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This paper introduces a general area-level model-based formulation to small area estimation based on generalized linear mixed models. By applying an optimization algorithm to the Laplace approximation of the likelihood, the maximum likelihood estimators of the model parameters are calculated. Empirical best predictors of small area quantities are derived and the corresponding mean squared errors are estimated by parametric bootstrap. Some simulation experiments are carried out to study the behavior of the fitting algorithm, the small area predictors and the estimators of the mean squared errors. By using data of the Spanish living condition survey of 2008, an application to the estimation of average annual net incomes in Spanish provinces by sex is given. [ABSTRACT FROM AUTHOR]

Optimisation of automatic tool changer (ATC) indexing problem, where cutting tools are allocated to the stations on a turret magazine of a CNC machine, is one of the challenging problems in machining. The aim of the problem is to minimise the total indexing time of ATC. This problem becomes even more challenging if duplication of cutting tools is allowed and a bidirectional ATC is used. The problem has a unique feature which has not been stressed yet by other researchers, that is, although ATC indexing (master problem) is the main optimisation problem, objective function evaluation of this problem is a standalone optimisation problem (sub problem) indeed. Although an approximation algorithm does not guarantee optimality for the master problem, the subproblem must be solved optimally; otherwise, deficiencies arising from ill-defined objective function might be encountered. Considering this interesting future, a novel methodology, which employs a shortest path algorithm, is developed. Thus, the subproblem of this complicated problem can be optimally solved. Moreover, two metaheuristics, based on threshold accepting and descent first improvement greedy methodologies, are proposed for generating efficient solutions. Finally, several benchmarking instances are generated and solved to test the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonsmooth vector optimization problem involving locally Lipschitz generalized approximate convex functions and find some relations between approximate convexity and generalized approximate convexity. We establish relationships between vector variational inequalities and nonsmooth vector optimization problem using the generalized approximate convexity as a tool. [ABSTRACT FROM AUTHOR]

The clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem using the squared regression error function. The objective function in this problem is represented as a difference of convex functions. Optimality conditions are derived, and an algorithm is designed based on such a representation. An incremental approach is proposed to generate starting solutions. The algorithm is tested on small to large data sets. [ABSTRACT FROM AUTHOR]

When faced with the mathematical modeling of any engineering system, whether for design, performance assessment, optimization, or control, the engineer has to determine the level of accuracy versus the simplicity of the mathematical formulation. Although it is universally accepted that the more complex the formulation, the more accurate the results will be, these usually come at the expense of larger CPU times, a substantial amount of computer resources, and are generally limited by the capacity of computers and computing power, which most times precludes their use in favor of simpler models. Many times, however, engineers do not realize the potential risk that oversimplification of a problem generates in terms of accuracy of the results; that is, the model solution does not resemble the system behavior. Through a demonstrative example, the present study addresses the issue of oversimplification of the resulting mathematical model and the corresponding accuracy of its solution. After constructing three sets of models of the physical system, each with a different level of detail, the solutions are then compared to experimental data. The results show that the accuracy of the numerical approximation depends directly on the level of complexity of the mathematical model used, and that oversimplification may result in up to a ninefold degradation of the results. In addition, minor changes in the inlet boundary condition and geometry result in significant changes in the flow pattern, up to a fivefold difference between different models in the recirculation bubble relative error. This information is fundamental for engineering professionals to consider during the modeling process in applications. [ABSTRACT FROM AUTHOR]

This article presents a novel method to compute averaged Hausdorff () approximations of the Pareto fronts of multi-objective optimization problems. The underlying idea is to utilize directly the scalar optimization problem that is induced by theperformance indicator. This method can be viewed as a certain set based scalarization approach and can be addressed both by mathematical programming techniques and evolutionary algorithms (EAs). In this work, the focus is on the latter where a first single objective EA for suchapproximations is proposed. Finally, the strength of the novel approach is demonstrated on some bi-objective benchmark problems with different shapes of the Pareto front. [ABSTRACT FROM PUBLISHER]

In this article, we use the method of finite-dimensional approximations to derive second-order necessary optimality conditions for singular Pontryagin local minimizers for an unconstrained nonlinear Mayer problem. [ABSTRACT FROM AUTHOR]

In this article, we present a primal-dual 3-approximation algorithm for the stochastic priority facility location problem. Combined with greedy augmentation procedure, such performance factor is further improved to 1.8526. [ABSTRACT FROM PUBLISHER]

This paper presents an algorithm for assigning flight departure delays under probabilistic airport capacity. The algorithm dynamically adapts to weather forecasts by revising, if necessary, departure delays. The proposed algorithm leverages state-of-the-art optimization techniques that have appeared in recent literature. As a case study, the algorithm is applied to assigning departure delays to flights scheduled to arrive at San Francisco International Airport in the presence of uncertainty in the fog clearance time. The cumulative distribution function of fog clearance time was estimated from historical data. Using daily weather forecasts to update the probabilities of fog clearance times resulted in improvement of the algorithm's performance. Experimental results also indicate that if the proposed algorithm is applied to assign ground delays to flights inbound at San Francisco International airport, overall delays could be reduced up to 25% compared to current level. [ABSTRACT FROM PUBLISHER]

We consider the problem of approximating a sequence of data points with a 'nearly-isotonic,' or nearly-monotone function. This is formulated as a convex optimization problem that yields a family of solutions, with one extreme member being the standard isotonic regression fit. We devise a simple algorithm to solve for the path of solutions, which can be viewed as a modified version of the well-known pool adjacent violators algorithm, and computes the entire path in O( n log n) operations ( n being the number of data points). In practice, the intermediate fits can be used to examine the assumption of monotonicity. Nearly-isotonic regression admits a nice property in terms of its degrees of freedom: at any point along the path, the number of joined pieces in the solution is an unbiased estimate of its degrees of freedom. We also extend the ideas to provide 'nearly-convex' approximations. [ABSTRACT FROM AUTHOR]

The generalized robust colouring problem (GRCP) deals with a robust colouring for a given graph with a fixed number of colours, not necessarily the chromatic number and considers the distance between colours as the penalization of complementary edges. This problem provides a way to solve timetabling problems that consider 'event spread constraints' such as 'there must be at least d days between two events'. Because this problem is NP-hard, a heuristic approach is necessary to produce good solutions in a reasonable amount of time for large instances. In this work a greedy randomized adaptive search procedure (GRASP) is proposed to solve GRCP, which was used in instances to schedule course lectures requiring from 30 to 120 h per week in total, in which the bound of the optimal solution is reached in almost every instance. [ABSTRACT FROM AUTHOR]

Common deficiencies found in previous studies that modelled quay crane scheduling with non-crossing constraints (QCSNC) in port container terminals are identified. Remedies for the problems are proposed to prevent the occurrence of unrealistic optimal solutions for QCSNC. Additionally, two approximation schemes for QCSNC are studied. The first one is called the best partition (BP) method, which can be solved by dynamic programming (DP) with time complexity of O(mn2). A more efficient algorithm is designed to improve the original DP by adopting binary search. Next, based on BP and an exact algorithm for QCSNC (with pseudo-polynomial computational time), the second approximation scheme, called the enhanced best partition (EBP) method, is proposed to achieve a better estimation of the optimal makespan for QCSNC. The results of numerical experiments show that EBP is an effective approximation scheme for the problem of QCSNC. [ABSTRACT FROM AUTHOR]

Fractional approximations ofeand π are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research. [ABSTRACT FROM AUTHOR]