Set Of Admissible Solutions Research Articles

Scheduling the Repetitive Production: Constraints Propagation Approach

A computer-aided method for production planning in a repetItIve manufacturing system which allows for estimating the possibility of processing work orders in due time is presented. The approach proposed in this paper consists in defining sufficient conditions to filter all solutions and providing a set of admissible solutions for both the client and the producer. Upon discussing constraint propagation and sequencing procedures, the paper presents a computer program called the System of Production Order Validation (SWZ) that has been developed based on the presented methodology. Finally, an example illustrating our approach is presented.

Optimization Problem on Permutations with Linear-Fractional Objective Function: Properties of the Set of Admissible Solutions

We consider an optimization problem on permutations with a linear-fractional objective function. We investigate the properties of the domain of admissible solutions of the problem.

On the development of a kinetic model for a gas with allowance for nonequilibrium processes

The problems of developing a kinetic model of a medium (gas and plasma) are considered from the viewpoint of choice of the most important physicochemical processes. For the problem of a direct shock wave propagating in the atmosphere, kinetic models are selected with allowance for the error in specifying reaction-rate constants. The investigation was performed using an automated system that incorporates structured bases of physicochemical data, a generator of kinetic equations, a complex of programs for direct calculation, and program modules for determining, from a set of admissible solutions, the one satisfying specified criteria.

Modeling of multiple mobile manipulators handling a common deformable object

The dynamic equations of motion for a system of multiple mobile manipulators carrying a common deformable object are developed. The derived centralized model is based on Kane's approach to dynamics. The imposed kinematic nonholonomic constraints are included and incorporated into the dynamics. It is pointed out, however, that these kinematic constraints are only necessary, and they only become sufficient to impose nonholonomic motion when accompanied by the dynamic counterparts. Sufficient conditions for avoiding tipping over by the mechanisms are also provided. The whole set of constraint equations is analyzed and useful properties for the set of admissible solutions for the ground reaction forces are obtained. The deformable object under manipulation is modeled and the simplest approximating grid structure is indicated. © 1998 John Wiley & Sons, Inc.

An admissible solution approach to inverse electrocardiography.

The goal of the inverse problem of electrocardiography is noninvasive discrimination and characterization of normal/abnormal cardiac electrical activity from measurements of body surface potentials. Smoothing and attenuation in the torso volume conductor cause the problem to be ill posed. Standard regularized solutions employ an a priori constraint to achieve reliability and may be biased by the constraint chosen as well as the regularization parameter used to weight it. In this paper, we describe an approach that reformulates this inverse problem as the search for a solution that is a member of an admissible solution set; admissibility is defined in terms of the available constraints. In principle, this approach can utilize as many constraints as may be available, unlike standard techniques which do not easily permit the use of multiple constraints. No regularization parameter is required; instead, we need to choose the nature and size of the constraint sets. Constraints described include several spatial constraints, weighted constraints, and temporal constraints. We describe a solution approach based on iterative convex optimization, and the algorithm--the ellipsoid algorithm--which we have used. Accuracy and feasibility of the method are illustrated with simulation results using dipole sources and measured epicardial potentials.

Lexicographic optima in the multicriteria discrete optimization problem

It is shown that any lexicographic optimum in vector optimization problems on a finite set of admissible solutions can be obtained by a classical technique, the linear convolution of criteria.

Control system synthesis through inductive learning of Boolean concepts

In control, learning is often used to identify a single controller satisfying a particular performance measure. In certain cases, however, it is desirable to identify the set of all controllers which ensure that the controlled plant satisfies a control property such as Lyapunov stability, robust stability, or robust performance. A set of procedures identifying such sets of admissible solutions can be devised using Boolean concept learning algorithms. This type of learning procedure is applicable to computational learning. The objective of this article is to provide some examples illustrating how Boolean concept learning can be used in control systems. The first example examined in this article uses concept learning to identify the set of stabilizing controllers for certain classes of linear time-invariant plants. Another example illustrates the use of concept learning in the identification of discrete event system (DES) controllers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Ambiguities in AVO inversion of reflections from a gas‐sand

We examine the reflections from a thick sand layer embedded in shales deposited in an open marine environment of Miocene age. Borehole data indicate that the sand bed is gas saturated. Making the assumptions of single interface reflections, plane‐wave propagation in elastic and isotropic media, and correct amplitude recovery of the actual seismic data, we try to invert the amplitude variation with offset (AVO) response for the compressional velocity [Formula: see text], shear velocity [Formula: see text], and density [Formula: see text] of the gas‐sand layer, knowing the parameters of the upper layer and the calibration constant. The actual reflections reach incidence angles up to 54 degrees at the farthest offset. Notwithstanding the large range of incidence angles, the outcomes of the inversion are ambiguous for we find many solutions that fit equally well, in a least‐squares sense, the observed AVO response. We present the locus of the solutions as curves in compressional velocity [Formula: see text], shear velocity [Formula: see text], and density [Formula: see text] space. To gain a better understanding of the results, we also perform the same inversion experiment on synthetic AVO data derived from the borehole information. We find that when inverting the AVO response in the same range of incidence angles as in the real data case, the exact solution is found whichever starting point we choose; that is, we have no ambiguity. However, if we limit the incidence angle range, e.g., to 15 degrees, the invention is no longer able to find a unique solution and the set of admissible solutions defines regular curves in [Formula: see text], [Formula: see text], [Formula: see text] space. We infer that residual noise in the recorded data is responsible for the ambiguities of the solutions, and that because of numerical noise, a wide range of incidence angle is required to obtain a unique solution even in noise‐free synthetic data.

