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We consider the multiple-time-period, short-term production scheduling problem for a network of multiple open-pit mines and ports. Ore produced at each mine, in each period, is transported by rail to a set of ports and blended into products for shipping. Each port forms these blends to a specification, as stipulated in contracts with downstream customers. This problem belongs to a class of multiple producer/consumer scheduling problems in which producers are able to generate a range of products, a combination of which are required by consumers to meet specified demands. In practice, short-term schedules are formed independently at each mine, tasked with achieving a grade and quality target outlined in a medium-term plan. Because of uncertainty in the data available to a medium-term planner and the dynamics of the mining environment, such targets may not be feasible in the short term. In this paper, we present an algorithm in which the grade and quality targets assigned to each mine are iteratively adapted, ensuring the satisfaction of blending constraints at each port while generating schedules for each mine that maximise resource utilisation. Keywords: short-term open-pit mine production scheduling; hybrid optimisation; nonlinear programming History: Received June 18, 2014; accepted June 7, 2015, by Yinyu Ye, optimization. Published online in Articles in Advance January 8, 2016., 1. Introduction We consider the multiple-time-period, multiple mine planning problem (MTP-MMPP) of scheduling the production of multiple open-pit mines, across a horizon of multiple time periods, to supply several ports [...]

A nonlinear programming model is formulated in this paper to determine the optimal scheme of capacity allocation and prices over a multi-period planning horizon for a service provider in the absence and presence of uncertain competitive entry. The model is solved for constant, decreasing, and increasing price sensitivities employing a combination of analytical and numerical methods. The study highlights the importance of advance selling of service prior to its eventual consumption in the spot period and investigates the impact of uncertain competitive entry on the optimal capacity allocation policy and its related profit if the entry is more or less likely or if the rival is more or less influential. The findings of the study reveal that the conclusions drawn from a two-period model are not necessarily generalizable to a model of a multi-period planning horizon. Journal of the Operational Research Society (2010) 61, 780-789. doi: 10.1057/jors.2009.29 Published online 8 April 2009 Keywords: capacity allocation; nonlinear programming; pricing; service operations: simulation

The operational airspace of aerospace vehicles, including airplanes and unmanned aerial vehicles, is often restricted so that constraints on three-dimensional climbs, descents, and other maneuvers are necessary. In this paper, the problem of determining constrained, three-dimensional, minimum time-to-climb, and minimum fuel-to-climb trajectories for an aircraft in an airspace defined by a rectangular prism of arbitrary height is considered. The optimal control problem is transformed to a parameter optimization problem. Because a helical geometry appears to be a natural choice for climbing and descending trajectories subject to horizontal constraints, helical curves are chosen as starting trajectories. A procedure for solving the minimum time-to-climb and minimum fuel-to-climb problems by using the direct collocation and nonlinear programming methods including Chebyshev pseudospectral and Gauss pseudospectral discretization is discussed. Results obtained when different constraints are placed on airspace and state variables are presented to show their effect on the performance index. The question of 'optimality' of the numerical results is also considered.

This paper proposes a hybrid algorithm based on particle swarm optimization (PSO) for a multiobjective permutation flow shop scheduling problem, which is a typical NP-hard combinatorial optimization problem with strong engineering backgrounds. Not only does the proposed multiobjective algorithm (named MOPSO) apply the parallel evolution mechanism of PSO characterized by individual improvement, population cooperation, and competition to effectively perform exploration but it also utilizes several adaptive local search methods to perform exploitation. First, to make PSO suitable for solving scheduling problems, a ranked-order value (ROV) rule based on a random key technique to convert the continuous position values of particles to job permutations is presented. Second, a multiobjective local search based on the Nawaz--Enscore--Ham heuristic is applied to good solutions with a specified probability to enhance the exploitation ability. Third, to enrich the searching behavior and to avoid premature convergence, a multiobjective local search based on simulated annealing with multiple different neighborhoods is designed, and an adaptive meta-Lamarckian learning strategy is employed to decide which neighborhood will be used. Due to the fusion of multiple different searching operations, good solutions approximating the real Pareto front can be obtained. In addition, MOPSO adopts a random weighted linear sum function to aggregate multiple objectives to a single one for solution evaluation and for guiding the evolution process in the multiobjective sense. Due to the randomness of weights, searching direction can be enriched, and solutions with good diversity can be obtained. Simulation results and comparisons based on a variety of instances demonstrate the effectiveness, efficiency, and robustness of the proposed hybrid algorithm. Index Terms--Adaptive meta-Lamarckian learning, hybrid algorithm, local search, multiobjective optimization (MOO), Pareto front, particle swarm optimization (PSO), permutation flow shop scheduling.

