求解HP格点模型的最佳优先搜索算法

HP格点模型是目前预测蛋白质折叠结构的一种最简单和最流行的模型,该模型已被证明是NP完全问题。将问题的解空间组织成树型结构,利用启发式规则—k步探测法对结点的可能分支进行评估,采用最佳优先策略搜索解空间树。最后用最佳优先搜索算法(BF)对一组公认的算例进行了实算,计算结果表明,BF计算效率优于传统的遗传算法和Monte Carlo方法。     

The Protein Structure Prediction Problem: A Constraint Optimization Approach using a New Lower Bound

The protein structure prediction problem is one of the most (if not the most) important problem in computational biology. This problem consists of finding the conformation of a protein with minimal energy. Because of the complexity of this problem, simplified models like Dill's HP-lattice model [15], [16] have become a major tool for investigating general properties of protein folding. Even for this simplified model, the structure prediction problem has been shown to be NP-complete [5], [7]. We describe a constraint formulation of the HP-model structure prediction problem, and present the basic constraints and search strategy. Of course, the simple formulation would not lead to an efficient algorithm. We therefore describe redundant constraints to prune the search tree. Furthermore, we need bounding function for the energy of an HP-protein. We introduce a new lower bound based on partial knowledge about the final conformation (namely the distribution of H-monomers to layers).     

An efficient memory-based electromagnetism-like mechanism for the redundancy allocation problem

Meta-heuristic algorithms have been successfully applied to solve the redundancy allocation problem in recent years. Among these algorithms, the electromagnetism-like mechanism (EM) is a powerful population-based algorithm designed for continuous decision spaces. This paper presents an efficient memory-based electromagnetism-like mechanism called MBEM to solve the redundancy allocation problem. The proposed algorithm employs a memory matrix in local search to save the features of good solutions and feed it back to the algorithm. This would make the search process more efficient. To verify the good performance of MBEM, various test problems, especially the 33 well-known benchmark instances in the literature, are examined. The experimental results show that not only optimal solutions of all benchmark instances are obtained within a reasonable computer execution time, but also MBEM outperforms EM in terms of the quality of the solutions obtained, even for large-size problems.     

Model accuracy in the Bayesian optimization algorithm

Evolutionary algorithms (EAs) are particularly suited to solve problems for which there is not much information available. From this standpoint, estimation of distribution algorithms (EDAs), which guide the search by using probabilistic models of the population, have brought a new view to evolutionary computation. While solving a given problem with an EDA, the user has access to a set of models that reveal probabilistic dependencies between variables, an important source of information about the problem. However, as the complexity of the used models increases, the chance of overfitting and consequently reducing model interpretability, increases as well. This paper investigates the relationship between the probabilistic models learned by the Bayesian optimization algorithm (BOA) and the underlying problem structure. The purpose of the paper is threefold. First, model building in BOA is analyzed to understand how the problem structure is learned. Second, it is shown how the selection operator can lead to model overfitting in Bayesian EDAs. Third, the scoring metric that guides the search for an adequate model structure is modified to take into account the non-uniform distribution of the mating pool generated by tournament selection. Overall, this paper makes a contribution towards understanding and improving model accuracy in BOA, providing more interpretable models to assist efficiency enhancement techniques and human researchers.     

Combinations of Estimation of Distribution Algorithms and Other Techniques

This paper summaries our recent work on combining estimation of distribution algorithms (EDA) and other techniques for solving hard search and optimization problems:a) guided mutation,an offspring generator in which the ideas from EDAs and genetic algorithms are combined together,we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem,b)evolutionary algorithms refining a heuristic,we advocate a strategy for solving a hard optimization problem with complicated data structure,and c) combination of two different local search techniques and EDA for numerical global optimization problems,its basic idea is that not all the new generated points are needed to be improved by an expensive local search.     

