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.

Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

Synthesis and evaluation of asperlicin analogues as non-peptidal cholecystokinin-antagonists

The SAR of Asperlicin analogues is reported, leading to bioactive 1,4-benzodiazepine-2-ones, which were prepared in a 3 step reaction sequence. The Asperlicin substructure was built up using Tryptophan and readily available 2-amino-acetophenones. This template, containing a 1,4-benzodiazepin-2-one moiety with a 3-indolmethyl side chain, was transformed into mono- and di-substituted 3-indol-3 '-yl-methyl-1,4-benzodi-azepine-2-ones by selective alkylation and acylation reactions. The SAR optimization of the 1,4-benzodiazepine scaffold has included variations at the 5-, 7-, 8-position, at the N1, N-indole nitrogen and the configuration of the C3-position. The most active Asperlicin analogue, having an IC50 of 1.6 microM on the CCKA receptor subtype, was obtained from Tryptophan in only 3 steps in an overall yield of 48%.

EM optimization of latent-variable density models

There is currently considerable interest in developing general non-linear density models based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying `causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, to train such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general non-linear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multi-phase oil pipeline.

SAS/OWA:ordered weighted averaging in SAS optimization

This paper explores the use of the optimization procedures in SAS/OR software with application to the ordered weight averaging (OWA) operators of decision-making units (DMUs). OWA was originally introduced by Yager (IEEE Trans Syst Man Cybern 18(1):183-190, 1988) has gained much interest among researchers, hence many applications such as in the areas of decision making, expert systems, data mining, approximate reasoning, fuzzy system and control have been proposed. On the other hand, the SAS is powerful software and it is capable of running various optimization tools such as linear and non-linear programming with all type of constraints. To facilitate the use of OWA operator by SAS users, a code was implemented. The SAS macro developed in this paper selects the criteria and alternatives from a SAS dataset and calculates a set of OWA weights. An example is given to illustrate the features of SAS/OWA software. © Springer-Verlag 2009.

Investigating local delivery by road to retail and non-retail customers in the UK logistics sector

Over recent years, hub-and-spoke distribution techniques have attracted widespread research attention. Despite there being a growing body of literature in this area there is less focus on the spoke-terminal element of the hub-and-spoke system as being a key component in the overall service received by the end-user. Current literature is highly geared towards discussing bulk optimization of freight units rather than to the more discrete and individualistic profile characteristics of shared-user Less-than-truckload (LTL) freight. In this paper, a literature review is presented to review the role hub-and-spoke systems play in meeting multi-profile customer demands, particularly in developing sectors with more sophisticated needs, such as retail. The paper also looks at the use of simulation technology as a suitable tool for analyzing spoke-terminal operations within developing hub-and spoke systems.

Characterization and optimization of bilosomes for oral vaccine delivery

Oral vaccines offer significant benefits due to the ease of administration, better patient compliance and non-invasive, needle-free administration. However, this route is marred by the harsh gastro intestinal environment which is detrimental to many vaccine formats. To address this, a range of delivery systems have been considered including bilosomes; these are bilayer vesicles constructed from non-ionic surfactants combined with the inclusion of bile salts which can stabilize the vesicles in the gastro intestinal tract by preventing membrane destabilization. The aim of this study was to investigate the effect of formulation parameters on bilosome carriers using Design of Experiments to select an appropriate formulation to assess in vivo. Bilosomes were constructed from monopalmitoylglycerol, cholesterol, dicetyl phosphate and sodium deoxycholate at different blends ratios. The optimized bilosome formulation was identified and the potential of this formulation as an oral vaccine delivery system were assessed in biodistribution and vaccine efficacy studies. Results showed that the larger bilosomes vesicles (~6 µm versus 2 µm in diameter) increased uptake within the Peyer's patches and were able to reduce median temperature differential change and promote a reduction in viral cell load in an influenza challenge study. © 2013 Informa UK, Ltd.

