Global optimization methods for engineering applications: A review

A review of the methods for global optimization reveals that most methods have been developed for unconstrained problems. They need to be extended to general constrained problems because most of the engineering applications have constraints. Some of the methods can be easily extended while others need further work. It is also possible to transform a constrained problem to an unconstrained one by using penalty or augmented Lagrangian methods and solve the problem that way. Some of the global optimization methods find all the local minimum points while others find only a few of them. In any case, all the methods require a very large number of calculations. Therefore, the computational effort to obtain a global solution is generally substantial. The methods for global optimization can be divided into two broad categories: deterministic and stochastic. Some deterministic methods are based on certain assumptions on the cost function that are not easy to check. These methods are not very useful since they are not applicable to general problems. Other deterministic methods are based on certain heuristics which may not lead to the true global solution. Several stochastic methods have been developed as some variation of the pure random search. Some methods are useful for only discrete optimization problems while others can be used for both discrete and continuous problems. Main characteristics of each method are identified and discussed. The selection of a method for a particular application depends on several attributes, such as types of design variables, whether or not all local minima are desired, and availability of gradients of all the functions.Notation Number of equality constraints - () ^T A transpose of a vector - A A hypercubic cell in clustering methods - Distance between two adjacent mesh points - Probability that a uniform sample of sizeN contains at least one point in a subsetA ofS - A(v, x) Aspiration level function - A The set of points with cost function values less thanf(x _G ^* ) +. Same asA _f () - A _f () A set of points at which the cost function value is within off(x _G ^* ) - A () A set of points x with[f(x)] smaller than - A _N The set ofN random points - A _q The set of sample points with the cost function value f _q - _Q The contraction coefficient; –1 _Q 0 - _R The expansion coefficient; _E > 1 - _R The reflection coefficient; 0 < _R 1 - A _x () A set of points that are within the distance from x _G ^* - D Diagonal form of the Hessian matrix - det() Determinant of a matrix - d _j A monotonic function of the number of failed local minimizations - d _t Infinitesimal change in time - d _x Infinitesimal change in design - A small positive constant - (t) A real function called the noise coefficient - ₀ Initial value for(t) - exp() The exponential function - f ^(c) The record; smallest cost function value over X^(C) - [f(x)] Functional for calculating the volume fraction of a subset - Second-order approximation tof(x) - f(x) The cost function - An estimate of the upper bound of global minimum - f ^E The cost function value at x^E - f ^L The cost function value at x^L - f _opt The current best minimum function value - f ^P The cost function value at x ^P - f ^Q The cost function value at x ^Q - f _q A function value used to reduce the random sample - f ^R The cost function value at x ^R - f ^S The cost function value at x^S - f _{T F min} A common minimum cost function value for several trajectories - f _{TF opt} The best current minimum value found so far forf _{TF min} - f ^W The cost function value at x ^W - G Minimum number of points in a cell (A) to be considered full - The gamma function - A factor used to scale the global optimum cost in the zooming method - Minimum distance assumed to exist between two