A dynamic programming-based heuristic for the variable sized two-dimensional bin packing problem

This paper addresses a variable sized two-dimensional bin packing problem. We propose two heuristics, H1 and H2, stemming from the dynamic programming idea by aggregating states to avoid the explosion in the number of states. These algorithms are elaborated for different purposes: H1 builds a general packing plan for items, while H2 can provide solutions by considering a variety of customer demands, such as guillotine cutting style and rotation of items. The performance of both algorithms is evaluated based on randomly generated instances reported in the literature by comparing them with the lower bounds and optimal solutions for identical bins. Computational results show that the average gaps are 8.97% and 13.41%, respectively, for H1 and H2 compared with lower bounds, and 5.26% and 6.26% compared with optimal solutions for identical bins. We also found that we can save 6.67% of space, on average, by considering variable sized bins instead of a bin packing problem with identical bins.     

On the computation of the pure Neumann problem in 2-dimensional elasticity

The accurate computation of stress intensity factors (SIFs) plays a decisive role in the determination of crack paths. The calculation of SIFs with the help of singular weight functions leads to pure Neumann problem for anisotropic elasticity in a plane domain with a crack. Here a method is presented to overcome the specific numerical difficulties which arises while calculating these solutions with Finite Element methods. The accuracy and advantage of this method are shown by a numerical example, the calculation of SIFs of a compact tension specimen.      

Solution of heat-conduction problem with variable heat-exchange coefficient

Exact solution is obtained in the form of an infinite series of the heat-conduction equation with boundary condition of the third kind and time-variable heat-exchange coefficient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.18, No.1, pp. 133–138, January, 1970.     

A periodic problem in viscoelasticity with variable coefficient

A numerical method is proposed for solving a periodic problem for a material subjected to dynamic and thermal loading. Because of the considerable variations involved, a law of viscoelasticity of the fluid type with variable coefficients is adopted: secular terms of displacement and strain are brought into evidence. A theoretical asymptotic stability result of the related Cauchy problem makes it possible to measure a priori the rate of convergence of this solution towards the solution the periodic problem. The behaviour predicted for the solutions is in fact observed in the examples presented. A Finite Element Method is used in combination with a Runge-Kutta method. In the case of the Maxwell law, a theoretical condition is explicitly provided for numerical stability that is independent of the space discretization, and error estimates are given for the approached solution. These theoretical results are tested numerically on the examples provided. Lastly, the method proposed is applied to an example where the loading comes within the scope of research on an aircraft turbine blade during flight or at overspeed. The results lead to a better understanding of stress development and distribution, and indicate areas of high stress concentration that correspond to the real cases of damage observed.     

An experimental stationary quadrotor with variable DOF

Unmanned air vehicles (UAV) and especially quadrotors have drawn great attention in recent years because of their maneuverability, ease of design and control. Most of the works concentrate mostly on control; yet, design and communication are also some sub-topics. In this research, a stationary, four rotor air vehicle with limited/controlled degree of freedom is constructed so that various control algorithms and their changing effects with varying vehicle dynamics can be studied on the ground for safety purposes. Ascending/descending, pitch/yaw/roll motions can be limited/controlled by setting the vehicle’s degree of freedom mechanically, resulting better net observability of the control algorithms on the vehicle’s dynamic performance. Design, in terms of mechanics, mechatronics and software is presented and the usability of the system is shown. Parallel self tuning fuzzy PD + PD control is applied to the system for preliminary studies and results are discussed. Inspite of the sensor noise, satisfactory pitch/roll/yaw control is achieved.     

Asymptotic approach to transient thermal shock problem with variable material properties

In this paper, an asymptotic approach is proposed to solve the transient thermal shock problem with variable material properties. The governing equations of isotropic elastic medium with temperature-dependent properties are derived in the context of the Lord–Shulman generalized theory of thermoelasticity, where the higher-order expansion with respected to increment temperature of the Helmholtz free energy is used to describe the relation of each material parameter with real temperature. Then, the layer method is used to deal with the variation of material properties with real temperature, and a system with discrete linear equations is obtained by ignoring some higher-order quantities. This system is then solved analytically by the integral transform method, where the Laplace transform technique and its limit theorem is employed to deal with these linear partial differential equations. This asymptotic approach is applied to solve the thermoelastic response of a thin plate with variable material properties. The asymptotic solutions of the displacement, temperature and stresses, induced by a sudden temperature rise at the boundary of thin plate, are obtained. The corresponding results for each physical field are discussed, as well as the comparison with the results obtained from the case with constant properties is also conducted to evaluate the effect of temperature dependency of material properties.     

