Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

Genetic algorithms for continuous optimization problems - a concept of parameter-space size adjustment

The concept of parameter-space size adjustment is pn,posed in order to enable successful application of genetic algorithms to continuous optimization problems. Performance of genetic algorithms with six different combinations of selection and reproduction mechanisms, with and without parameter-space size adjustment, were severely tested on eleven multiminima test functions. An algorithm with the best performance was employed for the determination of the model parameters of the optical constants of Pt, Ni and Cr.

The cross-entropy method for continuous multi-extremal optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

A cognitive genetic algorithm for power distribution system planning

Power systems are large scale nonlinear systems with high complexity. Various optimization techniques and expert systems have been used in power system planning. However, there are always some factors that cannot be quantified, modeled, or even expressed by expert systems. Moreover, such planning problems are often large scale optimization problems. Although computational algorithms that are capable of handling large dimensional problems can be used, the computational costs are still very high. To solve these problems, in this paper, investigation is made to explore the efficiency and effectiveness of combining mathematic algorithms with human intelligence. It had been discovered that humans can join the decision making progresses by cognitive feedback. Based on cognitive feedback and genetic algorithm, a new algorithm called cognitive genetic algorithm is presented. This algorithm can clarify and extract human's cognition. As an important application of this cognitive genetic algorithm, a practical decision method for power distribution system planning is proposed. By using this decision method, the optimal results that satisfy human expertise can be obtained and the limitations of human experts can be minimized in the mean time.

Asymmetric MRI magnet design using a hybrid numerical method

This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. (C) 1999 Academic Press.

A hybrid, inverse approach to the design of magnetic resonance imaging magnets

This paper describes a hybrid numerical method of an inverse approach to the design of compact magnetic resonance imaging magnets. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first, kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. The emphasis of this work is on the optimal design of short MRI magnets. Details of the hybrid numerical model are presented, and the model is used to investigate compact, symmetric MRI magnets as well as asymmetric magnets. The results highlight that the method can be used to obtain a compact MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1 m in length, significantly shorter than current designs. Viable asymmetric magnet designs, in which the edge of the homogeneous region is very close to one end of the magnet system are also presented. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. (C) 2000 American Association of Physicists in Medicine. [S0094-2405(00)00303-5].

Genetic algorithms for design of liquid retaining structure

In this paper, genetic algorithm (GA) is applied to the optimum design of reinforced concrete liquid retaining structures, which comprise three discrete design variables, including slab thickness, reinforcement diameter and reinforcement spacing. GA, being a search technique based on the mechanics of natural genetics, couples a Darwinian survival-of-the-fittest principle with a random yet structured information exchange amongst a population of artificial chromosomes. As a first step, a penalty-based strategy is entailed to transform the constrained design problem into an unconstrained problem, which is appropriate for GA application. A numerical example is then used to demonstrate strength and capability of the GA in this domain problem. It is shown that, only after the exploration of a minute portion of the search space, near-optimal solutions are obtained at an extremely converging speed. The method can be extended to application of even more complex optimization problems in other domains.

Materialized view selection under the maintenance time constraint

A data warehouse is a data repository which collects and maintains a large amount of data from multiple distributed, autonomous and possibly heterogeneous data sources. Often the data is stored in the form of materialized views in order to provide fast access to the integrated data. One of the most important decisions in designing a data warehouse is the selection of views for materialization. The objective is to select an appropriate set of views that minimizes the total query response time with the constraint that the total maintenance time for these materialized views is within a given bound. This view selection problem is totally different from the view selection problem under the disk space constraint. In this paper the view selection problem under the maintenance time constraint is investigated. Two efficient, heuristic algorithms for the problem are proposed. The key to devising the proposed algorithms is to define good heuristic functions and to reduce the problem to some well-solved optimization problems. As a result, an approximate solution of the known optimization problem will give a feasible solution of the original problem. (C) 2001 Elsevier Science B.V. All rights reserved.

Empirical evidence for ultrametric structure in multi-layer perceptron error surfaces

Combinatorial optimization problems share an interesting property with spin glass systems in that their state spaces can exhibit ultrametric structure. We use sampling methods to analyse the error surfaces of feedforward multi-layer perceptron neural networks learning encoder problems. The third order statistics of these points of attraction are examined and found to be arranged in a highly ultrametric way. This is a unique result for a finite, continuous parameter space. The implications of this result are discussed.