The numerical optimization of continuous parameters in electrotechnical design using electromagnetic field simulation is already standard. When integer-valued variables are involved, the complexity of the optimization problem rises drastically. In this paper, we describe a new sequential surrogate optimization approach for simulation-based mixed-integer nonlinear programming (NLP) problems. We apply the method for the optimization of combined integer- and real-valued geometrical parameters of the coils of a superconductive magnet. Index Terms--Design optimization, mixed-integer nonlinear optimization, nonlinear programming, optimization methods, simulation-based optimization.

Methods to reduce location and inventory costs of distribution centers, using nonlinear integer programming model, are presented.

We give a functional generalization of fractal scaling laws applied to response problems as well as to probability distributions. We consider excitations and responses, which are functions of a given state vector. Based on scaling arguments, we derive a general nonlinear response functional scaling law, which expresses the logarithm of a response at a given state as a superposition of the values of the logarithms of the excitations at different states, Such a functional response law may result from the balance of different growth processes, characterized by variable growth rates, and it is the first order approximation of a perturbation expansion similar to the phase expansion. Our response law is a generalization of the static fractal scaling law and can be applied to the study of various problems from physics, chemistry, and biology. We consider some applications to heterogeneous and disordered kinetics, organ growth (allometry), and population genetics. Kinetics on inhomogeneous reconstructing surfaces leads to rate equations described by our nonlinear scaling law. For systems with dynamic disorder with random energy barriers, the probability density functional of the rate coefficient is also given by our scaling law. The relative growth rates of different biological organs (allometry) can be described by a similar approach. Our scaling law also emerges by studying the variation of macroscopic phenotypic variables in terms of genotypic growth rates. We study the implications of the causality principle for our theory and derive a set of generalized Kramers-Kronig relationships for the fractal scaling exponents.

A method for solving the optimization problem, using KarushuKuhnuTucker model, is presented.

This paper presents new characterizations of uniform global asymptotic stability for nonlinear and time-varying discrete-time systems. Under mild assumptions, it is shown that weak zero-state detectability is equivalent to uniform global asymptotic stability for globally uniformly stable systems. By employing the notion of reduced limiting systems, another characterization of uniform global asymptotic stability is proposed on the basis of the detectability for the reduced limiting systems associated with the original system. As a by-product, we derive a generalized, discrete-time version of the well-known Krasovskii-LaSalle theorem for general time-varying, not necessarily periodic, systems. Furthermore, we apply the obtained stability results to analyze uniform asymptotic stability of cascaded time-varying systems, and show that some technical assumptions in recent papers can be relaxed. Through a practical application, it is shown that our results play a similar role to the classic LaSalle invariance principle in guaranteeing attractivity, noting that reduced limiting systems are used instead of the original system. To validate the conceptual characterizations, we study the problem of sampled-data stabilization for the benchmark example of nonholonomic mobile robots via the exact discrete-time model rather than approximate models. This case study also reveals that in general, sampled-data systems may become non-periodic even though their original continuous-time system is periodic. A novel sampled-data stabilizer design is proposed using the new stability results and is supported via simulation results. Index Terms--Cascaded systems, discrete-time systems, mobile robots, reduced limiting systems, sampled-data controllers, uniform global asymptotic stability, weak zero-state detectability.