local minimum points - gi(x) Constraints of the optimization problem - H The size of the tabu list - H(x^*) The Hessian matrix of the cost function at x^* - h _j Half side length of a hypercube - h _m Minimum half side lengths of hypercubes in one row - I The unity matrix - ILIM A limit on the number of trials before the temperature is reduced - J The set of active constraints - K Estimate of total number of local minima - k Iteration counter - The number of times a clustering algorithm is executed - L Lipschitz constant, defined in Section 2 - L The number of local searches performed - _i The corresponding pole strengths - log () The natural logarithm - LS Local search procedure - M Number of local minimum points found inL searches - m Total number of constraints - m(t) Mass of a particle as a function of time - m() TheLebesgue measure of thea set - Average cost value for a number of random sample of points inS - N The number of sample points taken from a uniform random distribution - n Number of design variables - n(t) Nonconservative resistance forces - n _c Number of cells;S is divided inton _c cells - NT Number of trajectories - Pi (3.1415926) - P _i ^(j) Hypersphere approximating thej-th cluster at stagei - p(x ⁽ⁱ⁾⁾ Boltzmann-Gibbs distribution; the probability of finding the system in a particular configuration - pg A parameter corresponding to each reduced sample point, defined in (36) - Q An orthogonal matrix used to diagonalize the Hessian matrix - _i (i = 1, K) The relative size of thei-th region of attraction - r _i ^(j) Radius of thej-th hypersp here at stagei - R _x ^* Region of attraction of a local minimum x^* - r _j Radius of a hypersphere - r A critical distance; determines whether a point is linked to a cluster - R ⁿ A set ofn tuples of real numbers - A hyper rectangle set used to approximateS - S The constraint set - A user supplied parameter used to determiner - s The number of failed local minimizations - T The tabu list - t Time - T(x) The tunneling function - T _c (x) The constrained tunneling function - T _i The temperature of a system at a configurationi - TLIMIT A lower limit for the temperature - TR A factor between 0 and 1 used to reduce the temperature - u(x) A unimodal function - V(x) The set of all feasible moves at the current design - v(x) An oscillating small perturbation. - V(y⁽ⁱ⁾) Voronoi cell of the code point y⁽ⁱ⁾ - v^–1 An inverse move - v _k A move; the change from previous to current designs - w(t) Ann-dimensional standard. Wiener process - x Design variable vector of dimensionn - x^# A movable pole used in the tunneling method - x⁽⁰⁾ A starting point for a local search procedure - X^(c) A sequence of feasible points {x⁽¹⁾, x⁽²⁾,,x^(c)} - x(t) Design vector as a function of time - X^* The set of all local minimum points - x^* A local minimum point forf(x) - x^*(i) Poles used in the tunneling method - x _G ^* A global minimum point forf(x) - Transformed design space - The velocity vector of the particle as a function of time - Acceleration vector of the particle as a function of time - x ^C Centroid of the simplex excluding x ^L - x ^c A pole point used in the tunneling method - x ^E An expansion point of x ^R along the direction x ^C x ^R - x ^L The best point of a simplex - x ^P A new trial point - x ^Q A contraction point - x ^R A reflection point; reflection of x ^W on x ^C - x ^S The second worst point of a simplex - x ^W The worst point of a simplex - The reduced sample point with the smallest function value of a full cell - Y The set of code points - y ⁽ⁱ⁾ A code point; a point that represents all the points of thei-th cell - z A random number uniformly distributed in (0,1) - Z ^(c) The set of points x where [f ^(c) – ] is smaller thanf(x) - []₊ Max (0,) - | | Absolute value - The Euclidean norm - f[x(t)] The gradient of the cost function     