Using previous models to bias structural learning in the hierarchical BOA

Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum or at least its accurate approximation, besides this, any EDA provides us with a sequence of probabilistic models, which in most cases hold a great deal of information about the problem. Although using problem-specific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of problem-specific information has been practically ignored by the EDA community. This paper takes the first step toward the use of probabilistic models obtained by EDAs to speed up the solution of similar problems in the future. More specifically, we propose two approaches to biasing model building in the hierarchical Bayesian optimization algorithm (hBOA) based on knowledge automatically learned from previous hBOA runs on similar problems. We show that the proposed methods lead to substantial speedups and argue that the methods should work well in other applications that require solving a large number of problems with similar structure.     

Automatically obtaining a cellular automaton scheme for modeling protein folding using the FCC model

This paper proposes to model protein folding as an emergent process, using machine learning to infer the folding modeling only from information of known protein structures. Using the face-centered cubic lattice for protein conformation representation, the dynamic nature of protein folding is captured with an evolved neural cellular automaton that defines the amino acids moves along the protein chain and across time. The results of the final folded conformations are compared, using different protein benchmarks, with other methods used in the traditional protein structure prediction problem, highlighting the capabilities and problems found with this modeling.

     

The IBMAP approach for Markov network structure learning

In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum.     

Environment identification-based memory scheme for estimation of distribution algorithms in dynamic environments

In estimation of distribution algorithms (EDAs), the joint probability distribution of high-performance solutions is presented by a probability model. This means that the priority search areas of the solution space are characterized by the probability model. From this point of view, an environment identification-based memory management scheme (EI-MMS) is proposed to adapt binary-coded EDAs to solve dynamic optimization problems (DOPs). Within this scheme, the probability models that characterize the search space of the changing environment are stored and retrieved to adapt EDAs according to environmental changes. A diversity loss correction scheme and a boundary correction scheme are combined to counteract the diversity loss during the static evolutionary process of each environment. Experimental results show the validity of the EI-MMS and indicate that the EI-MMS can be applied to any binary-coded EDAs. In comparison with three state-of-the-art algorithms, the univariate marginal distribution algorithm (UMDA) using the EI-MMS performs better when solving three decomposable DOPs. In order to understand the EI-MMS more deeply, the sensitivity analysis of parameters is also carried out in this paper.     

On discrete models and immunological algorithms for protein structure prediction

Discrete models for protein structure prediction embed the protein amino acid sequence into a discrete spatial structure, usually a lattice, where an optimal tertiary structure is predicted on the basis of simple assumptions relating to the hydrophobic–hydrophilic character of amino acids in the sequence and to relevant interactions for free energy minimization. While the prediction problem is known to be NP complete even in the simple setting of Dill’s model with a 2D-lattice, a variety of bio-inspired algorithms for this problem have been proposed in the literature. Immunological algorithms are inspired by the kind of optimization that immune systems perform when identifying and promoting the replication of the most effective antibodies against given antigens. A quick, state-of-the-art survey of discrete models and immunological algorithms for protein structure prediction is presented in this paper, and the main design and performance features of an immunological algorithm for this problem are illustrated in a tutorial fashion.     

Extended artificial chromosomes genetic algorithm for permutation flowshop scheduling problems

In our previous researches, we proposed the artificial chromosomes with genetic algorithm (ACGA) which combines the concept of the Estimation of Distribution Algorithms (EDAs) with genetic algorithms (GAs). The probabilistic model used in the ACGA is the univariate probabilistic model. We showed that ACGA is effective in solving the scheduling problems. In this paper, a new probabilistic model is proposed to capture the variable linkages together with the univariate probabilistic model where most EDAs could use only one statistic information. This proposed algorithm is named extended artificial chromosomes with genetic algorithm (eACGA). We investigate the usefulness of the probabilistic models and to compare eACGA with several famous permutation-oriented EDAs on the benchmark instances of the permutation flowshop scheduling problems (PFSPs). eACGA yields better solution quality for makespan criterion when we use the average error ratio metric as their performance measures. In addition, eACGA is further integrated with well-known heuristic algorithms, such as NEH and variable neighborhood search (VNS) and it is denoted as eACGA_hybrid to solve the considered problems. No matter the solution quality and the computation efficiency, the experimental results indicate that eACGA_hybrid outperforms other known algorithms in literature. As a result, the proposed algorithms are very competitive in solving the PFSPs.     

