Material Distribution Problem Research Articles

Optimization of emergency material distribution routes in flood disaster with truck‐speedboat‐drone coordination

AbstractTo improve the effectiveness of flood disaster relief operations, by ensuring timely and accurate delivery of urgently needed supplies to affected areas, this study focuses on the problem of emergency material distribution during floods. With the objective of minimizing the overall delivery time of emergency materials, we propose a coordinated optimization model that integrates trucks, speedboats, and drones for effective distribution of emergency supplies in flood‐affected areas. To solve this optimization problem, we introduce an improved adaptive large neighborhood search (IALNS) algorithm, which builds on the traditional ALNS framework through refined tuning of deletion and insertion operators. Comparative analyses are conducted with a genetic algorithm, simulated annealing algorithm, and tabu search algorithm. The results reveal that the average performance gap of IALNS compared to these methods is 91.13%, 152.72%, and 16.92%, respectively. The experimental results demonstrate that the efficiency of the proposed model and algorithm in addressing the emergency supply distribution problem during flood disasters, highlighting the superior performance of IALNS. This research contributes to enhancing disaster response strategies, ultimately leading to improved outcomes for flood‐affected communities.

A dynamic material distribution scheduling of automotive assembly line considering material-handling errors

PurposeIn a kitting supply system, the occurrence of material-handling errors is unavoidable and will cause serious production losses to an assembly line. To minimize production losses, this paper aims to present a dynamic scheduling problem of automotive assembly line considering material-handling mistakes by integrating abnormal disturbance into the material distribution problem of mixed-model assembly lines (MMALs).Design/methodology/approachA multi-phase dynamic scheduling (MPDS) algorithm is proposed based on the characteristics and properties of the dynamic scheduling problem. In the first phase, the static material distribution scheduling problem is decomposed into three optimization sub-problems, and the dynamic programming algorithm is used to jointly optimize the sub-problems to obtain the optimal initial scheduling plan. In the second phase, a two-stage rescheduling algorithm incorporating removing rules and adding rules was designed according to the status update mechanism of material demand and multi-load AGVs.FindingsThrough comparative experiments with the periodic distribution strategy (PD) and the direct insertion method (DI), the superiority of the proposed dynamic scheduling strategy and algorithm is verified.Originality/valueTo the best of the authors’ knowledge, this study is the first to consider the impact of material-handling errors on the material distribution scheduling problem when using a kitting strategy. By designing an MPDS algorithm, this paper aims to maximize the absorption of the disturbance caused by material-handling errors and reduce the production losses of the assembly line as well as the total cost of the material transportation.

Topology optimization of engine mounting bracket

Topology optimization is an effective approach for optimizing the layout of the component under operating constraints without losing its functionality. Density based approach is usually employed for solving material distribution problems resulting in minimization of structural compliance. Finite element method is proven to be the best tool for analyzing components under various circumstances. The need of this research is to explore the process of material removal in density based topology optimization which is exemplified by analysing an engineering component. In this work, Engine mounting bracket is chosen for optimization as it mounts the engine with the chassis. Design enhancement is subjected to 5% and 10% mass reduction percentages. Static structural analysis was performed and the results were compared for the basic and optimized design models. As a result, 9.97% mass reduction, a change of 27.9 MPa in maximum stress and change of 0.04526 mm in deformation were achieved.

Integrated topology and packaging optimization for conceptual-level electric vehicle chassis design via the component-existence method

Conventional vehicle architectures are undergoing significant transformation as automakers embrace electrification. With increased emphasis on lightweight structures design and efficient packaging of new electric powertrains, numerical tools are now essential to help solve these complex material and component distribution problems. To address these challenges, methods for integrated topology and packaging optimization (iTOPO) have been developed to couple these problem statements and form dynamic component-structure interactions. In this work, a component-existence approach is used for conducting iTOPO of self-contained electric vehicle chassis structures to demonstrate the benefits and scalability of this emerging methodology. Examples focus on incorporating simplified components for battery modules and electric motors within the underlying vehicle structure, integrating up to 43 components simultaneously in a 3D design domain. Here, discussion highlights the development of unique integrated layouts, methodology tunability, and practical insights of the formed component-structure interactions. iTOPO results are also compared to equivalent topology-only problems and show less than a 10% difference in compliance despite the addition of various complex integration requirements (e.g. multiple geometries, packaging symmetry).