A technique to perform unsupervised data classification or clustering is developed, using modified fuzzy-c means algorithm. The new clustering method can automatically recognize multidimensional clusters of non-convex shape.

Role of economies of scale in object-oriented software component is analyzed using data envelopment analysis and non-linear regression.

A nonlinear programming model for planning municipal solid waste management system in Hamilton is presented.

Incomplete data, due to missing observations or interval measurement of variables, usually cause parameters of interest in applications to be unidentified except under untestable and often controversial assumptions. However, it is often possible to identify sharp bounds on parameters without making untestable assumptions about the process through which data become incomplete. The bounds contain all logically possible values of the parameters and can be estimated consistently by replacing the population distribution of the data with the empirical distribution. This is straightforward in some circumstances but computationally burdensome in others. This paper describes the general problem and presents an empirical illustration. JEL classification: C1; C4; C6 Keywords: Bounds; Missing data; Non-linear programming

The problem of redundancy allocations and nonconvex nonlinear programming problems are addressed.

A study examines the use of nonlinear programming for quality control in batch manufacturing process.

A nonlinear programming solution for workforce scheduling problem related to diverging employee productivity is evaluated.

A mathematical model for minimizing the cash-out problems and penalties of a natural gas shipper is presented. The model uses nonlinear and bilevel programming.

The assembly-type supply chain system is modeled as mixed-integer nonlinear programming problem (MINLP) and controlled using kanban chain mechanism. The problem is divided into small problems and each small problem is solved using branch-and-bound technique.

Optimization of functions that depend on large-scale data via a linear transformation of rank two is studied. An algorithm is presented, which finds the global solution with polynomial complexity in the worst case u under mild assumptions. However the critical points could be controlled with the same effort. Researchers arrive at a linear type algorithm when dealing with important subclasses of objectives including the linear-fractional, and the quadratic case.

Application of ratio objectives to explore profits of firms in different capacity expansions with the help of no-linear programming is analyzed.

This paper studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization. Using a new parameter separation technique and the tool of adding a power integrator, we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation. In contrast to the existing results in the literature, a key feature of our adaptive regulator is its minimum-order property, namely, no matter how big the number of unknown parameters is, the order of the dynamic compensator is identical to one, and is therefore minimal. As a consequence, global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one-dimensional adaptive controllers, without imposing any extra (e.g., convex/concave) conditions on the unknown parameters. Index Terms--Adding a power integrator, global adaptive stabilization, nonlinear parameterization, nonlinear systems with uncontrollable linearization, smooth feedback.

With the recent introduction of multislice computed tomography (MCT) scanners, image reconstruction techniques for multislice helical CT has become an active research topic. The majority of the previously proposed algorithms limits the plane-of-reconstruction (POR) to a flat plane (either tilted or nontilted). Additionally, linear interpolation is typically employed to estimate the projections at the POR from the measured conjugate samples. In this paper, we propose a new helical reconstruction algorithm for multislice helical CT. To avoid discontinuity in the helical weighting function, a double cone-shaped region is selected as the POR. All available projection samples that are located within a predefined distance from the POR are utilized to estimate a set of projections at the POR. In addition, a weighted interpolation-extrapolation approach is proposed to replace linear interpolation. The proposed scheme has the advantage of an improved slice sensitivity profile due to a better preservation of high-frequency contents present in the projection data set. It also exhibits better performance in terms of helical artifact suppression. Phantom experiments have been conducted to demonstrate the efficacy of our approach.