An efficient hybrid Taguchi-genetic algorithm for protein folding simulation

Given the amino-acid sequence of a protein, the prediction of a protein’s tertiary structure is known as the protein folding problem. The protein folding problem in the hydrophobic–hydrophilic lattice model is to find the lowest energy conformation. In order to enhance the performance of predicting protein structure, in this paper we propose an efficient hybrid Taguchi-genetic algorithm that combines genetic algorithm, Taguchi method, and particle swarm optimization (PSO). The GA has the capability of powerful global exploration, while the Taguchi method can exploit the optimum offspring. In addition, we present the PSO inspired by a mutation mechanism in a genetic algorithm. We demonstrate that our algorithm can be applied successfully to the protein folding problem based on the hydrophobic-hydrophilic lattice model. Simulation results indicate that our approach performs very well against existing evolutionary algorithm.     

Exploiting Bivariate Dependencies to Speedup Structure Learning in Bayesian Optimization Algorithm

Bayesian optimization algorithm (BOA) is one of the successful and widely used estimation of distribution algorithms (EDAs) which have been employed to solve different optimization problems. In EDAs, a model is learned from the selected population that encodes interactions among problem variables. New individuals are generated by sampling the model and incorporated into the population. Different probabilistic models have been used in EDAs to learn interactions. Bayesian network (BN) is a well-known graphical model which is used in BOA. Learning a proper model in EDAs and particularly in BOA is distinguished as a computationally expensive task. Different methods have been proposed in the literature to improve the complexity of model building in EDAs. This paper employs bivariate dependencies to learn accurate BNs in BOA efficiently. The proposed approach extracts the bivariate dependencies using an appropriate pairwise interaction-detection metric. Due to the static structure of the underlying problems, these dependencies are used in each generation of BOA to learn an accurate network. By using this approach, the computational cost of model building is reduced dramatically. Various optimization problems are selected to be solved by the algorithm. The experimental results show that the proposed approach successfully finds the optimum in problems with different types of interactions efficiently. Significant speedups are observed in the model building procedure as well.     

Optimization based on phylogram analysis

Estimation of Distribution Algorithms (EDAs) is evolutionary algorithms with relevant performance in handling complex problems. Nevertheless, their efficiency and effectiveness directly depends on how accurate the deployed probabilistic models are, which in turn depend on methods of model building. Although the best models found in the literature are often built by computationally complex methods, whose corresponding EDAs require high running time, these methods may evaluate a lesser number of points in the search space. In order to find a better trade-off between running time (efficiency) and the number of evaluated points (effectiveness), this work uses probabilistic models built by algorithms of phylogenetic reconstruction, since some of them are able to efficiently produce accurate models. Then, an EDA, namely, Optimization based on Phylogram Analysis, and a new search technique, namely, Composed Exhaustive Search, are developed and proposed to find solutions for combinatorial optimization problems with different levels of difficulty. Experimental results show that the proposed new EDA features an interesting trade-off between running time and number of evaluated points, attaining solutions near to the best results found in the literature for each one of such performance measures.     

Maintenance scheduling problems as benchmarks for constraint algorithms

The paper focuses on evaluating constraint satisfaction search algorithms on application based random problem instances. The application we use is a well-studied problem in the electric power industry: optimally scheduling preventive maintenance of power generating units within a power plant. We show how these scheduling problems can be cast as constraint satisfaction problems and used to define the structure of randomly generated non-binary CSPs. The random problem instances are then used to evaluate several previously studied algorithms. The paper also demonstrates how constraint satisfaction can be used for optimization tasks. To find an optimal maintenance schedule, a series of CSPs are solved with successively tighter cost-bound constraints. We introduce and experiment with an “iterative learning” algorithm which records additional constraints uncovered during search. The constraints recorded during the solution of one instance with a certain cost-bound are used again on subsequent instances having tighter cost-bounds. Our results show that on a class of randomly generated maintenance scheduling problems, iterative learning reduces the time required to find a good schedule. This revised version was published online in June 2006 with corrections to the Cover Date.     

