A modified active set algorithm for transportation discrete network design bi-level problem

Transportation discrete network design problem (DNDP) is about how to modify an existing network of roads and highways in order to improve its total system travel time, and the candidate road building or expansion plan can only be added as a whole. DNDP can be formulated into a bi-level problem with binary variables. An active set algorithm has been proposed to solve the bi-level discrete network design problem, while it made an assumption that the capacity increase and construction cost of each road are based on the number of lanes. This paper considers a more general case when the capacity increase and construction cost are specified for each candidate plan. This paper also uses numerical methods instead of solvers to solve each step, so it provides a more direct understanding and control of the algorithm and running procedure. By analyzing the differences and getting corresponding solving methods, a modified active set algorithm is proposed in the paper. In the implementation of the algorithm and the validation, we use binary numeral system and ternary numeral system to avoid too many layers of loop and save storage space. Numerical experiments show the correctness and efficiency of the proposed modified active set algorithm.     

A robust algorithm for identification of proteins in a database

In recent years, more and more algorithms and software for reconstruction of partial or entire amino acid sequences by the mass spectra of peptides appear. However, with rare exception, such sequences always contain errors due to many reasons like a chemical noise in the spectrum, incomplete fragmentation, etc. Posttranslational modifications of proteins cause additional difficulties. In this paper, we suggest a PepTiger algorithm, which can correctly identify peptides in a database by de novo sequences containing errors. The algorithm is based on the method of approximate string matching and a specially developed system of scoring, which takes into account the string distance between the de novo sequence and the sequence of the peptide candidate in the database, the difference between their masses, and the similarity between the experimental mass spectrum and the theoretical spectrum of the peptide candidate. The algorithm suggested here correctly identifies a larger number of de novo sequences than other algorithms for identification of peptides by their de novo sequences.     

A simple and space-efficient fragment-chaining algorithm for alignment of DNA and protein sequences

In the segment-based approach to sequence alignment, nucleic acid, and protein sequence alignments are constructed from fragments, i.e., from pairs of ungapped segments of the input sequences. Given a set F of candidate fragments and a weighting function w : F → R⁺₀, the score of an alignment is defined as the sum of weights of the fragments it consists of, and the optimization problem is to find a consistent collection of pairwise disjoint fragments with maximum sum of weights. Herein, a sparse dynamic programming algorithm is described that solves the pairwise segment-alignment problem in O(L + N_max) space where L is the maximum length of the input sequences while N_max ≤ #F holds. With a recently introduced weighting function w, small sets F of candidate fragments are sufficient to obtain alignments of high quality. As a result, the proposed algorithm runs in essentially linear space.     

Mann type iterative methods for finding a common solution of split feasibility and fixed point problems

The purpose of this paper is to study and analyze three different kinds of Mann type iterative methods for finding a common element of the solution set ?? of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in the setting of infinite-dimensional Hilbert spaces. By combining Mann??s iterative method and the extragradient method, we first propose Mann type extragradient-like algorithm for finding an element of the set ${{{\rm Fix}}(S) \cap \Gamma}$ ; moreover, we derive the weak convergence of the proposed algorithm under appropriate conditions. Second, we combine Mann??s iterative method and the viscosity approximation method to introduce Mann type viscosity algorithm for finding an element of the ${{{\rm Fix}}(S)\cap \Gamma}$ ; moreover, we derive the strong convergence of the sequences generated by the proposed algorithm to an element of set ${{{\rm Fix}}(S) \cap \Gamma}$ under mild conditions. Finally, by combining Mann??s iterative method and the relaxed CQ method, we introduce Mann type relaxed CQ algorithm for finding an element of the set ${{{\rm Fix}}(S)\cap \Gamma}$ . We also establish a weak convergence result for the sequences generated by the proposed Mann type relaxed CQ algorithm under appropriate assumptions.     

DNA序列的分类

本文对 A题中给出的 DNA序列分类问题进行了讨论 .从“不同序列中碱基含量不同”入手建立了欧氏距离判别模型 ,马氏距离判别模型以及 Fisher准则判定模型 ;又从“不同序列中碱基位置不同”入手建立了利用序列相关知识的相关度分类判别算法 ,并进一步研究了带反馈的相关度分类判别算法 .对于题中所给的待分类的人工序列和自然序列 ,本文都一一作了分类 .接着 ,本文又对其它各种常见的分类算法进行了讨论 ,并着重从分类算法的稳定性上对几种方法作了比较 .     

Dynamic algorithm selection for pareto optimal set approximation

This paper presents a meta-algorithm for approximating the Pareto optimal set of costly black-box multiobjective optimization problems given a limited number of objective function evaluations. The key idea is to switch among different algorithms during the optimization search based on the predicted performance of each algorithm at the time. Algorithm performance is modeled using a machine learning technique based on the available information. The predicted best algorithm is then selected to run for a limited number of evaluations. The proposed approach is tested on several benchmark problems and the results are compared against those obtained using any one of the candidate algorithms alone.     