A design method for superconducting MRI magnets with ferromagnetic material

The emphasis of this work is on the optimal design of MRI magnets with both superconducting coils and ferromagnetic rings. The work is directed to the automated design of MRI magnet systems containing superconducting wire and both `cold' and `warm' iron. Details of the optimization procedure are given and the results show combined superconducting and iron material MRI magnets with excellent field characteristics. Strong, homogeneous central magnetic fields are produced with little stray or external field leakage. The field calculations are performed using a semi-analytical method for both current coil and iron material sources. Design examples for symmetric, open and asymmetric clinical MRI magnets containing both superconducting coils and ferromagnetic material are presented.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.

Aquatic passive sampling of herbicides on naked particle loaded membranes: Accelerated measurement and empirical estimation of kinetic parameters

Water-sampler equilibrium partitioning coefficients and aqueous boundary layer mass transfer coefficients for atrazine, diuron, hexazionone and fluometuron onto C18 and SDB-RPS Empore disk-based aquatic passive samplers have been determined experimentally under a laminar flow regime (Re = 5400). The method involved accelerating the time to equilibrium of the samplers by exposing them to three water concentrations, decreasing stepwise to 50% and then 25% of the original concentration. Assuming first-order Fickian kinetics across a rate-limiting aqueous boundary layer, both parameters are determined computationally by unconstrained nonlinear optimization. In addition, a method of estimation of mass transfer coefficients-therefore sampling rates-using the dimensionless Sherwood correlation developed for laminar flow over a flat plate is applied. For each of the herbicides, this correlation is validated to within 40% of the experimental data. The study demonstrates that for trace concentrations (sub 0.1 mu g/L) and these flow conditions, a naked Empore disk performs well as an integrative sampler over short deployments (up to 7 days) for the range of polar herbicides investigated. The SDB-RPS disk allows a longer integrative period than the C18 disk due to its higher sorbent mass and/or its more polar sorbent chemistry. This work also suggests that for certain passive sampler designs, empirical estimation of sampling rates may be possible using correlations that have been available in the chemical engineering literature for some time.

A general-purpose tunable landscape generator

The research literature on metalieuristic and evolutionary computation has proposed a large number of algorithms for the solution of challenging real-world optimization problems. It is often not possible to study theoretically the performance of these algorithms unless significant assumptions are made on either the algorithm itself or the problems to which it is applied, or both. As a consequence, metalieuristics are typically evaluated empirically using a set of test problems. Unfortunately, relatively little attention has been given to the development of methodologies and tools for the large-scale empirical evaluation and/or comparison of metaheuristics. In this paper, we propose a landscape (test-problem) generator that can be used to generate optimization problem instances for continuous, bound-constrained optimization problems. The landscape generator is parameterized by a small number of parameters, and the values of these parameters have a direct and intuitive interpretation in terms of the geometric features of the landscapes that they produce. An experimental space is defined over algorithms and problems, via a tuple of parameters for any specified algorithm and problem class (here determined by the landscape generator). An experiment is then clearly specified as a point in this space, in a way that is analogous to other areas of experimental algorithmics, and more generally in experimental design. Experimental results are presented, demonstrating the use of the landscape generator. In particular, we analyze some simple, continuous estimation of distribution algorithms, and gain new insights into the behavior of these algorithms using the landscape generator.

Biodiversity conservation planning tools: Present status and challenges for the future

Species extinctions and the deterioration of other biodiversity features worldwide have led to the adoption of systematic conservation planning in many regions of the world. As a consequence, various software tools for conservation planning have been developed over the past twenty years. These, tools implement algorithms designed to identify conservation area networks for the representation and persistence of biodiversity features. Budgetary, ethical, and other sociopolitical constraints dictate that the prioritized sites represent biodiversity with minimum impact on human interests. Planning tools are typically also used to satisfy these criteria. This chapter reviews both the concepts and technical choices that underlie the development of these tools. Conservation planning problems can be formulated as optimization problems, and we evaluate the suitability of different algorithms for their solution. Finally, we also review some key issues associated with the use of these tools, such as computational efficiency, the effectiveness of taxa and abiotic parameters at choosing surrogates for biodiversity, the process of setting explicit targets of representation for biodiversity surrogates, and