A multi-shift vehicle routing problem with windows and cycle times

In many applications of the vehicle routing problem with time windows (VRPTW), goods must be picked up within desired time frames. In addition, they have some limitations on their arrival time to the central depot. In this paper, we present a new version of VRPTW that minimizes the total cycle time of the goods. In order to meet the time windows and also minimize the cycle time, the courier’s schedule is allowed to vary. An algorithm, named VeRSA, is proposed to solve this problem. VeRSA employs concepts of scheduling theorems and algorithms to determine feasible routes and schedules of the available couriers. We prove a theoretical lower bound that provides a useful bound on the optimality gap. We also conduct a set of numerical experiments. VeRSA obtains a feasible solution faster than solving the MIP. The optimality gap using our proposed lower bound is smaller than the gap found with the standard LP relaxation.     

A Model-Based Approach and Analysis for Multi-Period Networks

The aim of this contribution is to address a general class of network problems, very common in process systems engineering, where spoilage on arcs and storage in nodes are inevitable as time changes. Having a set of capacities, so-called horizon capacity which limits the total flow passing arcs over all periods, the min-cost flow problem in the discrete-time model with time-varying network parameters is investigated. While assuming a possibility of storage or and spoilage, we propose some approaches employing polyhedrals to obtain optimal solutions for a pre-specified planning horizon. Our methods describe some reformulations based on polyhedrals that lead to LP problems comprising a set of sparse subproblems with exceptional structures. Considering the sparsity and repeating structure of the polyhedrals, algorithmic approaches based on decomposition techniques of block-angular and block-staircase cases are proposed to handle the global problem aiming to reduce the computational resources required.     

A New Steepest Descent Differential Inclusion-Based Method for Solving General Nonsmooth Convex Optimization Problems

In this paper, we investigate a steepest descent neural network for solving general nonsmooth convex optimization problems. The convergence to optimal solution set is analytically proved. We apply the method to some numerical tests which confirm the effectiveness of the theoretical results and the performance of the proposed neural network.     

Characterization of ZnO:Si nanocomposite films grown by thermal evaporation

Composite films were fabricated by co-evaporating Zinc Oxide with Silicon at room temperatures. The resulting films had polycrystalline grains of Zinc Oxide whose grain size were few hundred nanometers, embedded in the silicon matrix. These nanocrystalline grains of ZnO showed good photoluminescence emission at 520 nm along with a photoluminescence emission at 620 nm being contributed by the silicon background. Thus, the nanocomposite films gave a board emission, making it a potentially useful candidate for optoelectronic devices. The photo-luminescent property of the films was found to be stable since the homgenously dispersed ZnO nanocrystals were not allowed to agglomerate by the silicon background.     

Optimal preventive maintenance policy for electric power distribution systems based on the fuzzy AHP methods

In power distribution systems, with their great vastness and various outage causes, one of the most important problems of power distribution companies is to select a suitable maintenance strategy of system elements and method of financial planning for the maintenance of system elements with the two objectives of decrease in outage costs and improvement of system reliability. In this article, a practical method is introduced for the selection of a suitable system elements maintenance strategy; moreover, to plan the preventive maintenance budget for the system elements, two methods are offered: the cost optimization method and the fuzzy Analytic Hierarchy Process (AHP) method. In the former method, a new model of system maintenance cost is offered. This model, based on system outage information, the elements maintenance costs are determined as functions of system reliability indices and preventive maintenance budget. The latter method, too, a new guideline is introduced for considering the cost and reliability criteria in the trend of preventive maintenance budget planning. In this method, the preventive maintenance budget for the elements is determined based on relative priority of elements with reliability criteria. © 2015 Wiley Periodicals, Inc. Complexity 21: 70–88, 2016     

Real-Linear Isometries on Spaces of Functions of Bounded Variation

Let X and Y be subsets of the real line with at least two points. We study the surjective real-linear isometries \({T:BV(X)\longrightarrow BV(Y)}\) between the spaces of functions of bounded variation on X and Y with respect to the supremum norm \({\|\cdot\|_\infty}\) and the complete norm \({\|\cdot\|:=\max(\|\cdot\|_\infty,\mathcal{V}(\cdot))}\), where \({\mathcal{V}(\cdot)}\) denotes the total variation of a function. Additively norm preserving maps between these spaces are also characterized as a corollary.     

A Relation Between Closure Operators on a Small Category and Its Category of Presheaves

In this paper we show that each factorization structure on a small category , satisfying certain conditions, yields a presheaf on and a morphism of presheaves . We then give connections, and set up one to one correspondences, between subclasses of the following classes: (a) closure operators on (b) subobjects of (c) morphisms from to (d) weak Lawvere–Tierney topologies (e) weak Grothendieck topologies (f) closure operators on .     

Neuro-fuzzy based constraint programming

Constraint programming models appear in many sciences including mathematics, engineering and physics. These problems aim at optimizing a cost function joint with some constraints. Fuzzy constraint programming has been developed for treating uncertainty in the setting of optimization problems with vague constraints. In this paper, a new method is presented into creation fuzzy concept for set of constraints. Unlike to existing methods, instead of constraints with fuzzy inequalities or fuzzy coefficients or fuzzy numbers, vague nature of constraints set is modeled using learning scheme with adaptive neural-fuzzy inference system (ANFIS). In the proposed approach, constraints are not limited to differentiability, continuity, linearity; also the importance degree of each constraint can be easily applied. Unsatisfaction of each weighted constraint reduces membership of certainty for set of constraints. Monte-Carlo simulations are used for generating feature vector samples and outputs for construction of necessary data for ANFIS. The experimental results show the ability of the proposed approach for modeling constrains and solving parametric programming problems.     

Exact solutions of some nonlinear systems of partial differential equations by using the first integral method

In recent years, many approaches have been utilized for finding the exact solutions of nonlinear systems of partial differential equations. In this paper, the first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including, KdV, Kaup–Boussinesq and Wu–Zhang systems, analytically. By means of this method, some exact solutions for these systems of equations are formally obtained. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.     

Large diameter MWNTs growth on iron-sprayed catalyst by CCVD method under atmospheric pressure

In this work, we have synthesized large diameter multi-walled carbon nanotubes (MWNTs), by simple catalyst chemical vapor deposition (CCVD). Fe powder was spread on quartz substrate as a catalyst by a simple method and then heated under Ar atmosphere. Carbon’s products can be synthesized by the decomposition of ethylene gas and deposition of carbon atoms on the Fe catalyst particles in Ar atmosphere at 930°C. XRD pattern, SEM and TEM images were used to investigate the characteristics, morphology and structure of carbon’s products.