Wolbachia-based biocontrol for dengue reduction using dynamic optimization approach

Aedes aegypti females mosquitoes are the principal transmitters of dengue and other arboviral infections. In recent years, it was disclosed that, when deliberately infected with Wolbachia symbiont, this mosquito species loses its vectorial competence and becomes less capable of transmitting the virus to human hosts. Thanks to this important discovery, Wolbachia-based biocontrol is now accepted as an ecologically friendly and potentially cost-effective method for prevention and control of dengue and other arboviral infections. In this paper, we propose a dengue transmission model that accounts for the presence of wild Aedes aegypti females and those deliberately infected with wMelPop Wolbachia strain, which is regarded as the best blocker of dengue and other arboviral infections. However, wMelPop strain of Wolbachia considerably reduces the individual fitness of mosquitoes, what makes rather challenging to achieve the gradual extrusion of wild mosquitoes and ensure their posterior replacement by Wolbachia-carriers. Nonetheless, this obstacle have been overcome by employing the optimal control approach for design of specific intervention programs based on daily releases of Wolbachia-carrying mosquitoes. The resulting optimal release programs ensure the population replacement and eventual local extinction of wild mosquitoes in the finite time and also entail a significant reduction in the number of expected dengue infections among human hosts under the long-term settings.     

Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation

We propose a family of retrospective optimization (RO) algorithms for optimizing stochastic systems with both integer and continuous decision variables. The algorithms are continuous search procedures embedded in a RO framework using dynamic simplex interpolation (RODSI). By decreasing dimensions (corresponding to the continuous variables) of simplex, the retrospective solutions become closer to an optimizer of the objective function. We present convergence results of RODSI algorithms for stochastic “convex” systems. Numerical results show that a simple implementation of RODSI algorithms significantly outperforms some random search algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).     

An abstract approach to rational interpolation

The Hermite rational interpolation is described in terms of linear polynomial projections.     

An inexact line search approach using modified nonmonotone strategy for unconstrained optimization

This paper concerns with a new nonmonotone strategy and its application to the line search approach for unconstrained optimization. It has been believed that nonmonotone techniques can improve the possibility of finding the global optimum and increase the convergence rate of the algorithms. We first introduce a new nonmonotone strategy which includes a convex combination of the maximum function value of some preceding successful iterates and the current function value. We then incorporate the proposed nonmonotone strategy into an inexact Armijo-type line search approach to construct a more relaxed line search procedure. The global convergence to first-order stationary points is subsequently proved and the R-linear convergence rate are established under suitable assumptions. Preliminary numerical results finally show the efficiency and the robustness of the proposed approach for solving unconstrained nonlinear optimization problems.     

An approach to the solution of the vector optimization problem of dynamic systems

The optimal control problem with vector-valued criteria is considered. A new approach to the generalization of this problem and a method of constructing the Bellman function are given.Paper prepared during the author's visiting period at the Centro di Studio dei Sistemi di Controllo e Calcolo Automatici, Consiglio Nazionale delle Richerche, Roma, Italia; at Istituto di Mathematica Applicata; and at the Sezione Automatica, Informatica, e Sistemistica, Instituto di Elettronica, Facolta di Ingegneria, Universita di Firenze, Firenze, Italia.     

An interactive approach for vector optimization problems

This paper deals with an interactive approach for vector optimization problems. The best compromise solutions are obtained using one of the methods which depends on the global preference, namely Geoffrion's method. The stability set of the first kind is analyzed and used to reduce the parametric space of the problem. An example is given for the sake of illustration.     

