Juan Antonio Sicilia

An optimization algorithm for solving the rich vehicle routing problem based on Variable Neighborhood Search and Tabu Search metaheuristics

This paper presents a novel optimization algorithm that consists of metaheuristic processes to solve the problem of the capillary distribution of goods in major urban areas taking into consideration the features encountered in real life: time windows, capacity constraints, compatibility between orders and vehicles, maximum number of orders per vehicle, orders that depend on the pickup and delivery and not returning to the depot. With the intention of reducing the wide variety of constraints and complexities, known as the Rich Vehicle Routing Problem, this algorithm proposes feasible alternatives in order to achieve the main objective of this research work: the reduction of costs by minimizing distances and reducing the number of vehicles used as long as the service quality to customers is optimum and a load balance among vehicles is maintained.

Decision model for siting transport and logistic facilities in urban environments

In this study, based on the use of a geographic information system (GIS), we define a decision model for determining the possible optimal locations of various facilities in an urban setting, which can be used by the transport infrastructure or logistics sector. The proposed methodology is based on the superposition of layers in GIS software, thereby enabling the prioritization or exclusion of certain areas depending on whether they meet specific requirements defined in each of the layers. This formulation assigns one degree of decision to each area of the map and it then classifies all of the areas to obtain the best solution according to the Jenks optimization method. We provide five case studies of transport-related facilities, including an example where the location of a hydrogen refueling station is determined using the proposed methodology.

Local convergence of a relaxed two-step Newton like method with applications

We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fréchet derivative and on the center divided-difference of order one are used. In earlier studies such as Amat et al. (Numer Linear Algebra Appl 17:639–653, 2010, Appl Math Lett 25(12):2209–2217, 2012, Appl Math Comput 219(24):11341–11347, 2013, Appl Math Comput 219(15):7954–7963, 2013, Reducing Chaos and bifurcations in Newton-type methods. Abstract and applied analysis. Hindawi Publishing Corporation, Cairo, 2013) these methods are analyzed under hypotheses up to the second Fréchet derivative and divided differences of order one. Numerical examples are also provided in this work.

New improved convergence analysis for Newton-like methods with applications

We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include, under the same computational cost as previous studies, a more precise convergence analysis under the same computational cost on the Lipschitz constants involved. Numerical studies including a chemical application are also provided in this study.

Improving the domain of parameters for Newton's method with applications

We present a new technique to improve the convergence domain for Newtons method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newtons method are weaker, the error bounds are tighter and the information on the location of the solution is at least as precise as in earlier studies. Numerical examples are given showing that our results apply to solve nonlinear equations in cases where the old results cannot apply.

Ball convergence of a sixth-order Newton-like method based on means under weak conditions

We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative or even higher. The convergence in this study is shown under hypotheses on the first derivative although only the first derivative appears in these methods. Hence, the applicability of the method is expanded. Finally, we solve the problem of the fractional conversion in the ammonia process showing the applicability of the theoretical results.

Improved semilocal convergence analysis in Banach space with applications to chemistry

We present a new semilocal convergence analysis for Secant methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost on the parameters involved our convergence criteria are weaker and the error bounds more precise than in earlier studies. A numerical example is also presented to illustrate the theoretical results obtained in this study.

Secant-like methods for solving nonlinear models with applications to chemistry

We present a local as well a semilocal convergence analysis of secant-like methods under g eneral conditions in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The new conditions are more flexible than in earlier studies. This way we expand the applicability of these methods, since the new convergence conditions are weaker. Moreover, these advantages are obtained under the same conditions as in earlier studies. Numerical examples are also provided in this study, where our results compare favorably to earlier ones.

Different methods for solving STEM problems

We first present a local convergence analysis for some families of fourth and six order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies have used hypotheses on the fourth Fréchet-derivative of the operator involved. We use hypotheses only on the first Fréchet-derivative in one local convergence analysis. This way, the applicability of these methods is extended. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study based on Lipschitz constants. Numerical examples illustrating the theoretical results are also presented in this study.

Developments on the Convergence of Some Iterative Methods

Iterative methods, play an important role in computational sciences. In this chapter, we present new semilocal and local convergence results for the Newton-Kantorovich method. These new results extend the applicability of the Newton-Kantorovich method on approximate zeros by improving the convergence domain and ratio given in earlier studies.