Evolution of gypsy-group retrotransposons: phylogenetic analysis of domains included in the pol-polyprotein

Transposons of gypsy group are assigned to LTR-containing retrotransposons present in the genomes of invertebrates, fungi, and plants. In this work, a theoretical analysis of the potential products of ORFs of these retrotranposons was conducted. Alignments were obtained and trees of similarity were constructed for domains of the POL region. On the basis of the obtained data, two hypothetically monophyletic subgroups of transposons were distinguished within the framework of the gypsy group, settling the genomes of taxonomically related organisms (the subgroup of "true" gypsy of insects and the subgroup of gypsy-like transposons of plants and fungi). A number of peculiarities of the topology of these trees hypothetically indicate cases of genetic conversion and recombination of domains accompanying the evolution of this group. The amino acid substitution fixation rate was evaluated on the basis of comparison of sequences of the protein products of ORFs. Estimates of the time of divergence of subgroups of gypsy-group transposons are significantly less than estimates of the times of divergence of their host species. One explanation for this discrepancy might be the hypothesis of settlement by transposons of the genomes of isolated host species.     

Automated sampling decision scheme for the AVM system

Reducing the sampling rate to as low as possible is a high priority for many factories to reduce production cost. Automatic virtual metrology based intelligent sampling decision (ISD) scheme had been previously developed for reducing the sampling rate and sustaining the virtual metrology (VM) accuracy. However, the desired sampling rate of the ISD scheme is fixed and set manually. Hence, whenever the VM accuracy gets worse, it cannot adaptively increase the default sampling rate in the ISD scheme. As a consequence, it would take more time to collect enough samples for improving the VM accuracy. Moreover, when the VM accuracy performs well all the time, it cannot automatically decrease the default sampling rate in ISD, which may result in unnecessary waste. Accordingly, this paper proposes an automated sampling decision (ASD) scheme to adaptively and automatically modify the sampling rate online and in real time for continuous improvement. The ASD scheme can monitor the VM accuracy online as well as update the VM models in real time for maintaining the VM accuracy when the VM accuracy becomes poor. Also, the ASD scheme can automatically reduce the sampling rate while the VM accuracy performs well.     

Protein kinase C modulates estrogen receptors in differentiated osteoblastic cells in vitro

Ventriculo-peritoneal shunts (VPS) are the most frequent operative procedures used to treat hydrocephalic children. Abdominal complications of VPS are now a rare event; however, their frequency varies from 5% to 47% according to reports. Anything that causes an obstruction or impediment of the VP derivation system will lead to intracranial hypertension, which requires immediate surgery. From 1985 to 1995 at the Division of Pediatric Surgery of the Federico II University of Naples, ten laparoscopies were performed in ten children with VPS complications. Cerebrospinal fluid pseudocysts were found in four infants. There was one case of abdominal wall perforation by the tip of the catheter at the umbilical level, two bowel obstructions, and one catheter was lost in the abdominal cavity. Finally, two children had malfunctioning of the peritoneal limb of the catheter. The laparoscopic technique was curative in all ten cases, thus avoiding a conventional laparotomy and the consequent risk of adhesions, which could cause further complications.     

Polarization-Dependent Periodic Pulse Oscillation in a Diode-Laser-Pumped and Intracavity Frequency-Doubled Nd:YVO 4 Laser

We demonstrate that two cross-polarized longitudinal modes can have 50% higher conversion efficiency than two parallel-polarized longitudinal modes in a diode-laser-pumped and intracavity frequency-doubled Nd:YVO(4) laser when operated under periodic pulse oscillation. Through simulations of the rate equations for primary frequency intensities and gains, we also verify that this effect can be attributed to gain competition and complementary conversion coefficient between second-harmonic and sum-frequency generations.     

Traffic of dynamin within individual Drosophila synaptic boutons relative to compartment-specific markers

Presynaptic terminals contain several specialized compartments, which have been described by electron microscopy. We show in an identified Drosophila neuromuscular synapse that several of these compartments-synaptic vesicle clusters, presynaptic plasma membrane, presynaptic cytosol, and axonal cytoskeleton-labeled by specific reagents may be resolved from one another by laser scanning confocal microscopy. Using a panel of compartment-specific markers and Drosophila shibire(ts1) mutants to trap an intermediate stage in synaptic vesicle recycling, we have examined the localization and redistribution of dynamin within single synaptic varicosities at the larval neuromuscular junction. Our results suggest that dynamin is not a freely diffusible molecule in resting nerve terminals; rather, it appears localized to synaptic sites by association with yet uncharacterized presynaptic components. In shi(ts1) nerve terminals depleted of synaptic vesicles, dynamin is quantitatively redistributed to the plasma membrane. It is not, however, distributed uniformly over presynaptic plasmalemma; instead, fluorescence images show "hot spots" of dynamin on the plasma membrane of vesicle-depleted nerve terminals. We suggest that these dynamin-rich domains may mark the active zones for synaptic vesicle endocytosis first described at the frog neuromuscular junction.     