An isogeometric boundary element approach for topology optimization using the level set method

Among the various types of structural optimization, topology has been occupying a prominent place over the last decades. It is considered the most versatile because it allows structural geometry to be determined taking into account only loading and fixing constraints. This technique is extremely useful in the design phase, which requires increasingly complex computational modeling. Modern geometric modeling techniques are increasingly focused on the use of NURBS basis functions. Consequently, it seems natural that topology optimization techniques also use this basis in order to improve computational performance. In this paper, we propose a way to integrate the isogeometric boundary techniques to topology optimization through the level set function. The proposed coupling occurs by describing the normal velocity field from the level set equation as a function of the normal shape sensitivity. This process is not well behaved in general, so some regularization technique needs to be specified. Limiting to plane linear elasticity cases, the numerical investigations proposed in this study indicate that this type of coupling allows to obtain results congruent with the current literature. Moreover, the additional computational costs are small compared to classical techniques, which makes their advantage for optimization purposes evident, particularly for boundary element method practitioners.     

An approach to geometric interpolation by Pythagorean-hodograph curves

The problem of geometric interpolation by Pythagorean-hodograph (PH) curves of general degree n is studied independently of the dimension d????2. In contrast to classical approaches, where special structures that depend on the dimension are considered (complex numbers, quaternions, etc.), the basic algebraic definition of a PH property together with geometric interpolation conditions is used. The analysis of the resulting system of nonlinear equations exploits techniques such as the cylindrical algebraic decomposition and relies heavily on a computer algebra system. The nonlinear equations are written entirely in terms of geometric data parameters and are independent of the dimension. The analysis of the boundary regions, construction of solutions for particular data and homotopy theory are used to establish the existence and (in some cases) the number of admissible solutions. The general approach is applied to the cubic Hermite and Lagrange type of interpolation. Some known results are extended and numerical examples provided.     

An algorithm for the interpolation of functions using quintic splines

A method is described for the interpolation of N arbitrarily given data points using fifth degree polynomial spline functions. The interpolating spline is built from a set of basis functions belonging to the fifth degree smooth Hermite space. The resulting algebraic system is symmetric and bloc-tridiagonal. Its solution is calculated using a direct inversion method, namely a block-gaussian elimination without pivoting. Various boundary conditions are provided for independently at each end point. The stability of the algorithm is examined and some examples are given of experimental convergence rates for the interpolation of elementary analytical functions. A listing is given of the two FORTRAN subroutines INSPL5 and SPLIN5 which form the algorithm.     

A data-driven approach for a class of stochastic dynamic optimization problems

Computational Optimization and Applications - Dynamic stochastic optimization models provide a powerful tool to represent sequential decision-making processes. Typically, these models use...     

An approach to the interpolation of nonuniformly spaced data

In this paper, we consider the spline in tension as an interpolatory tool that helps us avoid large projector norm. Tension parameters are computed in advance in such a way that the prescribed exponential decay of fundamental functions is assured. Further, an interpolation error bound for a smooth function is produced. This bound depends on the choice of tension parameters, and is of order 4 for small tension values but reduces to 2 as parameters grow to infinity.     

An optimization approach for planning daily drayage operations

Daily drayage operations involve moving loaded or empty equipment between customer locations and rail ramps. Our goal is to minimize the cost of daily drayage operations in a region on a given day. Drayage orders are generally pickup and delivery requests with time windows. The repositioning of empty equipment may also be required in order to facilitate loaded movements. The drayage orders are satisfied by a heterogeneous fleet of drivers. Driver routes must satisfy various operational constraints. We present an optimization methodology for finding cost-effective schedules for regional daily drayage operations. The core of the formulation is a set partitioning model whose columns represent routes. Routes are added to the formulation by column generation. We present numerical results for real-world data which demonstrate that our methodology produces low cost solutions in a reasonably short time.     

An acceleration method for integral equations by using interpolation post-processing

Two post-processing techniques are widely used in the literature in the context of convergence acceleration. One of them is an interpolation technique, used for partial differential equations and integral differential equations, and the other is an iteration technique used for integral equations. These two techniques, interpolation and iteration, are quite different, and the former is simpler. Can we use the interpolation technique for integral equations instead of using the second iteration technique? This report gives a positive answer.