Topology optimization of structures subject to non-Newtonian fluid–structure interaction loads using integer linear programming

This paper proposes a topology optimization design method for fluid–structure interaction (FSI) problems considering Non-Newtonian fluid such as blood and polymer solution. Non-Newtonian fluid does not obey the Newtonian relationship between the shear stress and shear rate. Fluid–structure interaction involving Non-Newtonian fluid has a wide range of application in oil and gas, chemical, food industries, microfluidics, and bio-engineering. We solve a compliance minimization problem subject to volume constraints of structures under FSI loads considering Non-Newtonian laminar flow. The structure is considered to undergo small deformation. The TOBS (Topology Optimization of Binary Structures) method is applied to solve the material distribution problem. The TOBS approach uses binary {0,1} design variables, which can be advantageous when dealing with design-dependent physics interactions, e.g., in cases where fluid–structure boundaries are allowed to change during optimization. The finite elements method is used to solve the fluid–structure equations and output the sensitivities using automatic differentiation. The TOBS optimizer provides a new set of {0,1} variables at every iteration. Optimization results show that Non-Newtonian effects have a significant influence on FSI design.

A genetic algorithm of optimal design of beam at restricted sagging

A genetic algorithm for solving the problem of optimal beam material distribution along length at a given restriction on maximum sagging value is suggested. A review of literature sources is conducted and it was shown that existing solutions cover partial cases only in which the position of the point with maximum sagging was defined previously. In the paper presented I-section beam with constant proportions is considered, i.e., beam width, caps, and web thickness are proportional to beam height in the current cross-section. A statically determined beam is being considered. The load applied to a beam can be arbitrary, including cases of non-symmetrical loads and differently oriented ones. The position of point(s) at which beam sagging is maximum are unknown at the beginning of optimization and are found in the process solution. The problem is solved in the linear definition. Beam mass was assumed to be an optimization criterion. The method of finite differences is used for beam sagging finding, i.e., for the solution of the differential equation of the bending beam with a variable cross-section. Discretization allows transforming the problem of design into the problem of beam height determination at a system of reference points. At this stage, found values of beam height must satisfy restrictions on reference point displacements. The suggested technique allows controlling beam displacement quite flexibly because restrictions on point displacement are considered separately and do not depend on each other. The suggested objective function is the linear superposition of beam mass and the possible penalty in case of beam maximum sagging over exceeding predefined values. The application of a genetic algorithm allows getting sets of beam thicknesses those, which guaranty reaching the minimum of the objective function. The model problem is solved. It is shown that the suggested algorithm allows effectively solves problems of optimal design of beams with restrictions on the maximum sagging value. The suggested approach can be developed for strength restrictions, statically undetermined structures, etc.

Intelligent material distribution and optimization in the assembly process of large offshore crane lifting equipment

The constraint of the material distribution for offshore crane lifting equipment is complicated. Taking into account the characteristics of the material distribution problem of the general assembly of offshore lifting equipment, this paper proposes a scheduling method based on the improved Particle Swarm Optimization algorithm by considering vehicle material matching relationships. Firstly, this we establish a vehicle scheduling model for the final assembly logistics distribution process and then propose a two-stage hierarchical solution framework for minimizing the number of vehicles and the transportation distance. Secondly, the optimization aims to minimize the number of vehicles, we obtain the optimal solution by CPLEX Optimizer. The vehicle transportation distance is then optimized by the improved particle swarm optimization algorithm. The initial solution performance of the algorithm is improved by our heuristic rules. The discretization of the problem is achieved by coding, decoding and location updating methods according to the characteristics of the problem. Additionally, the updating mechanism of simulated annealing algorithm is introduced to update the location to avoid the algorithm falling into local optimum. Through case analysis and comparisons, the improved Particle Swarm Optimization based scheduling method proposed in this paper combined with the vehicle-material matching relationship can effectively improve the efficiency of the material distribution with better performance.

