, although unable to eradicate the virus, they are quite effective in maintaining control of the infection. However, since HAART have several undesirable side effects, it is considered useful to suspend the therapy according to a suitable schedule of Structured Therapeutic Interruptions (STI). In the present article we describe an application of genetic algorithms (GA) aimed at finding the optimal schedule for a HAART simulated with an agent-based model (ABM) of the immune system that reproduces the most significant features of the response of an organism to the HIV-1 infection. RESULTS: The genetic algorithm helps in finding an optimal therapeutic schedule that maximizes immune restoration, minimizes the viral count and, through appropriate interruptions of the therapy, minimizes the dose of drug administered to the simulated patient. To validate the efficacy of the therapy that the genetic algorithm indicates as optimal, we ran simulations of opportunistic diseases and found that the selected therapy shows the best survival curve among the different simulated control groups. AVAILABILITY: A version of the C-ImmSim simulator is available at http://www.iac.cnr.it/~filippo/c-ImmSim.html     

A Mathematical Model of Optimal Saccadic Eye Movement by a Pair of Muscles

This paper presents a model of saccadic eye movements. Eye movements are considered as being ballistic, since saccades (rapid concurrent movements of both eyes) occur several hundred thousand times per day; visual perception of the environment is interrupted by a saccade. The optimal control was constructed for the motion considered in three consecutively refined assumptions. The controls included in the time-optimal problem were the resultant moment of force exerted by the extraocular muscles, individual moments of force exerted by either muscle of the agonist–antagonist pair, and finally, the rate of change of these moments. This approach is consistent with the view that is currently upheld by physiologists, who believe that a saccade is programmed by the central nervous system before the beginning of an eye movement and is scarcely adjusted during the movement itself. The solution of the optimal control problem and the results obtained by subsequent numerical modeling of saccadic trajectories were compared with the published experimental data. The saccadic trajectories were compared based on the main sequence, the known consistent relationship between saccade amplitude and duration, which is the most widely applied and commonly accepted way of describing saccade data. The main sequence of saccades obtained from the solution of the optimal control problem formulated in the most complete form agreed well with published experimental results.