A cumulative not-first/not-last filtering algorithm in O(n 2log(n))

In cumulative and disjunctive constraint-based scheduling, the resource constraint is enforced by several filtering rules. Among these rules, we have (extended) edge-finding and not-first/not-last rules. The not-first/not-last rule detects tasks that cannot run first/last relatively to a set of tasks and prunes their time bounds. In this paper, it is presented a sound O (n ² log n) algorithm for the cumulative not-first/not-last rule where n is the number of tasks. This algorithm reaches the same fix point as previous not-first/not-last algorithms, although it may take additional iterations to do so. The worst case complexity of this new algorithm for the maximal adjustment is the same as our previous complete O (n ²|H| log n) not-first/not-last algorithm [7] where |H| is the maximum between the number of distinct earliest completion and latest start times of tasks. But, experimental results on benchmarks from the Project Scheduling Problem Library (PSPLib) and the Baptiste and Le Pape data set (BL) suggest that the new not-first/not-last algorithm has a substantially reduced runtime. Furthermore, the results demonstrate that in practice the new algorithm rarely requires more propagations than previous not-first/not-last algorithms.     

An approach to construction of modified Kalman filter

We propose a modified dynamic filtering algorithm for estimating perturbations of programmed values of state parameters. The implementation of the proposed Kaiman filtering approach for estimating the state of an aircraft under given modeling assumptions has reduced the multidimensional filtering problem to several one-dimensional problems.     

Independent sets in bounded-degree hypergraphs

In this paper we analyze several approaches to the Maximum Independent Set (MIS) problem in hypergraphs with degree bounded by a parameter Δ. Since independent sets in hypergraphs can be strong and weak, we denote by MIS (MSIS) the problem of finding a maximum weak (strong) independent set in hypergraphs, respectively. We propose a general technique that reduces the worst case analysis of certain algorithms on hypergraphs to their analysis on ordinary graphs. This technique allows us to show that the greedy algorithm for MIS that corresponds to the classical greedy set cover algorithm has a performance ratio of (Δ+1)/2. It also allows us to apply results on local search algorithms on graphs to obtain a (Δ+1)/2 approximation for the weighted MIS and (Δ+3)/5−? approximation for the unweighted case. We improve the bound in the weighted case to ⌈(Δ+1)/3⌉ using a simple partitioning algorithm. We also consider another natural greedy algorithm for MIS that adds vertices of minimum degree and achieves only a ratio of Δ−1, significantly worse than on ordinary graphs. For MSIS, we give two variations of the basic greedy algorithm and describe a family of hypergraphs where both algorithms approach the bound of Δ.     

A new multiobjective evolutionary algorithm

The Pareto-based approaches have shown some success in designing multiobjective evolutionary algorithms (MEAs). Their methods of fitness assignment are mainly from the information of dominated and nondominated individuals. On the top of the hierarchy of MEAs, the strength Pareto evolutionary algorithm (SPEA) has been elaborately designed with this principle in mind. In this paper, we propose a (μ+λ) multiobjective evolutionary algorithm ((μ+λ) MEA), which discards the dominated individuals in each generation. The comparisons of the experimental results demonstrate that the (μ+λ) MEA outperforms SPEA on five benchmark functions with less computational efforts.     

Design and shape adjustment of developable surfaces

This paper presents two direct explicit methods of computer-aided design for developable surfaces. The developable surfaces are designed by using control planes with C-Bézier basis functions. The shape of developable surfaces can be adjusted by using a control parameter. When the parameter takes on different values, a family of developable surfaces can be constructed and they keep the characteristics of Bézier surfaces. The thesis also discusses the properties of designed developable surfaces and presents geometric construction algorithms, including the de Casteljau algorithm, the Farin–Boehm construction for G² continuity, and the G² Beta restricted condition algorithm. The techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design, but go beyond the limitations of traditional approaches in designing developable surfaces and resolve problems frequently encountered in engineering by adjusting the position and shape of developable surfaces.     

Noisy colored point set matching

We propose a process for determining approximated matches, in terms of the bottleneck distance, under color preserving rigid motions, between two colored point sets A,B∈R², |A|≤|B|. We solve the matching problem by generating all representative motions that bring A close to a subset B^′ of set B and then using a graph matching algorithm. We also present an approximate matching algorithm with improved computational time. In order to get better running times for both algorithms we present a lossless filtering preprocessing step. By using it, we determine some candidate zones which are regions that contain a subset S of B such that A may match one or more subsets B^′ of S. Then, we solve the matching problem between A and every candidate zone. Experimental results using both synthetic and real data are reported to prove the effectiveness of the proposed approach.     