This paper is concerned with the membrane shell analysis of filament overwound toroidal pressure vessels and optimum design of such pressure vessels using the results of the analysis by means of mathematical nonlinear programming. The nature of the coupling between overwind and linear has been considered based on two extreme idealizations. In the first, the overwind is rigidly coupled with the liner, so that the two deform together in the meridional direction as the vessel dilates. In the second, the overwind is free to slide relative to the linear, but the overall elongations of the two around a meridian are identical. Optimized designs with the two idealizations show only minor differences, and it is concluded that either approximation is satisfactory for the purposes of vessel design. Aspects taken into account are the intrinsic overwind thickness variation arising from the winding process and the effects of fiber pre-tension. Pre-tension can be used not only to defer the onset of yielding, but also to achieve a favorable in-plane stress ratio which minimizes the von Mises equivalent stress in the metal liner. Aramid fibers are the most appropriate fibers to be used for the overwind in this type of application. The quantity of fiber required is determined by both its short-term strength and its long-term stress rupture characteristics. An optimization procedure for the design of such vessels, taking all these factors into account, has been established. The stress distributions in the vessels designed in this way have been examined and discussed through the examples. A design which gives due consideration of possible mechanical damage to the surface of the overwind has also been addressed. [DOI: 10.1115/1.1430671]

This brief presents a novel algorithm for optimizing the design of infinite-impulse response (IIR) switched-capacitor (SC) decimators. It is implemented with a computer-assisted iterative methodology to achieve minimum capacitance spread and usually leading also to the minimization of the total capacitor area, while considering scaling for maximum signal handling capability. A linear/nonlinear programming method is adopted for optimum adjustment of the capacitance values, within a specific decimator structure and a finite number of iterations. Several examples of automatic and optimum design of second-order IIR SC decimators are presented, together with a comparison against previous designs, obtained for the same circuits through the use of traditional methods. Index Terms--Automated optimum design, infinite-impulse response (IIR) switched-capacitor (SC) decimator, linear/nonlinear programming.

Byline: O. Diekmann (1), M. Gyllenberg (2), H. Huang (3), M. Kirkilionis (4), J.A.J. Metz (5), H.R. Thieme (7) Keywords: Key words or phrases: Population dynamics -- Physiological structure -- Nonlinear feedback via the environment -- Deterministic at population level -- Cannibalism Abstract: This paper is as much about a certain modelling methodology, as it is about the constructive definition of future population states from a description of individual behaviour and an initial population state. The key idea is to build a nonlinear model in two steps, by explicitly introducing the environmental condition via the requirement that individuals are independent from one another (and hence equations are linear) when this condition is prescribed as a function of time. A linear physiologically structured population model is defined by two rules, one for reproduction and one for development and survival, both depending on the initial individual state and the prevailing environmental condition. In Part I we showed how one can constructively define future population state operators from these two ingredients. A nonlinear model is a linear model together with a feedback law that describes how the environmental condition at any particular time depends on the population size and composition at that time. When applied to the solution of the linear problem, the feedback law yields a fixed point problem. This we solve constructively by means of the contraction mapping principle, for any given initial population state. Using subsequently this fixed point as input in the linear population model, we obtain a population semiflow. We then say that we solved the nonlinear problem. For models formulated as first order partial differential equations with nonlocal boundary conditions our approach amounts to deriving an integral equation by integrating along characteristics. This integral equation is then solved by a successive approximation procedure. By formalizing the biological ingredients directly as integral kernels and using these to construct the semigroup of population state transition operators we (a) can do with rather minimal regularity conditions on the coefficients (i.e., on individual behaviour), (b) do not have to worry about regularity properties of solutions to guarantee that we really have constructed a solution of a pde. The paper is organized in a top-down spirit: We describe a general abstract setting first and then specialise, while becoming more technical. The results are not restricted to a single population but also cover the interaction (including predation) of several structured (and unstructured) populations. Author Affiliation: (1) Department of Mathematics, University of Utrecht, P.O. Box 80010, 3580 TA Utrecht, The Netherlands, NL (2) Department of Mathematics, University of Turku, 20014 Turku, Finland. e-mail: matsgyl@utu.fi, FI (3) Department of Mathematics, Beijing Normal University, Beijing 100875, P.R. of China, CN (4) University of Heidelberg, Interdisziplinaeres Inst. f. wiss. Rechnen, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany, DE (5) Institute for Evolutionary and Ecological Sciences, Leiden University, Kaiserstraat 63, NL-2311 GP Leiden, The Netherlands, NL (6) Adaptive Dynamics Network, IIASA, A-2361 Laxenburg, Austria, AT (7) Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA, US Article note: Received: 28 march 2000/Revised version: 18 October 2000APPublished online: 17 July 2001