An integral equation method for the numerical solution of a Dirichlet problem for second-order elliptic equations with variable coefficients

We study how fiber-reinforced materials will naturally undergo swelling deformations in which a relatively greater stretch occurs transverse to the fibers than in the fiber direction. This means that a pattern of initially curved fibers prior to swelling will tend to straighten out as swelling proceeds. This can lead to swelling-induced deformations with a high degree of localized shearing and significant overall twisting. Such a process is examined for a plane strain swelling deformation that combines twist with radial expansion. Analytical results are obtained for both types: small and large swelling. Of particular interest is the relation of the extensible fiber theory to a theory for inextensible fibers. We examine the extent to which the former approaches the latter in the limit as the fibers are taken to be progressively stiffer.     

考虑拉剪耦合的二维编织物各向异性超弹性本构模型

基于连续介质力学理论,提出了一种考虑二维编织物拉剪耦合作用的各向异性超弹性本构模型。该模型中应变能被分解为纤维拉伸应变能和拉剪耦合作用下的剪切应变能两部分。给出了模型参数的确定方法,通过拟合实验数据,得到了本构模型参数。利用确定的本构模型对文献中不同预拉状态下的镜框剪切实验进行了预测,通过与实验结果对照,验证了所提出的本构模型正确性。该模型不仅具有明确的物理意义且参数确定简单,为更加全面精确的二维编织物成型有限元分析奠定了理论基础。     

A variable redefinition approach for the lot sizing problem with strong set-up interactions

We address a variant of the Joint Replenishment Problem, in which the products can only be produced in fixed proportions to each other. Such problems occur commonly in the manufacture of sheet metal and die-cast parts and some chemical products. We call it the Strong Interaction Problem (SIP). The general instance of the problem is NP-complete while single nest instances are polynomially solvable. We establish the boundary at which the problem becomes hard. We also present an exact algorithm for solving the problem using a variable redefinition approach. Computational testing on randomly generated problems indicates that our algorithm is several orders of magnitude faster than solution of the problems without reformulation using existing algorithms and commercial software.     

An experiment investigating the application of clustering procedures and similarity coefficients to the GT machine cell formation problem

This paper reports the development of a number of similarity-based coefficients designed for applying hierarchical cluster analysis to the group technology machine cell formation problem. The paper also discusses an experimental investigation applying these and other well-known similarity coefficients in conjunction with some well-known clustering algorithms. The mixture model experimental approach is used for the investigation. A number of problems were generated via simulation, randomly ‘mixed’ to hide the original cellular structure, and the clustering techniques applied. Extensions of prior research include the development of new similarity coefficients, their comparative evaluation, and the incorporation of the concept of part ‘weighting’ into the cluster analysis, and hence, cell formation     

Electronic structures of quinizarin complexed with TiO2 clusters

Electronic structure calculations using the semiempirical method PM3 were performed on quinizarin complexed with TiO₂ clusters. At first, electronic structure calculations of quinizarin complexed with small TiO₂ clusters were performed to check a reliability of the parameters. The calculated transition energies were correlated to the observed absorption spectra. Then, TiO₂ cluster was expanded into rutile type cluster which contained 11 Ti⁴⁺ ions. The LUMO of quinizarin complexed with the cluster was greater than the CB of the matrix. The replacements of Ti⁴⁺ ions by Si⁴⁺ ions changed the densitiy of states of the matrix. The increase of Si⁴⁺ sites shifted the CB to larger energy, and a change of relative energy level of the CB to the LUMO of the dye was observed. This result was consistent with a consideration from the TiO₂ content dependence of the fluorescence lifetimes of quinizarin.     

A multi-objective particle swarm optimisation algorithm for unequal sized dynamic facility layout problem with pickup/drop-off locations

This paper deals with a multi-objective unequal sized dynamic facility layout problem (DFLP) with pickup/drop-off locations. First, a mathematical model to obtain optimal solutions for small size instances of the problem is developed. Then, a multi-objective particle swarm optimisation (MOPSO) algorithm is implemented to find near optimal solutions. Two new heuristics to prevent overlapping of the departments and to reduce ‘unused gaps’ between the departments are introduced. The performance of the MOPSO is examined using some sets of available test problems in the literature and various random test problems in small, medium, and large sizes. The percentage of improvements on the initial solutions is calculated for small, medium and large size instances. Also, the generation metric and the space metric for non-dominated solutions are examined. These experiments show the good performance of the developed MOPSO and sensitivity analysis show the robustness of the obtained solutions.     