Structural optimization

The non-linear programming algorithms for the minimum weight design of structural frames are presented in this thesis. The first, which is applied to rigidly jointed and pin jointed plane frames subject to deflexion constraints, consists of a search in a feasible design space. Successive trial designs are developed so that the feasibility and the optimality of the designs are improved simultaneously. It is found that this method is restricted lo the design of structures with few unknown variables. The second non-linear programming algorithm is presented .in a general form. This consists of two types of search, one improving feasibility and the other optimality. The method speeds up the 'feasible direction' approach by obtaining a constant weight direction vector that is influenced by dominating constraints. For pin jointed plane and space frames this method is used to obtain a 'minimum weight' design which satisfies restrictions on stresses and deflexions. The matrix force method enables the design requirements to be expressed in a general form and the design problem is automatically formulated within the computer. Examples are given to explain the method and the design criteria are extended to include member buckling. Fundamental theorems are proposed and proved to confirm that structures are inter-related. These theorems are applicable to linear elastic structures and facilitate the prediction of the behaviour of one structure from the results of analysing another, more general, or related structure. It becomes possible to evaluate the significance of each member in the behaviour of a structure and the problem of minimum weight design is extended to include shape. A method is proposed to design structures of optimum shape with stress and deflexion limitations. Finally a detailed investigation is carried out into the design of structures to study the factors that influence their shape.

Stability of the Iteration Method for non Expansive Mappings

The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.

Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.

A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.

Duality in Constrained DC-Optimization via Toland’s Duality Approach

2000 Mathematics Subject Classification: 90C48, 49N15, 90C25

Optimality Conditions for D.C. Vector Optimization Problems under D.C. Constraints

2000 Mathematics Subject Classification: Primary 90C29; Secondary 49K30.

Optimization of Advertising Resources over Time: A Strategic Analysis

AMS subject classification: 90B60, 90B50, 90A80.

Hybrid multi-objective optimization and hybridized self-organizing response surface method

Numerical optimization is a technique where a computer is used to explore design parameter combinations to find extremes in performance factors. In multi-objective optimization several performance factors can be optimized simultaneously. The solution to multi-objective optimization problems is not a single design, but a family of optimized designs referred to as the Pareto frontier. The Pareto frontier is a trade-off curve in the objective function space composed of solutions where performance in one objective function is traded for performance in others. A Multi-Objective Hybridized Optimizer (MOHO) was created for the purpose of solving multi-objective optimization problems by utilizing a set of constituent optimization algorithms. MOHO tracks the progress of the Pareto frontier approximation development and automatically switches amongst those constituent evolutionary optimization algorithms to speed the formation of an accurate Pareto frontier approximation. Aerodynamic shape optimization is one of the oldest applications of numerical optimization. MOHO was used to perform shape optimization on a 0.5-inch ballistic penetrator traveling at Mach number 2.5. Two objectives were simultaneously optimized: minimize aerodynamic drag and maximize penetrator volume. This problem was solved twice. The first time the problem was solved by using Modified Newton Impact Theory (MNIT) to determine the pressure drag on the penetrator. In the second solution, a Parabolized Navier-Stokes (PNS) solver that includes viscosity was used to evaluate the drag on the penetrator. The studies show the difference in the optimized penetrator shapes when viscosity is absent and present in the optimization. In modern optimization problems, objective function evaluations may require many hours on a computer cluster to perform these types of analysis. One solution is to create a response surface that models the behavior of the objective function. Once enough data about the behavior of the objective function has been collected, a response surface can be used to represent the actual objective function in the optimization process. The Hybrid Self-Organizing Response Surface Method (HYBSORSM) algorithm was developed and used to make response surfaces of objective functions. HYBSORSM was evaluated using a suite of 295 non-linear functions. These functions involve from 2 to 100 variables demonstrating robustness and accuracy of HYBSORSM.