Optimization-based models for simulation of tile drainage systems are formulated and solved with a finite-difference approximated Richard's equation as an embedded constraint. The solution methodology minimizes the sum of absolute violations of the discretized variably saturated porous media flow equations. The optimal design minimizes the sum of the pressure heads to obtain optimal drain locations and discharges for a given lateral spacing. The projected augmented Lagrangian method of nonlinear programming is used to solve the optimization models. The performance of the simulation is verified using the steady-state square embankment drainage problem. Thereafter, the simulation and design models are solved for a hypothetical tile drainage system. The results demonstrate the capability of the models.

Byline: I-Lok Chang (1), P.A.V.B. Swamy (2), Charles Hallahan (3), George S. Tavlas (4) Keywords: realities of econometric model building; causality; random coefficient models; nonlinear programming Abstract: This paper states four realities of econometric model buildingand shows that an econometric model can be causal only if theinterpretations given to its coefficients are consistent withthese realities. A numerically stable algorithm for estimatingsuch a model subject to equality and inequality constraints onthe model parameters is presented. This algorithm is designed insuch a way that it can be applied even when the matrix ofobservations on the model's independent variables and thecovariance matrix of the model's errors are deficient in rank. Author Affiliation: (1) Department of Mathematics and Statistics, TheAmerican University, Washington, DC, 20016, U.S.A. (2) Office of the Comptroller of theCurrency, Bank Research Unit, Washington, DC, 20219, U.S.A. (3) United States Department ofAgriculture, Economics Research Service, Washington, DC, 20005, U.S.A. (4) Bank of Greece, Athens, Greece and International MonetaryFund, Washington, DC, 20431, U.S.A. Article History: Registration Date: 15/10/2004

Byline: Luis H.R. Alvarez (1) Abstract: We consider the determination of the harvesting strategy maximizing the present expected value of the cumulative yield from the present up to extinction. By relying on a combination of stochastic calculus, ordinary nonlinear programming, and the classical theory of diffusions, we show that if the underlying population evolves according to a logistic diffusion subject to a general diffusion coefficient, then there is a single threshold density at which harvesting should be initiated in a singular fashion. We derive the condition which uniquely determines the threshold and show that harvesting should be initiated only when the option value of further preserving another individual falls below its opportunity cost. In this way, we present a real option interpretation of rational harvesting planning. We also consider the comparative static properties of the value of the harvesting opportunity and state a set of usually satisfied conditions under which increased stochastic fluctuations (demographic or environmental) decrease the expected cumulative yield from harvesting and increase the optimal harvesting threshold, thus postponing the rational exercise of the irreversible harvesting decision. Author Affiliation: (1) Institute of Applied Mathematics, University of Turku, FIN-20014 Turku, Finland. e-mail: alvarez@utu.fi, FI Article note: Received: 19 January 1999/Revised version: 2 July 1999/Published online: 16 February 2000

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems, one of which is stable rather than asymptotically stable. A new cross-term construction in the Lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition. This method is instrumental in the global stabilization of feedforward systems, and new stabilization results are derived from the generalized construction. Index Terms - Forwarding, global stabilization, nonlinear systems.

In general, nonlinear output feedback dynamic games are infinite-dimensional. This paper treats a class of minimax games when the nonlinearities enter the dynamics of the unobservable states. An information state approach is introduced to recast these games as one of full information in infinite dimensions. Explicit solutions of the first-order partial differential information state equation are derived in terms of a finite-number of sufficient statistics. When the nonlinearities are sector bounded, suboptimal finite-dimensional strategies are derived. Index Terms - Information states, minimax games, output feedback.

