ConvAn: a convergence analyzing tool for optimization of biochemical networks

Dynamic models of biochemical networks usually are described as a system of nonlinear differential equations. In case of optimization of models for purpose of parameter estimation or design of new properties mainly numerical methods are used. That causes problems of optimization predictability as most of numerical optimization methods have stochastic properties and the convergence of the objective function to the global optimum is hardly predictable. Determination of suitable optimization method and necessary duration of optimization becomes critical in case of evaluation of high number of combinations of adjustable parameters or in case of large dynamic models. This task is complex due to variety of optimization methods, software tools and nonlinearity features of models in different parameter spaces. A software tool ConvAn is developed to analyze statistical properties of convergence dynamics for optimization runs with particular optimization method, model, software tool, set of optimization method parameters and number of adjustable parameters of the model. The convergence curves can be normalized automatically to enable comparison of different methods and models in the same scale. By the help of the biochemistry adapted graphical user interface of ConvAn it is possible to compare different optimization methods in terms of ability to find the global optima or values close to that as well as the necessary computational time to reach them. It is possible to estimate the optimization performance for different number of adjustable parameters. The functionality of ConvAn enables statistical assessment of necessary optimization time depending on the necessary optimization accuracy. Optimization methods, which are not suitable for a particular optimization task, can be rejected if they have poor repeatability or convergence properties. The software ConvAn is freely available on www.biosystems.lv/convan.     

Prediction of antagonistic muscle forces using inverse dynamic optimization during flexion/extension of the knee.

This paper examined the feasibility of using different optimization criteria in inverse dynamic optimization to predict antagonistic muscle forces and joint reaction forces during isokinetic flexion/extension and isometric extension exercises of the knee. Both quadriceps and hamstrings muscle groups were included in this study. The knee joint motion included flexion/extension, varus/valgus, and internal/external rotations. Four linear, nonlinear, and physiological optimization criteria were utilized in the optimization procedure. All optimization criteria adopted in this paper were shown to be able to predict antagonistic muscle contraction during flexion and extension of the knee. The predicted muscle forces were compared in temporal patterns with EMG activities (averaged data measured from five subjects). Joint reaction forces were predicted to be similar using all optimization criteria. In comparison with previous studies, these results suggested that the kinematic information involved in the inverse dynamic optimization plays an important role in prediction of the recruitment of antagonistic muscles rather than the selection of a particular optimization criterion. Therefore, it might be concluded that a properly formulated inverse dynamic optimization procedure should describe the knee joint rotation in three orthogonal planes.     

基于混合优化算法的经颅磁刺激线圈阵列设计

为了研究对经颅磁刺激激励线圈聚焦性能的优化,利用混合优化算法与CST软件的外部通信接口,建立优化的激励线圈模型。依据多信道线圈阵列方法,利用磁场叠加原理,对影响磁场分布的线圈可调参数进行分析,结合混合优化算法对可调参数进行优化。结果对比显示,经优化的线圈阵列有良好的磁聚焦性,其刺激强度与聚焦程度都有了不同程度提高。可用于改善TMS系统聚焦性能,实验有助于进一步探索全面优化激励线圈的空间结构。     

Simulated Evolutionary Optimization and Local Search: Introduction and Application to Tree Search

Tree search and its more complicated variant, tree search and simultaneous multiple DNA sequence alignment, are difficult NP-complete optimization problems, which require the application of advanced computational techniques, if large data sets are to be solved within reasonable computation times. Traditionally tree search has been attacked with a search strategy that is best described as multistart hill-climbing; local search by branch swapping has been performed on several different starting trees. Recently a different tree search strategy was tested in the Parsigal parsimony program, which used a combination of evolutionary optimization and local search. Evolutionary optimization algorithms use principles adopted from biological evolution to solve technical optimization tasks. Evolutionary optimization is a stochastic global search method, which means that the method is able to escape local optima, and is in principle able to produce any solution in the search space (although this may take a long time). Local search techniques, such as branch swapping, employ a completely different search strategy; they exploit local information maximally in order to achieve quick improvement in the value of the objective function. However, local search algorithms lack the ability to escape from local optima, which is a fundamental requirement for any search algorithm that aims to be able to discover the global optimum of a multimodal optimization problem. Hence it seems that an optimization strategy combining the good properties of both evolutionary algorithms and local search would be ideal. In this study, aspects of global optimization and local search are discussed, and the method of simulated evolutionary optimization is reviewed in detail. The application of simulated evolutionary optimization to tree search in Parsigal is then reviewed briefly.     