Using Competitive Population Evaluation in a differential evolution algorithm for dynamic environments

This paper proposes two adaptations to DynDE, a differential evolution-based algorithm for solving dynamic optimization problems. The first adapted algorithm, Competitive Population Evaluation (CPE), is a multi-population DE algorithm aimed at locating optima faster in the dynamic environment. This adaptation is based on allowing populations to compete for function evaluations based on their performance. The second adapted algorithm, Reinitialization Midpoint Check (RMC), is aimed at improving the technique used by DynDE to maintain populations on different peaks in the search space. A combination of the CPE and RMC adaptations is investigated. The new adaptations are empirically compared to DynDE using various problem sets. The empirical results show that the adaptations constitute an improvement over DynDE and compares favorably to other approaches in the literature. The general applicability of the adaptations is illustrated by incorporating the combination of CPE and RMC into another Differential Evolution-based algorithm, jDE, which is shown to yield improved results.     

Exact computational approaches to a stochastic uncapacitated single allocation p-hub center problem

The stochastic uncapacitated single allocation p-hub center problem is an extension of the deterministic version which aims to minimize the longest origin-destination path in a hub and spoke network. Considering the stochastic nature of travel times on links is important when designing a network to guarantee the quality of service measured by a maximum delivery time for a proportion of all deliveries. We propose an efficient reformulation for a stochastic p-hub center problem and develop exact solution approaches based on variable reduction and a separation algorithm. We report numerical results to show effectiveness of our new reformulations and approaches by finding global solutions of small-medium sized problems. The combination of model reformulation and a separation algorithm is particularly noteworthy in terms of computational speed.     

Multicriteria scheduling optimization using an elitist multiobjective population heuristic: the h-NSDE algorithm

In today’s manufacturing industry more than one performance criteria are considered for optimization to various degrees simultaneously. To deal with such hard competitive environments it is essential to develop appropriate multicriteria scheduling approaches. In this paper consideration is given to the problem of scheduling n independent jobs on a single machine with due dates and objective to simultaneously minimize three performance criteria namely, total weighted tardiness (TWT), maximum tardiness and maximum earliness. In the single machine scheduling literature no previous studies have been performed on test problems examining these criteria simultaneously. After positioning the problem within the relevant research field, we present a new heuristic algorithm for its solution. The developed algorithm termed the hybrid non-dominated sorting differential evolution (h-NSDE) is an extension of the author’s previous algorithm for the single-machine mono-criterion TWT problem. h-NSDE is devoted to the search for Pareto-optimal solutions. To enable the decision maker for evaluating a greater number of alternative non-dominated solutions, three multiobjective optimization approaches have been implemented and tested within the context of h-NSDE: including a weighted-sum based approach, a fuzzy-measures based approach which takes into account the interaction among the criteria as well as a Pareto-based approach. Experiments conducted on existing data set benchmarks problems show the effect of these approaches on the performance of the h-NSDE algorithm. Moreover, comparative results between h-NSDE and some of the most popular multiobjective metaheuristics including SPEA2 and NSGA-II show clear superiority for h-NSDE in terms of both solution quality and solution diversity.     

Symplectic Householder transformations for a QR-like decomposition,a geometric and algebraic approaches

The aim of this paper is to show how geometric and algebraic approaches lead us to a new symplectic elementary transformations: the 2-D symplectic Householder transformations. Their features are studied in details. Their interesting properties allow us to construct a new algorithm for computing a SR factorization. This algorithm is based only on these 2-D symplectic Householder transformations. Its new features are highlighted. The study shows that, in the symplectic case, the new algorithm is the corresponding one to the classical QR factorization algorithm, via the Householder transformations. Some numerical experiments are given.     

A branch-and-bound approach for maximum quasi-cliques

Detecting quasi-cliques in graphs is a useful tool for detecting dense clusters in graph-based data mining. Particularly in large-scale data sets that are error-prone, cliques are overly restrictive and impractical. Quasi-clique detection has been accomplished using heuristic approaches in various applications of graph-based data mining in protein interaction networks, gene co-expression networks, and telecommunication networks. Quasi-cliques are not hereditary, in the sense that every subset of a quasi-clique need not be a quasi-clique. This lack of heredity introduces interesting challenges in the development of exact algorithms to detect maximum cardinality quasi-cliques. The only exact approaches for this problem are limited to two mixed integer programming formulations that were recently proposed in the literature. The main contribution of this article is a new combinatorial branch-and-bound algorithm for the maximum quasi-clique problem.     

