Cooperative combinatorial optimization: evolutionary computation case study

This paper presents a formalization of the notion of cooperation and competition of multiple systems that work toward a common optimization goal of the population using evolutionary computation techniques. It is proved that evolutionary algorithms are more expressive than conventional recursive algorithms, such as Turing machines. Three classes of evolutionary computations are introduced and studied: bounded finite, unbounded finite, and infinite computations. Universal evolutionary algorithms are constructed. Such properties of evolutionary algorithms as completeness, optimality, and search decidability are examined. A natural extension of evolutionary Turing machine (ETM) model is proposed to properly reflect phenomena of cooperation and competition in the whole population.     

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.     

Turing on Super-Turing and adaptivity

Biological processes are often compared to computation and modeled on the Universal Turing Machine. While many systems or aspects of systems can be well described in this manner, Turing computation can only compute what it has been programmed for. It has no ability to learn or adapt to new situations. Yet, adaptation, choice and learning are all hallmarks of living organisms. This suggests that there must be a different form of computation capable of this sort of calculation. It also suggests that there are current computational models of biological systems that may be fundamentally incorrect. We argue that the Super-Turing model is both capable of modeling adaptive computation, and furthermore, a possible answer to the computational model searched for by Turing himself.     

Gait Optimization of a Quadruped Robot Using Evolutionary Computation

Evolutionary Computation(EC)has strengths in terms of computation for gait optimization.However,conventional evolutionary algorithms use typical gait parameters...     

Accelerated Simplified Swarm Optimization with Exploitation Search Scheme for Data Clustering

Data clustering is commonly employed in many disciplines. The aim of clustering is to partition a set of data into clusters, in which objects within the same cluster are similar and dissimilar to other objects that belong to different clusters. Over the past decade, the evolutionary algorithm has been commonly used to solve clustering problems. This study presents a novel algorithm based on simplified swarm optimization, an emerging population-based stochastic optimization approach with the advantages of simplicity, efficiency, and flexibility. This approach combines variable vibrating search (VVS) and rapid centralized strategy (RCS) in dealing with clustering problem. VVS is an exploitation search scheme that can refine the quality of solutions by searching the extreme points nearby the global best position. RCS is developed to accelerate the convergence rate of the algorithm by using the arithmetic average. To empirically evaluate the performance of the proposed algorithm, experiments are examined using 12 benchmark datasets, and corresponding results are compared with recent works. Results of statistical analysis indicate that the proposed algorithm is competitive in terms of the quality of solutions.     

Optimization by simulating molecular evolution

Based on the analogy between mathematical optimization and molecular evolution and on Eigen's quasi-species model of molecular evolution, an evolutionary algorithm for combinatorial optimization has been developed. This algorithm consists of a versatile variation scheme and an innovative decision rule, the essence of which lies in a radical revision of the conventional philosophy of optimization: A number of configurations of variables with better values, instead of only a single best configuration, are selected as starting points for the next iteration. As a result the search proceeds in parallel along a number of routes and is unlikely to get trapped in local optima. An important innovation of the algorithm is introduction of a constraint to let the starting points always keep a certain distance from each other so that the search is able to cover a larger region of space effectively. The main advantage of the algorithm is that it has more chances to find the global optimum and as many local optima as possible in a single run. This has been demonstrated in preliminary computational experiments.     

遗传算法在转录因子结合位点识别中的应用

遗传算法是模拟生物进化过程的计算模型,是一种全局优化搜索算法。将遗传算法与转录因子结合位点识别问题相结合的新方法,以一致性序列模型作为保守motif的描述模型,通过对motif序列与待测序列的比对问题进行编码,将其转化成搜索空间中的优化问题,利用遗传算法来搜索最优解,预测转录因子的结合位点。实验结果表明,这种新的方法是有效的,它在占用少量内存的情况下能够准确地识别出待测转录因子结合位点。     

Multi-Objective Community Detection Based on Memetic Algorithm

Community detection has drawn a lot of attention as it can provide invaluable help in understanding the function and visualizing the structure of networks. Since single objective optimization methods have intrinsic drawbacks to identifying multiple significant community structures, some methods formulate the community detection as multi-objective problems and adopt population-based evolutionary algorithms to obtain multiple community structures. Evolutionary algorithms have strong global search ability, but have difficulty in locating local optima efficiently. In this study, in order to identify multiple significant community structures more effectively, a multi-objective memetic algorithm for community detection is proposed by combining multi-objective evolutionary algorithm with a local search procedure. The local search procedure is designed by addressing three issues. Firstly, nondominated solutions generated by evolutionary operations and solutions in dominant population are set as initial individuals for local search procedure. Then, a new direction vector named as pseudonormal vector is proposed to integrate two objective functions together to form a fitness function. Finally, a network specific local search strategy based on label propagation rule is expanded to search the local optimal solutions efficiently. The extensive experiments on both artificial and real-world networks evaluate the proposed method from three aspects. Firstly, experiments on influence of local search procedure demonstrate that the local search procedure can speed up the convergence to better partitions and make the algorithm more stable. Secondly, comparisons with a set of classic community detection methods illustrate the proposed method can find single partitions effectively. Finally, the method is applied to identify hierarchical structures of networks which are beneficial for analyzing networks in multi-resolution levels.     