Research on Multiobjective Location of Urban Emergency Logistics under Major Emergencies

After the outbreak of major emergencies, the scheduling of emergency supplies is the key to the emergency rescue work, and the establishment of appropriate emergency logistics centers plays a crucial supporting role. In order to deal with the problem of emergency facility location and material distribution in urban emergency logistics system, this paper establishes a dual objective mixed integer nonlinear programming (MINLP) model with the objective of minimizing the emergency rescue time and maximizing the satisfaction rate of emergency material demand, designs a genetic algorithm to solve the emergency logistics location and allocation model, and obtains the Pareto optimal solution set of the model. Finally, a case study of COVID-19 epidemic in Beijing-Tianjin-Hebei region was carried out to verify the feasibility and effectiveness of the model and algorithm in the actual application, which can provide reference and suggestions for the location and material distribution of urban emergency logistics centers.

Optimization of Material Distribution Scheduling Based on Mixed Distribution Strategy

In order to effectively solve the scheduling problem of mixed flow assembly line material distribution, an optimization method of material distribution scheduling based on mixed distribution strategy was proposed. Firstly, the mixed distribution strategy is described, and the distribution strategy of materials is divided by taking the refrigerator assembly line as an example. Then the problem of mixed distribution strategy is simplified and a mathematical model is established for scheduling optimization. The construction of the model is different from the existing calculation of material consumption based on working hours. This model is based on the quantity of products on line, making the actual material consumption more accurate. Finally, an example is given to verify the feasibility of the model.

A topology optimization implementation for depth-of-focus extension of binary phase filters

Binary phase filters (BPFs) form a special class of optical structure characterized by their distinct concentric rings of alternating 0-π phases. Once placed in the pupil plane of a focusing lens, a BPF generates a sharp elongated focus, which can be utilized for diverse applications ranging from optical trapping to focus scanning microscopy. As demand for BPFs continues to expand, new design techniques are required to tune and optimize filter performance; in this paper, a topology optimization method is presented to extend BPF’s depth-of-focus while maintaining a sharp lateral resolution. In general, binary phase filters can be completely described by three designable characteristics: the radial location of each ring, the width of each ring, and the total number of rings. Conventional BPF design methods typically only consider two of these key design characteristics, often with a predefined number of rings and subsequent sizing optimization of radial locations and widths. Furthermore, these methods often rely on inefficient non-deterministic optimizers like particle swarm and simulated annealing. These implementations ultimately limit design freedom and often require manual investigation of multiple configurations at the expense of computational time and solution quality. Instead, this paper introduces topology optimization (TO) as the first and only method for BPF generation capable of considering all three design characteristics simultaneously and without any predefined assumptions. Here, the TO-based approach is first initialized with a series of concentric rings to cover the entire design domain. Then, similar to classical material distribution problems, the phase value of each concentric ring is optimized directly to satisfy the objective and constraint functions using gradient-based algorithms. This paper describes the new TO-based approach and demonstrates fundamental capabilities and design advantages. Numerical results are validated experimentally and compared with existing approaches with an emphasis on quantitative performance, non-intuitive structure generation, and computational efficiency.

A novel fuzzy bi-objective vehicle routing and scheduling problem with time window constraint for a distribution system: A case study

In the process of hazardous material transportation, the risk is a significant factor that should be considered due to the potential severe consequence of an incident. Regardless of risks, time is a paramount concern that should be considered in hazardous material transportation. In this way, this paper introduces a bi-objective model for a vehicle routing and scheduling problem of hazardous material distribution problems under the fuzzy condition to minimize both total distribution time and risks. In the proposed model, the fuzzy inference system and fuzzy failure mode and effects analysis are applied to identify and calculate the high-level risks instead of the previous simple methods for the first time. Moreover, Jimenez method and fuzzy goal programming are respectively utilized to convert the fuzzy bi-objective model into the same crisp and single-objective one. Besides, to cope with the NP-hardness of the large-sized problems, two meta-heuristic algorithms namely invasive weeds optimization and genetic algorithm is used, and several sensitivity analyses are performed to prove the efficiency of the proposed approach. The performance of the proposed algorithms is also assessed through a comparative study. Finally, the proposed model is implemented to a real case study to prove the validity of the model.

Workstation-oriented distribution optimization of shipbuilding materials

The optimization of material distribution is of great importance on shipbuilding project, which determines whether the production capacity of the ship is fully embodied. A workstation-oriented material distribution problem is formulated with reference to the production characteristics of shipyards. This problem can be considered as a complex vehicle routing problem (VRP) with capacity constraints, time windows and multiple distribution centers. In order to minimize the impact of distribution problems on production, a multi-population genetic algorithm (MPGA) that can minimize the sum of earliness and tardiness penalties is proposed in this paper. The proposed algorithm looks for near-optimal solutions for assigning distribution tasks and optimizing vehicle routing. Then, the evaluation of the solutions generated with MPGA is achieved with a priority-based heuristic algorithm. Simulation results of different cases show that the proposed MPGA allows logistics distribution system to operate more efficiently and solutions can be improved by 71% on average compared to those obtained with the traditional priority rule method.