Solving NP-hard problems in ‘almost trees’: Vertex cover

We present an algorithm which finds a minimum vertex cover in a graph G(V, E) in time $\text{O}\text{(|V|+(}\text{a}\text{k}\text{)2}{}^{\mathrm{<mtext>k</mtext><mtext>3</mtext>}}\text{)}$, where for connected graphs G the parameter a is defined as the minimum number of edges that must be added to a tree to produce G, and k is the maximum a over all biconnected components of the graph. The algorithm combines two main approaches for coping with NP-completeness, and thereby achieves better running time than algorithms using only one of these approaches.     

Designing routes for WEEE collection: the vehicle routing problem with split loads and date windows

This paper presents an integer programming model and describes a GRASP based algorithm to solve a vehicle routing and scheduling problem for the collection of Waste of Electric and Electronic Equipment (WEEE). The difficulty of this problem arises from the fact that it is characterized by four variants of the vehicle routing problem that have been studied independently in the literature, but not together. The experimental analysis on a large set of randomly-generated instances shows the good performance of the proposed algorithm. Moreover, computational results using real data show that the method outperforms real existing approaches to reverse logistics.     

An equivalent subproblem relaxation for improving the solution of a class of transportation scheduling problems

In this paper an algorithm is presented for determining the K best paths that may contain cycles in a directed network.The basic idea behind the algorithm is quite simple. Once the best path has been determined it is excluded from the network in such a way that no new path is formed and no more paths are excluded. This step leads to an enlarged network where all the paths, but the best one, can be determined. The method is repeated until the desired paths have been computed.The proposed algorithm can be used not only for the classical K shortest paths problem but also for ranking paths under a nonlinear objective function, provided that an algorithm to determine the best path exists.Computational results are presented and comparisons with other approaches for the classical problem are made.     

Determination of the limits for multivariate rational functions

The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions.It is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with f(0,...,0)=g(0,...,0)=0.For two such polynomials f and g,we establish two necessary and sufcient conditions for the rational functionf g to have its limit 0 at the origin.Based on these theoretic results,we present an algorithm for deciding whether or not lim(x1,...,xn)→(0,...,0)f g=0,where f,g∈R[x1,...,xn]are two non-zero polynomials.The design of our algorithm involves two existing algorithms:one for computing the rational univariate representations of a complete chain of polynomials,another for catching strictly critical points in a real algebraic variety.The two algorithms are based on the well-known Wu’s method.With the aid of the computer algebraic system Maple,our algorithm has been made into a general program.In the final section of this paper,several examples are given to illustrate the efectiveness of our algorithm.     

Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces

The aim of this work is to propose implicit and explicit viscosity-like methods for finding specific common fixed points of infinite countable families of nonexpansive self-mappings in Hilbert spaces. Two numerical approaches to solving this problem are considered: an implicit anchor-like algorithm and a nonimplicit one. The considered methods appear to be of practical interests from the numerical point of view and strong convergence results are proved.     

Minimax linear programming problem

In this paper, we consider the following minimax linear programming problem: min z = max_{1 ≤ j ≤ n}{C_jX_j}, subject to Ax = g, x ≥ 0. It is well known that this problem can be transformed into a linear program by introducing n additional constraints. We note that these additional constraints can be considered implicitly by treating them as parametric upper bounds. Based on this approach we develop two algorithms: a parametric algorithm and a primal—dual algorithm. The parametric algorithm solves a linear programming problem with parametric upper bounds and the primal—dual algorithm solves a sequence of related dual feasible linear programming problems. Computation results are also presented, which indicate that both the algorithms are substantially faster than the simplex algorithm applied to the enlarged linear programming problem.     

A new algorithm for the undesirable 1-center problem on networks

Recent papers have developed efficient algorithms for the location of an undesirable (obnoxious) 1-center on general networks with n nodes and m edges. Even though the theoretical complexity of these algorithms is fine, the computational time required to get the solution can be diminished using a different model formulation and slightly improving the upper bounds. Thus, we present a new O(mn) algorithm, which is more straightforward and computationally faster than the previous ones. Computing time results comparing the former approaches with the proposed algorithm are supplied.     

Cox Point Processes Driven by Ornstein–Uhlenbeck Type Processes

The paper is devoted to the development of Cox point processes driven by nonnegative processes of Ornstein–Uhlenbeck (OU) type. Starting with multivariate temporal processes we develop formula for the cross pair correlation function. Further filtering problem is studied by means of two different approaches, either with discretization in time or through the point process densities with respect to the Poisson process. The first approach is described mainly analytically while in the second case we obtain numerical solution by means of MCMC. The Metropolis–Hastings birth–death chain for filtering can be also used when estimating the parameters of the model. In the second part we try to develop spatial and spatio-temporal Cox point processes driven by a stationary OU process. The generating functional of the point process is derived which enables evaluation of basic characteristics. Finally a simulation algorithm is given and applied.