Synthesis of uniformly sized Cu2O crystals with star-like and flower-like morphologies

Uniformly sized single-crystalline Cu₂O crystals with star-like and flower-like morphologies have been successfully prepared via the reaction of d-glucose, copper (II) chloride and sodium hydroxide in aqueous solution. The products were characterized by X-ray powder diffraction (XRD), transmission electron microscopy (TEM) and electron diffraction (ED).     

A traveling salesman problem with time windows for the last mile delivery in online shopping

With the fast growth of the parcel volume of online shopping, home delivery (delivering parcels to customers’ homes or workplaces) has accentuated the pressure on last mile delivery actors. Customer pickup, which allows customers to pick up their parcels from shared delivery facilities near them, has become widely popular. This study introduces a novel travelling salesman problem with time windows for the last mile delivery in online shopping. The purpose is to find a minimum cost tour over given customers and/or shared delivery facilities (SDFs) in which unvisited customers are assigned to the SDFs. A general variable neighbourhood search heuristic is developed to solve the problem. Computational results corroborate that the proposed heuristic is competitive relative to well-known algorithms.     

Hotelling's T2 control chart with variable sampling intervals

Hotelling's T₂ chart is the most widely used multivariate procedure to control changes in the mean vector of p correlated quality characteristics. In this paper, it is shown how to increase the efficiency of the test using the variable sampling interval technique. Given a control scheme with constant size and frequency of sampling, tables are produced that give a scheme, with two possible periods of time between samples, that is equivalent to the standard procedure when the process is in control. However, the new chart, as it uses two possible intervals between samples, is faster in detecting a change in the process. Various alternatives are given for the possible users of this method.     

An approximate method for evaporation problem with mushy zone

In the present paper, a simple mushy zone model is used to track the moving boundaries in an evaporation problem in which the vapor is removed upon formation. Two main parameters for the mushy zone model are analyzed as well as their effect on the movement of the moving boundaries and the thickness of the mushy zone. A new approximate method is developed for analysis and tracking the moving boundaries appears throughout the process. The proposed method mainly based on applying the boundary integral equation corresponding to each phase in such a way that the associated boundary and initial conditions as well as energy equations at the moving boundaries achieved with minimum error and low number of iterations. The results of the present paper seem to be good because there are neither analytical or numerical solutions available.     

An inverse heat conduction problem with heat flux measurements

Using heat flux measurements as additional information to solve inverse heat conduction problems was and is still rarely employed. Lot of disadvantages linked to heat flux measurement specificities (local disturbance, intrusive measurement, lack of knowledge and proficiency, etc.) make people prefer temperature measurements which are well documented and very widespread. Solving inverse heat conduction problems with heat flux measurements is quite different than the one which uses temperatures and need to be investigated deeply. In this work, this problem is approached through the solution of a bioengineering problem consisting in the development of a non‐invasive blood perfusion probe. The effort here is focused on the development of a methodology for the estimation of time‐dependent blood perfusion from heat flux measurements. The physical probe incorporates a thin heat flux sensor, which is placed in contact with the tissue region where the perfusion is to be measured. The sensor records the heat flux due to an imposed thermal event, which is achieved by air flow. A one‐dimensional mathematical model is used to simulate the thermal event occurring at the contact region holding between the probe and the tissue. A combined parameter and function estimation procedure is developed to estimate simultaneously time‐dependent blood perfusion and thermal contact conductance between the probe and the tissue. The robustness of the method was demonstrated through several test cases using simulated data. The presented examples include various functional changes in the time evolution of blood perfusion. Results from this study have shown the feasibility of solving inverse problems with heat flux measurements and the two unknowns are estimated with no a priori information about their functional forms. Copyright © 2006 John Wiley & Sons, Ltd.     

An effective simultaneous approach with variable time nodes for dynamic optimization problems

An effective simultaneous approach with variable time nodes is proposed to solve the dynamic optimization problems with multiple control components, where the variable time nodes for each control component are considered as parameters directly and the interval between the neighbouring variable nodes is further refined uniformly to ensure accuracy. Consequently, the method does not treat all the nodes as parameters to ensure efficiency. The gradient formulae and the sensitivities of the states with respect to the controls and the variable time nodes are further derived to solve the nonlinear programming problem transformed from the original dynamic optimization problem. The complete framework and detailed steps of the proposed method are also given. Two classic constrained dynamic optimization problems have been tested as an illustration, and detailed comparisons of the reported literature methods are carried out. The research results show the characteristics and the effectiveness of the proposed approach.     

An order-level-lot-size model with uniform replenishing rate and variable mark-up of prices

This paper considers the interaction of an order-level—lot-size model having uniform replenishing rate with the marketing policy involving mark-up of prices varying with capital intensity and turnover of finished product. Under two different policies considered in this paper, the optimum values of decision variables are obtained so that the profit for the system is maximized.