Estimation-based ant colony optimization and local search for the probabilistic traveling salesman problem

The use of ant colony optimization for solving stochastic optimization problems has received a significant amount of attention in recent years. In this paper, we present a study of enhanced ant colony optimization algorithms for tackling a stochastic optimization problem, the probabilistic traveling salesman problem. In particular, we propose an empirical estimation approach to evaluate the cost of the solutions constructed by the ants. Moreover, we use a recent estimation-based iterative improvement algorithm as a local search. Experimental results on a large number of problem instances show that the proposed ant colony optimization algorithms outperform the current best algorithm tailored to solve the given problem, which also happened to be an ant colony optimization algorithm. As a consequence, we have obtained a new state-of-the-art ant colony optimization algorithm for the probabilistic traveling salesman problem.     

A global optimization method for prediction of muscle forces of human musculoskeletal system

Inverse dynamic optimization is a popular method for predicting muscle and joint reaction forces within human musculoskeletal joints. However, the traditional formulation of the optimization method does not include the joint reaction moment in the moment equilibrium equation, potentially violating the equilibrium conditions of the joint. Consequently, the predicted muscle and joint reaction forces are coordinate system-dependent. This paper presents an improved optimization method for the prediction of muscle forces and joint reaction forces. In this method, the location of the rotation center of the joint is used as an optimization variable, and the moment equilibrium equation is formulated with respect to the joint rotation center to represent an accurate moment constraint condition. The predicted muscle and joint reaction forces are independent of the joint coordinate system. The new optimization method was used to predict muscle forces of an elbow joint. The results demonstrated that the joint rotation center location varied with applied loading conditions. The predicted muscle and joint reaction forces were different from those predicted by using the traditional optimization method. The results further demonstrated that the improved optimization method converged to a minimum for the objective function that is smaller than that reached by using the traditional optimization method. Therefore, the joint rotation center location should be involved as a variable in an inverse dynamic optimization method for predicting muscle and joint reaction forces within human musculoskeletal joints.     

Search-based optimization

The problem of determining the minimum cost hypothetical ancestral sequences for a given cladogram is known to be NP-complete (Wang and Jiang, 1994). Traditionally, point estimations of hypothetical ancestral sequences have been used to gain heuristic, upper bounds on cladogram cost. These include procedures with such diverse approaches as non-additive optimization of multiple sequence alignment, direct optimization (Wheeler, 1996), and fixed-state character optimization (Wheeler, 1999). A method is proposed here which, by extending fixed-state character optimization, replaces the estimation process with a search. This form of optimization examines a diversity of potential state solutions for cost-efficient hypothetical ancestral sequences and can result in greatly more parsimonious cladograms. Additionally, such an approach can be applied to other NP-complete phylogenetic optimization problems such as genomic break-point analysis.     

Integrated process optimization: lessons from retrovirus and virus-like particle production

The optimization of production and purification processes is usually approached by engineers from a strictly biotechnological point of view. The present paper envisages the definition and application of an optimization model that takes into account the impact of both biological and technological issues upon the optimization protocols and strategies. For this purpose, the optimization of three analogous but different systems comprising animal cell growth and bioparticle production is presented. These systems were: human immunodeficiency 1 (HIV-1) and porcine parvovirus (PPV) virus-like particles (VLPs) produced in insect cells and retrovirus produced in mammalian cells. For the systematization of the optimization process four levels of optimization were defined-product, technology, design and integration. In this paper, the limits of each of the optimization levels defined are discussed by applying the concept to the systems described. This analysis leads to decisions regarding the production of VLPs and retrovirus as well as on the points relevant for further process development. Finally, the definition of the objective function or performance index, the possible strategies and tools for bioprocess optimization are described. Although developed from the three described processes, this approach can, based on the recent literature evidence reviewed here, be applied more universally for the process development of complex biopharmaceuticals.     

Set-based particle swarm optimization applied to the multidimensional knapsack problem

Particle swarm optimization algorithms have been successfully applied to discrete/valued optimization problems. However, in many cases the algorithms have been tailored specifically for the problem at hand. This paper proposes a generic set-based particle swarm optimization algorithm for use in discrete-valued optimization problems that can be formulated as set-based problems. A detailed sensitivity analysis of the parameters of the algorithm is conducted. The performance of the proposed algorithm is then compared against three other discrete particle swarm optimization algorithms from literature using the multidimensional knapsack problem and is shown to statistically outperform the existing algorithms.     