Enhanced hybrid search algorithm for protein structure prediction using the 3D-HP lattice model

The problem of protein structure prediction in the hydrophobic-polar (HP) lattice model is the prediction of protein tertiary structure. This problem is usually referred to as the protein folding problem. This paper presents a method for the application of an enhanced hybrid search algorithm to the problem of protein folding prediction, using the three dimensional (3D) HP lattice model. The enhanced hybrid search algorithm is a combination of the particle swarm optimizer (PSO) and tabu search (TS) algorithms. Since the PSO algorithm entraps local minimum in later evolution extremely easily, we combined PSO with the TS algorithm, which has properties of global optimization. Since the technologies of crossover and mutation are applied many times to PSO and TS algorithms, so enhanced hybrid search algorithm is called the MCMPSO-TS (multiple crossover and mutation PSO-TS) algorithm. Experimental results show that the MCMPSO-TS algorithm can find the best solutions so far for the listed benchmarks, which will help comparison with any future paper approach. Moreover, real protein sequences and Fibonacci sequences are verified in the 3D HP lattice model for the first time. Compared with the previous evolutionary algorithms, the new hybrid search algorithm is novel, and can be used effectively to predict 3D protein folding structure. With continuous development and changes in amino acids sequences, the new algorithm will also make a contribution to the study of new protein sequences.     

Improving metabolic flux estimation via evolutionary optimization for convex solution space

MOTIVATION: Flux estimation by using (13) C-labeling pattern information of metabolites is currently the only method that can give accurate, detailed quantification of all intracellular fluxes in the central metabolism of a microorganism. In essence, it corresponds to a constrained optimization problem which minimizes a weighted distance between measured and simulated results. Characteristics, such as existence of multiple local minima, non-linear and non-differentiable make this problem a special difficulty. RESULTS: In the present work, we propose an evolutionary-based global optimization algorithm taking advantage of the convex feature of the problem's solution space. Based on the characteristics of convex spaces, specialized initial population and evolutionary operators are designed to solve (13)C-based metabolic flux estimation problem robustly and efficiently. The algorithm was applied to estimate the central metabolic fluxes in Escherichia coli and compared with conventional optimization technique. Experimental results illustrated that our algorithm is capable of achieving fast convergence to good near-optima and maintaining the robust nature of evolutionary algorithms at the same time. AVAILABILITY: Available from the authors upon request.     

Machine learning study of classifiers trained with biophysiochemical properties of amino acids to predict fibril forming Peptide motifs

It is important to understand the cause of amyloid illnesses by predicting the short protein fragments capable of forming amyloid-like fibril motifs aiding in the discovery of sequence-targeted anti-aggregation drugs. It is extremely desirable to design computational tools to provide affordable in silico predictions owing to the limitations of molecular techniques for their identification. In this research article, we tried to study, from a machine learning perspective, the performance of several machine learning classifiers that use heterogenous features based on biochemical and biophysical properties of amino acids to discriminate between amyloidogenic and non-amyloidogenic regions in peptides. Four conventional machine learning classifiers namely Support Vector Machine, Neural network, Decision tree and Random forest were trained and tested to find the best classifier that fits the problem domain well. Prior to classification, novel implementations of two biologically-inspired feature optimization techniques based on evolutionary algorithms and methodologies that mimic social life and a multivariate method based on projection are utilized in order to remove the unimportant and uninformative features. Among the dimenionality reduction algorithms considered under the study, prediction results show that algorithms based on evolutionary computation is the most effective. SVM best suits the problem domain in its fitment among the classifiers considered. The best classifier is also compared with an online predictor to evidence the equilibrium maintained between true positive rates and false positive rates in the proposed classifier. This exploratory study suggests that these methods are promising in providing amyloidogenity prediction and may be further extended for large-scale proteomic studies.     

Deterministic global optimization algorithm based on outer approximation for the parameter estima- tion of nonlinear dynamic biological systems

ABSTRACT: BACKGROUND: The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are typically classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. RESULTS: This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to the global minimum, reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. CONCLUSION: The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.     

