Algorithms for railway crew management

Crew management is concerned with building the work schedules of crews needed to cover a planned timetable. This is a well-known problem in Operations Research and has been historically associated with airlines and mass-transit companies. More recently, railway applications have also come on the scene, especially in Europe. In practice, the overall crew management problem is decomposed into two subproblems, called crew scheduling and crew rostering. In this paper, we give an outline of different ways of modeling the two subproblems and possible solution methods. Two main solution approaches are illustrated for real-world applications. In particular we discuss in some detail the solution techniques currently adopted at the Italian railway company, Ferrovie dello Stato SpA, for solving crew scheduling and rostering problems.     

Extracting embedded generalized networks from linear programming problems

If a linear program (LP) possesses a large generalized network (GN) submatrix, this structure can be exploited to decrease solution time. The problems of finding maximum sets of GN constraints and finding maximum embedded GN submatrices are shown to be NP-complete, indicating that reliable, efficient solution of these problems is difficult. Therefore, efficient heuristic algorithms are developed for identifying such structure and are tested on a selection of twenty-three real-world problems. The best of four algorithms for identifying GN constraint sets finds a set which is maximum in twelve cases and averages 99.1% of maximum. On average, the GN constraints identified comprise more than 62.3% of the total constraints in these problems. The algorithm for identifying embedded GN submatrices finds submatrices whose sizes, rows plus columns, average 96.8% of an LP upper bound. Over 91.3% of the total constraint matrix was identified as a GN submatrix in these problems, on average.The act of being wise is the act of knowing what to overlook.William James (ca. 1890)     

Computing a longest common subsequence for a set of strings

The known 2-string LCS problem is generalized to finding a Longest Common Subsequence (LCS) for a set of strings. A new, general approach that systematically enumerates common subsequences is proposed for the solution. Assuming a finite symbol set, it is shown that the presented scheme requires a preprocessing time that grows linearly with the total length of the input strings and a processing time that grows linearly with (K), the number of strings, and () the number of matches among them. The only previous algorithm for the generalized LCS problem takesO(K·|S ₁|·|S ₂|·...|S _k |) execution time, where |S _i | denotes the length of the stringS _i . Since typically is a very small percentage of |S ₁|·|S ₂|·...·|S _k |, the proposed method may be considered to be much more efficient than the straightforward dynamic programming approach.     

Parameterized matching with mismatches

The problem of approximate parameterized string searching consists of finding, for a given text t=t₁t₂…t_n and pattern p=p₁p₂…p_m over respective alphabets Σ_t and Σ_p, the injection π_i from Σ_p to Σ_t maximizing the number of matches between π_i(p) and t_it_i+1…t_i+m−1 (i=1,2,…,n−m+1). We examine the special case where both strings are run-length encoded, and further restrict to the case where one of the alphabets is binary. For this case, we give a construction working in time O(n+(r_p×r_t)α(r_t)log(r_t)), where r_p and r_t denote the number of runs in the corresponding encodings for y and x, respectively, and α is the inverse of the Ackermann's function.     

An effective architecture for learning and evolving flexible job-shop schedules

In recent years, the interaction between evolution and learning has received much attention from the research community. Some recent studies on machine learning have shown that it can significantly improve the efficiency of problem solving when using evolutionary algorithms. This paper proposes an architecture for learning and evolving of Flexible Job-Shop schedules called LEarnable Genetic Architecture (LEGA). LEGA provides an effective integration between evolution and learning within a random search process. Unlike the canonical evolution algorithm, where random elitist selection and mutational genetics are assumed; through LEGA, the knowledge extracted from previous generation by its schemata learning module is used to influence the diversity and quality of offsprings. In addition, the architecture specifies a population generator module that generates the initial population of schedules and also trains the schemata learning module. A large range of benchmark data taken from literature and some generated by ourselves are used to analyze the efficacy of LEGA. Experimental results indicate that an instantiation of LEGA called GENACE outperforms current approaches using canonical EAs in computational time and quality of schedules.     

An improved lower bound for the expected number of real zeros of a random algebraic polynomials

In this note we estimate the lower bound of the average number of real zeros of a random algebraic polynomials when the random coefficients are standard normal random variables     

k-Abelian pattern matching

Two words are called k-abelian equivalent, if they share the same multiplicities for all factors of length at most k. We present an optimal linear time algorithm for identifying all occurrences of factors in a text that are k-abelian equivalent to some pattern P. Moreover, an optimal algorithm for finding the largest k for which two words are k-abelian equivalent is given. Solutions for online versions of the k-abelian pattern matching problem are also proposed.     

Polynomial-time perfect matchings in dense hypergraphs

Let H be a k-graph on n   vertices, with minimum codegree at least n/k+cn$n/k+cn$ for some fixed c>0$c>0$. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in H   or a certificate that none exists. This essentially solves a problem of Karpiński, Ruciński and Szymańska; Szymańska previously showed that this problem is NP-hard for a minimum codegree of n/k−cn$n/k-cn$. Our algorithm relies on a theoretical result of independent interest, in which we characterise any such hypergraph with no perfect matching using a family of lattice-based constructions.     

Numerical Optimal Harvesting for an Age-Dependent Prey-Predator System

In this article, we develop a numerical study of an optimal harvesting problem for age-dependent prey-predator system. Here, the rates of growth and decay as well as the interaction effect between species are assumed to be depending on age, time and space. Existence, uniqueness, and necessary conditions for the optimal control are assured in case of a small final time T. The discrete parabolic nonlinear dynamical systems are obtained by using a finite difference semi-implicit scheme. Then a numerical algorithm is developed to approximate the optimal harvesting effort and the optimal harvest. Results of the numerical tests are given.     

Constructing arithmetic subgroups of unipotent groups

Let G be a unipotent algebraic subgroup of some defined over . We describe an algorithm for finding a finite set of generators of the subgroup . This is based on a new proof of the result (in more general form due to Borel and Harish-Chandra) that such a finite generating set exists.