A study to determine the impact of IMPT optimization techniques on prostate synthetic CT image sets dose comparison against CT image sets

BackgroundThe objective of this study is to determine the impact of intensity modulated proton therapty (IMPT) optimization techniques on the proton dose comparison of commercially available magnetic resonance for calculating attenuation (MRCA T) images, a synthetic computed tomography CT (sCT) based on magnetic resonance imaging (MRI) scan against the CT images and find out the optimization technique which creates plans with the least dose differences against the regular CT image sets.Material and methodsRegular CT data sets and sCT image sets were obtained for 10 prostate patients for the study. Six plans were created using six distinct IMPT optimization techniques including multi-field optimization (MFO), single field uniform dose (SFUD) optimization, and robust optimization (RO) in CT image sets. These plans were copied to MRCA T, sCT datasets and doses were computed. Doses from CT and MRCA T data sets were compared for each patient using 2D dose distribution display, dose volume histograms (DVH), homogeneity index (HI), conformation number (CN) and 3D gamma analysis. A two tailed t-test was conducted on HI and CN with 5% significance level with a null hypothesis for CT and sCT image sets.ResultsAnalysis of ten CT and sCT image sets with different IMPT optimization techniques shows that a few of the techniques show significant differences between plans for a few evaluation parameters. Isodose lines, DVH, HI, CN and t-test analysis shows that robust optimizations with 2% range error incorporated results in plans, when re-computed in sCT image sets results in the least dose differences against CT plans compared to other optimization techniques. The second best optimization technique with the least dose differences was robust optimization with 5% range error.ConclusionThis study affirmatively demonstrates the impact of IMPT optimization techniques on synthetic CT image sets dose comparison against CT images and determines the robust optimization with 2% range error as the optimization technique which gives the least dose difference when compared to CT plans.     

A Bayesian Interpretation of the Particle Swarm Optimization and Its Kernel Extension

Particle swarm optimization is a popular method for solving difficult optimization problems. There have been attempts to formulate the method in formal probabilistic or stochastic terms (e.g. bare bones particle swarm) with the aim to achieve more generality and explain the practical behavior of the method. Here we present a Bayesian interpretation of the particle swarm optimization. This interpretation provides a formal framework for incorporation of prior knowledge about the problem that is being solved. Furthermore, it also allows to extend the particle optimization method through the use of kernel functions that represent the intermediary transformation of the data into a different space where the optimization problem is expected to be easier to be resolved–such transformation can be seen as a form of prior knowledge about the nature of the optimization problem. We derive from the general Bayesian formulation the commonly used particle swarm methods as particular cases.     

Application of multiple response optimization design to quantum dot-encoded microsphere bioconjugates hybridization assay

The optimization of DNA hybridization for genotyping assays is a complex experimental problem that depends on multiple factors such as assay formats, fluorescent probes, target sequence, experimental conditions, and data analysis. Quantum dot-doped particle bioconjugates have been previously described as fluorescent probes to identify single nucleotide polymorphisms even though this advanced fluorescent material has shown structural instability in aqueous environments. To achieve the optimization of DNA hybridization to quantum dot-doped particle bioconjugates in suspension while maximizing the stability of the probe materials, a nonsequential optimization approach was evaluated. The design of experiment with response surface methodology and multiple optimization response was used to maximize the recovery of fluorescent probe at the end of the assay simultaneously with the optimization of target–probe binding. Hybridization efficiency was evaluated by the attachment of fluorescent oligonucleotides to the fluorescent probe through continuous flow cytometry detection. Optimal conditions were predicted with the model and tested for the identification of single nucleotide polymorphisms. The design of experiment has been shown to significantly improve biochemistry and biotechnology optimization processes. Here we demonstrate the potential of this statistical approach to facilitate the optimization of experimental protocol that involves material science and molecular biology.     

On the probabilistic optimization of spiking neural networks

The construction of a Spiking Neural Network (SNN), i.e. the choice of an appropriate topology and the configuration of its internal parameters, represents a great challenge for SNN based applications. Evolutionary Algorithms (EAs) offer an elegant solution for these challenges and methods capable of exploring both types of search spaces simultaneously appear to be the most promising ones. A variety of such heterogeneous optimization algorithms have emerged recently, in particular in the field of probabilistic optimization. In this paper, a literature review on heterogeneous optimization algorithms is presented and an example of probabilistic optimization of SNN is discussed in detail. The paper provides an experimental analysis of a novel Heterogeneous Multi-Model Estimation of Distribution Algorithm (hMM-EDA). First, practical guidelines for configuring the method are derived and then the performance of hMM-EDA is compared to state-of-the-art optimization algorithms. Results show hMM-EDA as a light-weight, fast and reliable optimization method that requires the configuration of only very few parameters. Its performance on a synthetic heterogeneous benchmark problem is highly competitive and suggests its suitability for the optimization of SNN.     