Extensions of optimal partition problems for spaces with measures

whose value we denote by c o . The fundamental difficulty presented by the indicated problem is that there are no linear or topological structures on the set D(S, ~). In the present paper we present a procedure for imbedding the set of admissible solutions to problem (i) in certain linear normed spaces, and subsequently compactifying the set of generalized solutions in the weak topology. Various examples of extremal problems in which the quality criterion is determined by a set-theoretic function on a space with a measure were also considered in [1, 2].

Method of multiobjective optimization for imprecise objectives

AbstractA method of multiobjective optimization for imprecise objectives is presented. The problem consisted in a minimization of the distance between the set of admissible solutions and an ideal point. Applicability of the method is illustrated by the choice of best impeller from a group of seven different types tested. The optimum process conditions were selected, taking as optimization objective the maximization of kLa and minimization of PG.

Modeling RNA secondary structures II. the geometric structural solution for tRNA

The set of admissible solutions of the configuration space of tRNA molecules is obtained after incorporating further restrictions based on the principles of local stability and homology as well as on geometric and energetic considerations.

Optimal periodic non-boundary control for a tubular reactor: A performance improvement criterion

The optimal periodic non-boundary control problem for a tubular chemical reactor depicted by first-order partial differential equations is interpreted as an optimal control problem for a system governed by an initial-valued abstract differential equation. A sufficient condition for the existence of a time-dependent periodic control superior to the unique time-invariant control is derived with the help of an analysis of a second variation of the objective function on the set of admissible solutions. The use of the condition is explained on a simple example.

Harmonic functions satisfying a radiation boundary condition

A conformal method is developed for generating solutions of Laplace's equation which satisfy the radiation boundary condition at a smooth convoluted surface, such as the membrane of a cell which is steadily absorbing a diffusing substance. It is shown that almost all solutions which are analytic in the neighborhood of the surface have one or more branch points somewhere outside the surface, and are therefore not admissible in general; this feature presents a difficulty for both analytical and numerical methods of solution. In two-dimensional problems the difficulty can be overcome by the superposition of solutions in two sheets of the complex plane, and a complete set of admissible solutions is obtained in this way. The method is illustrated by its application to corrugated planes and cylinders, where exact solutions, free of singularities, are obtained in terms of elliptic functions. It is shown that methods of obtaining radiation surfaces from analytical solutions may encounter analogous difficulties. An extension of the conformal method to three-dimensional problems is given and illustrated.

Weakly determinate problems of Boolean linear programming with a partially specified set of admissible solutions

Weakly determinate problems of Boolean programming comprise those in which the objective function or set of admissible solutions is partially but not completely specified. Using the properties of the monotonic Boolean functions which correspond to the constraints of the Boolean linear programming problems, an approach is given for constructing a complete definition of the partially specified set of admissible solutions, and for finding the optimal solutions in the completed definition. To check that the solutions obtained are admissible, a recognition algorithm for the class of admissible solutions is employed.

Construction of optimal solution procedures for operator equations

A method is proposed for constructing linear optimal (in the minimax sense) solution procedures for linear operator equations of the first kind with random errors in the initial data. The analytical form of an optimal solution procedure for an arbitrary absolutely convex set of admissible solutions (a well-posed set) is described, as well as a method of constructing this set.

Control problems for parabolic and hyperbolic equations via the theory ofG and Γ convergence

A sequence of optimal control problems for systems governed by PDE'sis considered. The parameter (index of an element of the sequence) appears in the cost functionals which have integral form, as well as in the state equations which are of parabolic or hyperbolic type. It is proved that, under some Γ-convergence of the cost functionals and some Γ convergence of the indicator functions of sets of admissible solutions, the optimal solutions exist and converge to an optimal solution of the limit problem.

Structural identifiability of "first-pass" models.

This paper considers the structural identifiability of two compartmental models classically used to describe the pharmacokinetics of drugs orally administered and transformed into a metabolite with a first-pass effect at the hepatic level. The simplest model proves not to be globally identifiable even when plasma and urinary measurements of the drug and metabolite concentrations are made. It admits two sets of admissible solutions, so that a priori knowledge must be introduced to distinguish them. The more complex model appears globally identifiable when blood and urine measurements are made.

The minimax approach to stochastic programming and an illustrative application

The minimax approach to stochastic programming with recourse deals with the case of incomplete knowledge of the distribution F of the random coefficients. It leads to the deterministic program [ILM0001] where x is a given set of admissible solutions, φis a recourse function and f is a given set of distributions. To express the objective function of (*) in a form suitable for further computation, general results on the moment problem can be used.In section 1, the main ideas are briefly surveyed. Subsequently, the method is applied to (*) in section 2. It is shown how the results can be used both to draw conclusions on robustness of the optimal value of the given stochastic program with respect to the set of distributions considered, and to study sensitivity of the optimal solution with respect to a specified distribution. In section 3, an application to a stochastic model of a water resource system with incomplete knowledge about the distribution of the random demand is suggested

Stability in stochastic programming with recourse-estimated parameters

In this paper, stability of the optimal solution of stochastic programs with recourse with respect to parameters of the given distribution of random coefficients is studied. Provided that the set of admissible solutions is defined by equality constraints only, asymptotical normality of the optimal solution follows by standard methods. If nonnegativity constraints are taken into account the problem is solved under assumption of strict complementarity known from the theory of nonlinear programming (Theorem 1). The general results are applied to the simple recourse problem with random right-hand sides under various assumptions on the underlying distribution (Theorems 2–4).

An inverse problem for a semilinear parabolic equation

In this paper we are concerned with the study of the stability of an unknown non-linear term in a parabolic equation in dependence on over specified Cauchy-Dirichlet data prescribed on the parabolic boundary of the open set under consideration. Since, in general, the dependence of the nonlinear term upon the data is not stable with respect to L∞ -metrics, we show how a Holder continuity may be restored under mild restrictions for the set of admissible solutions.