Mobile Robot Global Localization using an Evolutionary MAP Filter

A new algorithm based on evolutionary computation concepts is presented in this paper. This algorithm is a non linear evolutive filter known as the Evolutive Localization Filter (ELF) which is able to solve the global localization problem in a robust and efficient way. The proposed algorithm searches stochastically along the state space for the best robot pose estimate. The set of pose solutions (the population) represents the most likely areas according to the perception and motion information up to date. The population evolves by using the log-likelihood of each candidate pose according to the observation and the motion error derived from the comparison between observed and predicted data obtained from the probabilistic perception and motion model. The algorithm has been tested on a mobile robot equipped with a laser range finder to demonstrate the effectiveness, robustness and computational efficiency of the proposed approach.     

An Efficient Algorithm to Identify DNA Motifs

We consider the problem of identifying motifs that abstracts the task of finding short conserved sites in genomic DNA. The planted (l, d)-motif problem, PMP, is the mathematical abstraction of this problem, which consists of finding a substring of length l that occurs in each s _i in a set of input sequences S = {s ₁, s ₂, . . . ,s _t } with at most d substitutions. Our propose algorithm combines the voting algorithm and pattern matching algorithm to find exact motifs. The combined algorithm is achieved by running the voting algorithm on t′ sequences, t′ < t. After that we use the pattern matching on the output of the voting algorithm and the reminder sequences, t ? t′. Two values of t′ are calculated. The first value of t′ makes the running time of our proposed algorithm less than the running time of voting algorithm. The second value of t′ makes the running time of our proposed algorithm is minimal. We show that our proposed algorithm is faster than the voting algorithm by testing both algorithms on simulated data from (9, d ≤ 2) to (19, d ≤ 7). Finally, we test the performance of the combined algorithm on realistic biological data.     

Fixed point optimization algorithm and its application to network bandwidth allocation

A convex optimization problem for a strictly convex objective function over the fixed point set of a nonexpansive mapping includes a network bandwidth allocation problem, which is one of the central issues in modern communication networks. We devised an iterative algorithm, called a fixed point optimization algorithm, for solving the convex optimization problem and conducted a convergence analysis on the algorithm. The analysis guarantees that the algorithm, with slowly diminishing step-size sequences, weakly converges to a unique solution to the problem. Moreover, we apply the proposed algorithm to a network bandwidth allocation problem and show its effectiveness.     

Layered clusters of tightness set functions

A method for structural clustering is proposed involving data on subset-to-entity linkages that can be calculated with structural data such as graphs or sequences or images. The method is based on the layered structure of the problem of maximization of a set function defined as the minimum value of linkages between a set and its elements and referred to as the tightness function. When the linkage function is monotone, the layered cluster can be easily found with a greedy type algorithm.     

Network reinforcement

We give an algorithm for the following problem: given a graph G=(V,E) with edge-weights and a nonnegative integer k, find a minimum cost set of edges that contains k disjoint spanning trees. This also solves the following reinforcement problem: given a network, a number k and a set of candidate edges, each of them with an associated cost, find a minimum cost set of candidate edges to be added to the network so it contains k disjoint spanning trees. The number k is seen as a measure of the invulnerability of a network. Our algorithm has the same asymptotic complexity as |V| applications of the minimum cut algorithm of Goldberg & Tarjan. Received: April, 2004     

An improved heuristic for the far from most strings problem

The Far From Most Strings Problem (FFMSP) asks for a string that is far from as many as possible of a given set of strings. All the input and the output strings are of the same length, and two strings are far if their Hamming distance is greater than or equal to a given threshold. FFMSP belongs to the class of sequence consensus problems which have applications in molecular biology, amongst others. FFMSP is NP-hard. It does not admit a constant-ratio approximation either, unless P=NP. In the last few years, heuristic and metaheuristic algorithms have been proposed for the problem, which use local search and require a heuristic, also called an evaluation function, to evaluate candidate solutions during local search. The heuristic function used, for this purpose, in these algorithms is the problem’s objective function. However, since many candidate solutions can be of the same objective value, the resulting search landscape includes many points which correspond to local maxima. In this paper, we devise a new heuristic function to evaluate candidate solutions. We then incorporate the proposed heuristic function within a Greedy Randomized Adaptive Search Procedure (GRASP), a metaheuristic originally proposed for the problem by Festa. The resulting algorithm outperforms state-of-the-art with respect to solution quality, in some cases by orders of magnitude, on both random and real data in our experiments. The results indicate that the number of local optima is considerably reduced using the proposed heuristic.     

METHOD OF CENTERS ALGORITHM FOR MULTI-OBJECTIVE PROGRAMMING PROBLEMS

In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multiobjective programming problems.     