This paper deals with higher order approximation for discrete-time systems. It is shown that approximated feedback linearization at the second order can always be achieved under feedback compensation based on an approximated observer. An example is given in order to illustrate the control design and the efficiency of the proposed method. Index Terms - Dynamic state feedback, nonlinear discrete-time systems, nonlinear observer, quadratic approximation.

A particular polynomial is introduced in this paper which can be used to determine under what conditions a typical class of discrete-time nonlinear systems with uncertainties in both parameters and noises is not stabilizable by feedback, thus demonstrating the fundamental limitations of discrete-time adaptive nonlinear control. As a consequence, it is shown that for nonlinear systems with unknown parameters and noises, the systems may indeed be nonstabilizable, in general, whenever the usual linear growth condition is relaxed and the number of unknown parameters is large, even though the corresponding noise-free systems are globally stabilizable. Index Terms - Adaptive control, discrete-time, global stabilizability, nonlinear dynamics, stochastic systems.

Adaptive control of a class of discrete-time parametric-strict-feedback nonlinear systems with additive white noises is considered in this paper. The control law is designed based on weighted least squares (WLS) algorithms and on recursive adaptive predictors. Global stability and tracking error bounds are established for the closed-loop systems. Index Terms - Adaptive nonlinear control, discrete time, global stability, prediction, stochastic systems.

This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable. Index Terms - Controllability, mechanical systems, nonlinear control, stabilizability, underactuated.

This study proposes a design methodology for determining configurations of subambient pressure shaped rail sliders by using a nonlinear programming technique in order to meet the desired flying characteristics over the entire recording band. The desired flying characteristics considered in this study are to minimize the variation in flying height from a target value, to keep the pitch angle within a suitable range, and to ensure that the outside rail flies lower than the inside rail even with the roll distribution due to manufacturing process. The design variables selected are recess depth, geometry of the air bearing surface, and pivot location in the transverse direction of the slider. The method of feasible directions in Automated Design Synthesis (ADS) is utilized to automatically find the optimum design variables which simultaneously meet all the desired flying characteristics. To validate the suggested design methodology, a computer program is developed and applied to a 30 percent/15 nm twin rail slider and a 30 percent/15 nm tri-rail slider. Simulation results for both sliders demonstrated the effectiveness of the proposed design methodology by showing that the flying characteristics of the optimally designed sliders are enhanced in comparison with those of the initial ones.

Byline: Frances X. Frei (1), Patrick T. Harker (2) Keywords: Data envelopment analysis; Productivity; Nonlinear programming Abstract: Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception in 1978. The methodology behind the classical DEA, the oriented method, is to hold inputs (outputs) constant and to determine how much of an improvement in the output (input) dimensions is necessary in order to become efficient. This paper extends this methodology in two substantive ways. First, a method is developed that determines the least-norm projection from an inefficient DMU to the efficient frontier in both the input and output space simultaneously, and second, introduces the notion of the 'observable' frontier and its subsequent projection. The observable frontier is the portion of the frontier that has been experienced by other DMUs (or convex combinations of such) and thus, the projection onto this portion of the frontier guarantees a recommendation that has already been demonstrated by an existing DMU or a convex combination of existing DMUs. A numerical example is used to illustrate the importance of these two methodological extensions. Author Affiliation: (1) Harvard Business School, Harvard University, Boston, MA, 02163 (2) Department of Operations and Information Management, University of Pennsylvania, Philadelphia, PA, 19104-6366 Article History: Registration Date: 19/10/2004

A 2-dimensional shape optimization method for permanent magnet configurations, which is based on a combination of non-linear programming and field analysis with a complex representation technique of the 2-dimensional magnetic fields, has been developed. As a typical problem example, computational results for a segmented dipole magnet are presented. The results show that the objective function values are reduced significantly and a very uniform dipole field is obtained at the magnet center. The validity of the method is also discussed by comparing with the theoretically presumed solution. Index terms - Shape optimization, permanent magnet, non-linear programming, complex function