Thermo-fluid Topology Optimization and Experimental Study of Conformal Cooling Channels for 3D Printed Plastic Injection Molds

Abstract With the advent of additive manufacturing, innovative design methods, such as network-based techniques, and structural topology optimization have been used to generate complex and highly efficient cooling systems in recent years. However, methods that incorporate coupled thermal and fluid analysis remain scarce. In this paper, a coupled thermal-fluid topology optimization algorithm is introduced for the design of conformal cooling channels. The problem is formulated based on a coupling of Navier- Stokes equations and convection-diffusion equation. The problem is solved by gradient-based optimization after analytical sensitivity derived using adjoint method. With this method, the channel position problem is replaced to a material distribution problem. The material distribution directly depends on the effect of flow resistance, heat conduction, natural and forced convection. The algorithm leads to a two-dimensional conceptual design having optimal heat transfer and balanced flow, which is further transformed into three-dimensional cooling channel design. Here, a comprehensive study is presented, starting from design, simulation, 3D printing process and experimental testing of an injection mold with conformal cooling channels in industrial production environment. A traditional mold model is provided by an industrial collaborator. To enhance the overall thermo-fluid performance of the mold and improve final product quality, a redesign of this mold core is done with conformal cooling channels inside. The final design is 3D printed in pre-alloyed tool-steel powder Maraging Steel using Truprint 3000 metal 3D printing machine. The printed core required some heat treatment and finishing processes and added features to be incorporated to make it production ready. Once all the preparation was complete, the core was tested experimentally in a multicavity injection molding machine in real industrial environment at our industrial partner’s production facility. This paper describes all the steps starting from design, analysis, die 3D printing and finally ending at final experimental testing, as well as recommendations for tool designer and injection molding industry to implement additive manufacturing for their benefit. This paper is not just focused on a specific aspect such as design, simulation or manufacturing, but rather a comprehensive paper presenting a case study on implementation of topology optimization and additive manufacturing in real life industrial production scenario.

Model and Algorithm for the Large Material Distribution Problem in Maritime Transportation

ABSTRACT Hu, H., 2018. Model and algorithm for the large material distribution problem in maritime transportation. The ocean shipping industry has a monopoly on transportation of large volumes of cargo, which is an important factor in most situations. This paper presents an innovative maritime transportation model and algorithm to address the large material distribution problem in emergency situations. The ship routing problem is one of the most popular variations of the standard vehicle routing problem (VRP). The split delivery VRP with open routes is considered in this paper with the application to the distribution of relief-related materials. It is assumed that fleets start from one depot but are not obligated to return to the same depot, that the demands of customers can be fulfilled by more than one ship, and that the travel speed on each route is variable. The objective of the model is to minimize the total travel time, and the travel speed is defined as a continuously decreasing function with respe...

Continuous optimization of adaptive quadtree structures

We present a novel continuous optimization method to the discrete problem of quadtree optimization. The optimization aims at achieving a quadtree structure with the highest mechanical stiffness, where the edges in the quadtree are interpreted as structural elements carrying mechanical loads. We formulate quadtree optimization as a continuous material distribution problem. The discrete design variables (i.e., to refine or not to refine) are replaced by continuous variables on multiple levels in the quadtree hierarchy. In discrete quadtree optimization, a cell is only eligible for refinement if its parent cell has been refined. We propose a continuous analogue to this dependency for continuous multi-level design variables, and integrate it in the iterative optimization process. Our results show that the continuously optimized quadtree structures perform much stiffer than uniform patterns and the heuristically optimized counterparts. We demonstrate the use of adaptive structures as lightweight infill for 3D printed parts, where uniform geometric patterns have been typically used in practice.

Optimization of custom cementless stem using finite element analysis and elastic modulus distribution for reducing stress-shielding effect.