The crystal structure of the immunity protein of colicin E7 suggests a possible colicin-interacting surface

The immunity protein of colicin E7 (ImmE7) can bind specifically to the DNase-type colicin E7 and inhibit its bactericidal activity. Here we report the 1.8-angstrom crystal structure of the ImmE7 protein. This is the first x-ray structure determined in the superfamily of colicin immunity proteins. The ImmE7 protein consists of four antiparallel alpha-helices, folded in a topology similar to the architecture of a four-helix bundle structure. A region rich in acidic residues is identified. This negatively charged area has the greatest variability within the family of DNase-type immunity proteins; thus, it seems likely that this area is involved in specific binding to colicin. Based on structural, genetic, and kinetic data, we suggest that all the DNase-type immunity proteins, as well as colicins, share a "homologous-structural framework" and that specific interaction between a colicin and its cognate immunity protein relies upon how well these two proteins' charged residues match on the interaction surface, thus leading to specific immunity of the colicin.     

Some sexological characteristics of stress incontinent women

The goal of stress incontinence surgery is to prevent opening of the urethra during increases in intra-abdominal pressure. Greater refinements in the understanding of the pathophysiology of incontinence and experience with newer treatments have extended surgical thinking beyond the familiar paradigm "to place the urethra in a high retropubic position." When incontinence is associated with vaginal hypermobility, vaginal support may be sufficient to restore continence if the suburethral vaginal wall is sufficiently strong, an evaluation which must often be made by physical examination alone. However, when the vaginal wall is weak, the urethra will require an alternative form of support, usually a sling. If the urethra is intrinsically deficient, vaginal support may not be sufficient to prevent opening during increased intra-abdominal pressure, and coaptation by sling obstruction or periurethral bulking injection may be required. Most laparoscopic approaches to stress incontinence use Burch's method, which offers excellent urethral stability provided the suburethral vaginal wall is strong. Newer insights into the relation between vaginal mobility and urethral closure are discussed, as well as anatomic aspects of the Burch suspension relevant to laparoscopic repair.     

Inexpensive high availability solutions for the SIP-based VoIP service

In the era of IP-based service, people expect a simple, cheap, and competent Voice over IP (VoIP) service as an alternative of the traditional voice over PSTN. The introduction of the SIP protocol realizes the expectation. Following the cost saving spirit of VoIP, we focus on studying inexpensive high availability solutions for the SIP-based VoIP Service. In this paper, Peer-to-Peer (P2P) based and DN-LB based schemes are mainly compared in the paper. A P2P-based scheme enables an inexpensive high availability solution to the VoIP service by the shared computation resources form P2P nodes. Such a P2P-based solution may be appropriate for an individual VoIP user. However, a caller may take a large volume of messages to find out a callee via the proxy nodes in the P2P network. This inherent property of a P2P network may induce the message overhead and long call setup delay. Based on above, another inexpensive scheme, which is a probing-based name resolution solution, is proposed to achieve high availability and load balancing for the VoIP service. We tag the probing mechanism onto the open source project Domain Name Relay Daemon (DNRD) to become a domain name resolution based load balancer (DN-LB). With DN-LB, all request messages from clients can be fairly distributed to all failure-proof proxy servers in the server farm without using any additional costly intermediate network device and changing the standard SIP architecture. Such a DN-LB based solution may be a good choice for a VoIP service provider.     

Scalable continuous object detection and tracking in sensor networks

With the advancement of MEMS technologies, sensor networks have opened up broad application prospects. An important issue in wireless sensor networks is object detection and tracking, which typically involves two basic components, collaborative data processing and object location reporting. The former aims to have sensors collaborating in determining a concise digest of object location information, while the latter aims to transport a concise digest to sink in a timely manner. This issue has been intensively studied in individual objects, such as intruders. However, the characteristic of continuous objects has posed new challenges to this issue. Continuous objects can diffuse, increase in size, or split into multiple continuous objects, such as a noxious gas. In this paper, a scalable, topology-control-based approach for continuous object detection and tracking is proposed. Extensive simulations are conducted, which show a significant improvement over existing solutions.