Biasing Bayesian Optimization Algorithm using Case Based Reasoning

Studies show that application of the prior knowledge in biasing the Estimation of Distribution Algorithms (EDAs), such as Bayesian Optimization Algorithm (BOA), increases the efficiency of these algorithms significantly. One of the main advantages of the EDAs over other optimization algorithms is that the former provides a trail of probabilistic models of candidate solutions with increasing quality. Some recent studies have applied these probabilistic models, obtained from previously solved problems in biasing the BOA algorithm, to solve the future problems. In this paper, in order to improve the previous works and reduce their disadvantages, a method based on Case Based Reasoning (CBR) is proposed for biasing the BOA algorithm. Herein, after running BOA for solving optimization problems, each problem, the corresponding solution, as well as the last Bayesian network obtained from the BOA algorithm, will be stored as an entry in the case-base. Upon introducing a new problem, similar problems from the case-base are retrieved and the last Bayesian networks of these solved problems are combined according to the degree of their similarity with the new problem; hence, a compound Bayesian network is constructed. The compound Bayesian network is sampled and the initial population for the BOA algorithm is generated. This network will be applied efficiently for biasing future probabilistic models during the runs of BOA for the new problem. The proposed method is tested on three well-known combinatorial benchmark problems. Experimental results show significant improvements in algorithm execution time and quality of solutions, compared to previous methods.     

一种求解车间作业调度问题的混合邻域结构搜索算法

车间作业调度问题是优化组合中一个著名的难题,问题的目标是在满足约束条件的前提下,使调度的加工周期尽可能小。文章中提出了利用新的混合邻域结构进行搜索来求解车间作业调度问题。对于算法关键的邻域构造问题以及跳坑策略给出了提高算法优度的解决方案。采用43个不同规模和难度的国际标准算例做为本算法的测试实验集,39个算例找到了最优解,其中包括著名的难例FT10。与当前国外学者提出的一种先进算法进行了比较,算法的优度高于被比较的先进算法。     

A review of message passing algorithms in estimation of distribution algorithms

Message passing algorithms (MPAs) have been traditionally used as an inference method in probabilistic graphical models. Some MPA variants have recently been introduced in the field of estimation of distribution algorithms (EDAs) as a way to improve the efficiency of these algorithms. Multiple developments on MPAs point to an increasing potential of these methods for their application as part of hybrid EDAs. In this paper we review recent work on EDAs that apply MPAs and propose ways to further extend the useful synergies between MPAs and EDAs. Furthermore, we analyze some of the implications that MPA developments can have in their future application to EDAs and other evolutionary algorithms.     

SAT问题中局部搜索法的改进

局部搜索方法在求解SAT问题的高效率使其成为一研究热点．提出用初始概率的方法对局部搜索算法中变量的初始随机指派进行适当的约束．使在局部搜索的开始阶段,可满足的子句数大大增加,减少了翻转的次数,加快了求解的速度．用该方法对目前的一些重要的SAT问题的局部搜索算法(如WSAT,TSAT,NSAT,SDF等)进行改进,通过对不同规模的随机3-SAT问题的实例和一些不同规模的结构性SAT问题的实例,以及利用相变现象构造的难解SAT实例测试表明,改进后的这些局部搜索算法的求解效率有了很大的提高．该方法对其他局部搜索法的改进具有参考价值。     

An effective heuristic algorithm for the maximum satisfiability problem

Stochastic local search algorithms (SLS) have been increasingly applied to approximate solutions of the weighted maximum satisfiability problem (MAXSAT), a model for solutions of major problems in AI and combinatorial optimization. While MAXSAT instances have generally a strong intrinsic dependency between their variables, most of SLS algorithms start the search process with a random initial solution where the value of each variable is generated independently with the same uniform distribution. In this paper, we propose a new SLS algorithm for MAXSAT based on an unconventional distribution known as the Bose-Einstein distribution in quantum physics. It provides a stochastic initialization scheme to an efficient and very simple heuristic inspired by the co-evolution process of natural species and called Extremal Optimization (EO). This heuristic was introduced for finding high quality solutions to hard optimization problems such as colouring and partitioning. We examine the effectiveness of the resulting algorithm by computational experiments on a large set of test instances and compare it with some of the most powerful existing algorithms. Our results are remarkable and show that this approach is appropriate for this class of problems.