Choosing the best set of variables in regression analysis using integer programming

This paper is concerned with an algorithm for selecting the best set of s variables out of k(> s) candidate variables in a multiple linear regression model. We employ absolute deviation as the measure of deviation and solve the resulting optimization problem by using 0-1 integer programming methodologies. In addition, we will propose a heuristic algorithm to obtain a close to optimal set of variables in terms of squared deviation. Computational results show that this method is practical and reliable for determining the best set of variables.     

Extragradient methods for split feasibility problems and generalized equilibrium problems in Banach spaces

The purpose of this paper is the presentation of a new extragradient algorithm in 2‐uniformly convex real Banach spaces. We prove that the sequences generated by this algorithm converge strongly to a point in the solution set of split feasibility problem, which is also a common element of the solution set of a generalized equilibrium problem and fixed points of of two relatively nonexpansive mappings. We give a numerical example to investigate the behavior of the sequences generated by our algorithm.     

Fixed point methods for pseudomonotone variational inequalities involving strict pseudocontractions

We introduce a new iteration method for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of strict pseudocontractions in a real Hilbert space. The weak convergence of the iterative sequences generated by the method is obtained thanks to improve and extend some recent results under the assumptions that the cost mapping associated with the variational inequality problem only is pseudomonotone and not necessarily inverse strongly monotone. Finally, we present some numerical examples to illustrate the behaviour of the proposed algorithm.     

Boosting the Generalized Margin in Cost-Sensitive Multiclass Classification

The boosting algorithm is one of the most successful binary classification techniques due to its relative immunity to overfitting and flexible implementation. Several attempts have been made to extend the binary boosting algorithm to multiclass classification. In this article, a novel cost-sensitive multiclass boosting algorithm is proposed that naturally extends the popular binary AdaBoost algorithm and admits unequal misclassification costs. The proposed multiclass boosting algorithm achieves superior classification performance by combining weak candidate models that only need to be better than random guessing. More importantly, the proposed algorithm achieves a large margin separation of the training sample while attaining an L₁-norm constraint on the model complexity. Finally, the effectiveness of the proposed algorithm is demonstrated in a number of simulated and real experiments. The supplementary files are available online, including the technical proofs, the implemented R code, and the real datasets.     

Knot Placement for B-Spline Curve Approximation via $L_{∞, 1}$-Norm and Differential Evolution Algorithm

In this paper, we consider the knot placement problem in B-spline curve approximation. A novel two-stage framework is proposed for addressing this problem. In the first step, the $l_{\infty, 1}$-norm model is introduced for the sparse selection of candidate knots from an initial knot vector. By this step, the knot number is determined. In the second step, knot positions are formulated into a nonlinear optimization problem and optimized by a global optimization algorithm — the differential evolution algorithm (DE). The candidate knots selected in the first step are served for initial values of the DE algorithm. Since the candidate knots provide a good guess of knot positions, the DE algorithm can quickly converge. One advantage of the proposed algorithm is that the knot number and knot positions are determined automatically. Compared with the current existing algorithms, the proposed algorithm finds approximations with smaller fitting error when the knot number is fixed in advance. Furthermore, the proposed algorithm is robust to noisy data and can handle with few data points. We illustrate with some examples and applications.     

A correlative classifiers approach based on particle filter and sample set for tracking occluded target

Target tracking is one of the most important issues in computer vision and has been applied in many fields of science, engineering and industry. Because of the occlusion during tracking, typical approaches with single classifier learn much of occluding background information which results in the decrease of tracking performance, and eventually lead to the failure of the tracking algorithm. This paper presents a new correlative classifiers approach to address the above problem. Our idea is to derive a group of correlative classifiers based on sample set method. Then we propose strategy to establish the classifiers and to query the suitable classifiers for the next frame tracking. In order to deal with nonlinear problem, particle filter is adopted and integrated with sample set method. For choosing the target from candidate particles, we define a similarity measurement between particles and sample set. The proposed sample set method includes the following steps. First, we cropped positive samples set around the target and negative samples set far away from the target. Second, we extracted average Haar-like feature from these samples and calculate their statistical characteristic which represents the target model. Third, we define the similarity measurement based on the statistical characteristic of these two sets to judge the similarity between candidate particles and target model. Finally, we choose the largest similarity score particle as the target in the new frame. A number of experiments show the robustness and efficiency of the proposed approach when compared with other state-of-the-art trackers.     

Vectorial Approach to Fast Correlation Attacks

A new, vectorial approach to fast correlation attacks on binary memoryless combiners is proposed. Instead of individual input sequences or their linear combinations, the new attack is targeting subsets of input sequences as a whole thus exploiting the full correlation between the chosen subset and the output sequence. In particular, the set of all the input sequences can be chosen as the target. The attack is based on a novel iterative probabilistic algorithm which is also applicable to general memoryless combiners over finite fields or finite rings. To illustrate the effectiveness of the introduced approach, experimental results obtained for random balanced combining functions are presentedMost of this work was done while he was with Rome CryptoDesign Center, Gemplus, Italy