     

An extreme-distance approach to multiple criteria ranking

A distance approach based on extreme points, or predefined ideal and anti-ideal points, is proposed to improve on the TOPSIS (Technique for Order Performance [or Ordered Preference] by Similarity to Ideal Solution) method of multiple criteria ranking. Two case studies demonstrate how the analysis procedure works, and provide a basis for comparison of the proposed method to the original TOPSIS and similar methods. In applications, the new method produces results that are generally consistent with the original technique, but offers new features such as a clear interpretation of extreme points, more flexibility in setting extreme points, no normalization distortion, and the ability to handle non-monotonic criteria.     

An interactive dynamic approach based on hybrid swarm optimization for solving multiobjective programming problem with fuzzy parameters

Real engineering design problems are generally characterized by the presence of many often conflicting and incommensurable objectives. Naturally, these objectives involve many parameters whose possible values may be assigned by the experts. The aim of this paper is to introduce a hybrid approach combining three optimization techniques, dynamic programming (DP), genetic algorithms and particle swarm optimization (PSO). Our approach integrates the merits of both DP and artificial optimization techniques and it has two characteristic features. Firstly, the proposed algorithm converts fuzzy multiobjective optimization problem to a sequence of a crisp nonlinear programming problems. Secondly, the proposed algorithm uses H-SOA for solving nonlinear programming problem. In which, any complex problem under certain structure can be solved and there is no need for the existence of some properties rather than traditional methods that need some features of the problem such as differentiability and continuity. Finally, with different degree of α we get different α-Pareto optimal solution of the problem. A numerical example is given to illustrate the results developed in this paper.     

An infinite-horizon multistage dynamic optimization problem

Multiprocess problems are dynamic optimization problems in which there is a collection of control systems coupled through constraints in the endpoints of the constituent trajectories and through the cost function. Optimality conditions for such problems posed over a finite interval have already been derived. However, multiprocess problems arise, for example in the mathematical economics literature, in which one of the component processes operates over an infinite horizon. We give a proof of the relevant necessary conditions in the form of a maximum principle under mild and verifiable hypotheses and apply the theory to a two-stage problem in which an explicit dependence on the intermediate time (taken as a choice variable) is incorporated in the integrands of the cost functional.This research was carried out while the author was a Graduate Student at the Department of Electrical Engineering, Imperial College of Science, Technology, and Medicine, London, England. The author is grateful to Professor R. B. Vinter for his advice and helpful discussions.     

A time-variant performance measure approach for dynamic reliability based design optimization

In this work, a time-variant performance measure approach is proposed by searching the minimum performance value during the time period. A modified directional step method is proposed by obeying a search strategy that each iterative value should be smaller than that of previous one. With this strategy, the time-variant minimum performance target point can be quickly found in each inner loop. The proposed method is applied to three numerical examples. The results are compared with other two existing methods, which verifies the robust accuracy and effectiveness of the proposed method.     

A dynamic programming approach to adjustable robust optimization

In this paper we consider the adjustable robust approach to multistage optimization, for which we derive dynamic programming equations. We also discuss this from the point of view of risk averse stochastic programming. We consider as an example a robust formulation of the classical inventory model and show that, like for the risk neutral case, a basestock policy is optimal.     

The dynamic programming approach to multi-model robust optimization

The aim of this paper is to extend the dynamic programming (DP) approach to multi-model optimal control problems (OCPs). We deal with robust optimization of multi-model control systems and are particularly interested in the Hamilton-Jacobi-Bellman (HJB) equation for the above class of problems. In this paper, we study a variant of the HJB for multi-model OCPs and examine the natural relationship between the Bellman DP techniques and the Robust Maximum Principle (MP). Moreover, we describe how to carry out the practical calculations in the context of multi-model LQ-problems and derive the associated Riccati-type equation.     

An axiomatic approach to scalar data interpolation on surfaces

We discuss possible algorithms for interpolating data given on a set of curves in a surface of ℝ³. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The Absolutely Minimizing Lipschitz Extension model (AMLE) is singled out and studied in more detail. We study the correctness of our numerical approach and we show experiments illustrating the interpolation of data on some simple test surfaces like the sphere and the torus.