Efficient algorithms for protein sequence design and the analysis of certain evolutionary fitness landscapes.

Protein sequence design is a natural inverse problem to protein structure prediction: given a target structure in three dimensions, we wish to design an amino acid sequence that is likely fold to it. A model of Sun, Brem, Chan, and Dill casts this problem as an optimization on a space of sequences of hydrophobic (H) and polar (P) monomers; the goal is to find a sequence that achieves a dense hydrophobic core with few solvent-exposed hydrophobic residues. Sun et al. developed a heuristic method to search the space of sequences, without a guarantee of optimality or near-optimality; Hart subsequently raised the computational tractability of constructing an optimal sequence in this model as an open question. Here we resolve this question by providing an efficient algorithm to construct optimal sequences; our algorithm has a polynomial running time, and performs very efficiently in practice. We illustrate the implementation of our method on structures drawn from the Protein Data Bank. We also consider extensions of the model to larger amino acid alphabets, as a way to overcome the limitations of the binary H/P alphabet. We show that for a natural class of arbitrarily large alphabets, it remains possible to design optimal sequences efficiently. Finally, we analyze some of the consequences of this sequence design model for the study of evolutionary fitness landscapes. A given target structure may have many sequences that are optimal in the model of Sun et al.; following a notion raised by the work of J. Maynard Smith, we can ask whether these optimal sequences are "connected" by successive point mutations. We provide a polynomial-time algorithm to decide this connectedness property, relative to a given target structure. We develop the algorithm by first solving an analogous problem expressed in terms of submodular functions, a fundamental object of study in combinatorial optimization.     

Chaotic Artificial Bee Colony algorithm: A new approach to the problem of minimization of energy of the 3D protein structure

Prediction of the three-dimensional structure of a protein from its amino acid sequence can be considered as a global optimization problem. In this paper, the Chaotic Artificial Bee Colony (CABC) algorithm was introduced and applied to 3D protein structure prediction. Based on the 3D off-lattice AB model, the CABC algorithm combines global search and local search of the Artificial Bee Colony (ABC) algorithm with the chaotic search algorithm to avoid the problem of premature convergence and easily trapping the local optimum solution. The experiments carried out with the popular Fibonacci sequences demonstrate that the proposed algorithm provides an effective and high-performance method for protein structure prediction.     

A neural network methodology of quadratic optimization.

According to the basic optimization principle of artificial neural networks, a novel kind of neural network model for solving the quadratic programming problem is presented. The methodology is based on the Lagrange multiplier theory in optimization and seeks to provide solutions satisfying the necessary conditions of optimality. The equilibrium point of the network satisfies the Kuhn-Tucker condition for the problem. The stability and convergency of the neural network is investigated and the strategy of the neural optimization is discussed. The feasibility of the neural network method is verified with the computation examples. Results of the simulation of the neural network to solve optimum problems are presented to illustrate the computational power of the neural network method.     

Molecular Dynamics Simulation on the Connection Machine

An algorithm for the efficient calculation of macromolecular force fields on the Connection Machine is described. The full force field is separated into bond interactions and non-bonding interactions. Only the latter are implemented on the Connection Machine, the former, less computationally intensive tasks are performed by an existing, conventional molecular dynamics code on the front end. Parallelization of the evaluation of non-bonding interactions is achieved by the Replicated Systolic Loop algorithm introduced in this paper. The algorithm is a variant of the Systolic Loop scheme often used for the computation of 2-particle forces for the classical N-particle problem.     

Application of Artificial Bee Colony Algorithm to Maximum Likelihood DOA Estimation

Maximum Likelihood (ML) method has an excellent performance for Direction-Of-Arrival (DOA) estimation, but a multidimensional nonlinear solution search is required which complicates the computation and prevents the method from practical use. To reduce the high computational burden of ML method and make it more suitable to engineering applications, we apply the Artificial Bee Colony (ABC) algorithm to maximize the likelihood function for DOA estimation. As a recently proposed bio-inspired computing algorithm, ABC algorithm is originally used to optimize multivariable functions by imitating the behavior of bee colony finding excellent nectar sources in the nature environment. It offers an excellent alternative to the conventional methods in ML-DOA estimation. The performance of ABC-based ML and other popular meta-heuristic-based ML methods for DOA estimation are compared for various scenarios of convergence, Signal-to-Noise Ratio (SNR), and number of iterations. The computation loads of ABC-based ML and the conventional ML methods for DOA estimation are also investigated. Simulation results demonstrate that the proposed ABC based method is more efficient in computation and statistical performance than other ML-based DOA estimation methods.