A critical analysis of parameter adaptation in ant colony optimization

Applying parameter adaptation means operating on parameters of an algorithm while it is tackling an instance. For ant colony optimization, several parameter adaptation methods have been proposed. In the literature, these methods have been shown to improve the quality of the results achieved in some particular contexts. In particular, they proved to be successful when applied to novel ant colony optimization algorithms for tackling problems that are not a classical testbed for optimization algorithms. In this paper, we show that the adaptation methods proposed so far do not improve, and often even worsen the performance when applied to high performing ant colony optimization algorithms for some classical combinatorial optimization problems.     

A dynamic optimization technique for predicting muscle forces in the swing phase of gait

The muscle force sharing problem was solved for the swing phase of gait using a dynamic optimization algorithm. For comparison purposes the problem was also solved using a typical static optimization algorithm. The objective function for the dynamic optimization algorithm was a combination of the tracking error and the metabolic energy consumption. The latter quantity was taken to be the sum of the total work done by the muscles and the enthalpy change during the contraction. The objective function for the static optimization problem was the sum of the cubes of the muscle stresses. To solve the problem using the static approach, the inverse dynamics problem was first solved in order to determine the resultant joint torques required to generate the given hip, knee and ankle trajectories. To this effect the angular velocities and accelerations were obtained by numerical differentiation using a low-pass digital filter. The dynamic optimization problem was solved using the Fletcher-Reeves conjugate gradient algorithm, and the static optimization problem was solved using the Gradient-restoration algorithm. The results show influence of internal muscle dynamics on muscle control histories vis a vis muscle forces. They also illustrate the strong sensitivity of the results to the differentiation procedure used in the static optimization approach.     

Integral dose based inverse optimization objective function promises lower toxicity in head-and-neck

PurposeThe voxels in a CT data sets contain density information. Besides its use in dose calculation density has no other application in modern radiotherapy treatment planning. This work introduces the use of density information by integral dose minimization in radiotherapy treatment planning for head-and-neck squamous cell carcinoma (HNSCC).Materials and methodsEighteen HNSCC cases were studied. For each case two intensity modulated radiotherapy (IMRT) plans were created: one based on dose-volume (DV) optimization, and one based on integral dose minimization (Energy hereafter) inverse optimization. The target objective functions in both optimization schemes were specified in terms of minimum, maximum, and uniform doses, while the organs at risk (OAR) objectives were specified in terms of DV- and Energy-objectives respectively. Commonly used dosimetric measures were applied to assess the performance of Energy-based optimization. In addition, generalized equivalent uniform doses (gEUDs) were evaluated. Statistical analyses were performed to estimate the performance of this novel inverse optimization paradigm.ResultsEnergy-based inverse optimization resulted in lower OAR doses for equivalent target doses and isodose coverage. The statistical tests showed dose reduction to the OARs with Energy-based optimization ranging from ∼2% to ∼15%.ConclusionsIntegral dose minimization based inverse optimization for HNSCC promises lower doses to nearby OARs. For comparable therapeutic effect the incorporation of density information into the optimization cost function allows reduction in the normal tissue doses and possibly in the risk and the severity of treatment related toxicities.     

Coordinated Optimization of Visual Cortical Maps (I) Symmetry-based Analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps.     

Theoretical analysis of two ACO approaches for the traveling salesman problem

Bioinspired algorithms, such as evolutionary algorithms and ant colony optimization, are widely used for different combinatorial optimization problems. These algorithms rely heavily on the use of randomness and are hard to understand from a theoretical point of view. This paper contributes to the theoretical analysis of ant colony optimization and studies this type of algorithm on one of the most prominent combinatorial optimization problems, namely the traveling salesperson problem (TSP). We present a new construction graph and show that it has a stronger local property than one commonly used for constructing solutions of the TSP. The rigorous runtime analysis for two ant colony optimization algorithms, based on these two construction procedures, shows that they lead to good approximation in expected polynomial time on random instances. Furthermore, we point out in which situations our algorithms get trapped in local optima and show where the use of the right amount of heuristic information is provably beneficial.     

A three-dimensional topology optimization model for tooth-root morphology

To obtain the root of a lower incisor through structural optimization, we used two methods: optimization with Solid Isotropic Material with Penalization (SIMP) and Soft-Kill Option (SKO). The optimization was carried out in combination with a finite element analysis in Abaqus/Standard. The model geometry was based on cone-beam tomography scans of 10 adult males with healthy bone-tooth interface. Our results demonstrate that the optimization method using SIMP for minimum compliance could not adequately predict the actual root shape. The SKO method, however, provided optimization results that were comparable to the natural root form and is therefore suitable to set up the basic topology of a dental root.