This work proposes a methodology involving stiffness optimization for subject-specific cementless hip implant design based on finite element analysis for reducing stress-shielding effect. To assess the change in the stress-strain state of the femur and the resulting stress-shielding effect due to insertion of the implant, a finite element analysis of the resected femur with implant assembly is carried out for a clinically relevant loading condition. Selecting the von Mises stress as the criterion for discriminating regions for elastic modulus difference, a stiffness minimization method was employed by varying the elastic modulus distribution in custom implant stem. The stiffness minimization problem is formulated as material distribution problem without explicitly penalizing partial volume elements. This formulation enables designs that could be fabricated using additive manufacturing to make porous implant with varying levels of porosity. Stress-shielding effect, measured as difference between the von Mises stress in the intact and implanted femur, decreased as the elastic modulus distribution is optimized.

Application Designing Additive Structures

The objective of this paper is to demonstrate the opportunities of topology optimization applied to additive technology which will permit to design ultra-light structures practically without regard to the technological limits. The article gives a brief historical overview of the mutual influence of structures, materials and manufacturing technologies. The additive technology seems to have the broadest opportunities for producing existing structures using conventional materials without design changes. A hypothetical variable density material provides the means to solve an auxiliary problem of optimal material distribution considering stress or stiffness constraints.The special optimization algorithm allows the optimal topology layout to be found which will have a minimum value of the integral characteristic, called “load-carrying factor” (LCF). The LCF is a powerful tool for estimating the perfection limit of any structural and technological solution. Along with the optimal structure, such solutions are difficult for manufacturing using conventional materials and technologies. A creation of real material with the characteristics of hypothetical material is considered as one of the nearest areas of additive technology's development for finding optimal structures.

A bi-level network interdiction model for solving the hazmat routing problem

In the current work, we considered the problem of hazardous material distribution where the distributer chooses the routes on the network, and a regulatory agency controls the behaviour of the distributer to traverse the specified routes. In these circumstances, the distributer sets to select some routes to minimise the total distributing costs. Mostly, this occurs due to selecting risky arcs in which more individuals are exposed to risk. To prevent this and increase the capability to deal with the risk of hazardous material transportation through roads, the regulatory agency obliges carriers to traverse through the most secure arcs, though imposing more distribution costs. The problem is modelled as a bi-level routing problem. The bi-level model is difficult to solve and may be ill-posed. Two meta-heuristic algorithms are proposed to solve the bi-level model, and some randomly generated problems are applied to show the applicability and efficiency of the proposed algorithms.

An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases

Finding the optimum distribution of material phases in a multi-material structure is a frequent and important problem in structural engineering which involves topology optimization. The Bi-directional Evolutionary Structural Optimization (BESO) method is now a well-known topology optimization method. In this paper an improved soft-kill BESO algorithm is introduced which can handle both single and multiple material distribution problems. A new filtering scheme and a gradual procedure inspired by the continuation approach are used in this algorithm. Capabilities of the proposed method are demonstrated using different examples. It is shown that the proposed method can result in considerable improvements compared to the normal BESO algorithm particularly when solving problems involving very soft material or void phase.

Distributed material density and anisotropy for optimized eigenfrequency of 2D continua

A practical approach to optimize a continuum/structural eigenfrequency is presented, including design of the distribution of material anisotropy. This is often termed free material optimization (FMO). An important aspect is the separation of the overall material distribution from the local design of constitutive matrices, i.e., the design of the local anisotropy. For a finite element (FE) model the amount of element material is determined by a traditional optimality criterion (OC) approach. In this respect the major value of the present formulation is the derivation of simple eigenfrequency gradients with respect to material density and from this values of the element OC. Each factor of this expression has a physical interpretation. Stated alternatively, the optimization problem of material distribution is converted into a problem of determining a design of uniform OC values. The constitutive matrices are described by non-dimensional matrices with unity norms of trace and Frobenius, and thus this part of the optimized design has no influence on the mass distribution. Gradients of eigenfrequency with respect to the components of these non-dimensional constitutive matrices are therefore simplified, and an additional optimization criterion shows that the optimized redesign of anisotropy are described directly by the element strains. The fact that all components of an optimal constitutive matrix are expressed by the components of a strain state, imply a reduced number of independent components of an optimal constitutive matrix. For 3D problems from 21 to 6 parameters, for 2D from 6 to 3 parameters, and for axisymmetric problems from 10 to 4 parameters.