Mathematical Optimization Model Research Articles

An Improved Adaptive Genetic Algorithm for U-shaped Disassembly Line Balancing Problem Subject to Area Resource Constraint

The disassembly, recovery, and reuse of waste products are attracting more and more attention. It not only saves resources and protects the environment but also promotes economic development. In a disassembly process, the disassembly line balancing problem is one of the most important problems.At present, the consideration of the space area of workstations is relatively small, and the relatively large use of the area of workstations can also better reduce costs. Aiming at the balancing problem of u-shaped disassembly line, a single-objective optimization mathematical model with area constraints is established with the goal of maximizing profits. In order to solve this problem, we refer to Adaptive Genetic Algorithm and improve its crossover and mutation operator. We adopt elite strategy to avoid premature convergence and improve the global search ability. Its effectiveness is proved by comparison with the optimization results of CPLEX. Experimental results also verify the feasibility of the proposed model and the superiority of the improved Adaptive Genetic Algorithm when solving large-scale instances over another algorithm. At the same time, the experimental results also verify the superiority and effectiveness of the improved Adaptive Genetic Algorithm algorithm by comparing with Random Search.

Optimizing the ground intra-city express delivery network: An integrated multiple centrality assessment, multi-criteria decision-making, and multi-objective integer programming model

Optimization of an intra-city express delivery network from three to two levels is of great interest to suppliers and customers for reducing costs and improving service efficiency. One feasible solution is to identify critical nodes in the three-level network and upgrade them as transshipment facilities in the two-level one. However, traditional optimization models seldom combine empirical business data, composite metrics, and objective evaluation rules. We proposed an approach integrating empirical data, multi-criteria decision-making methods based on the real-world application of the SF Express Chengdu branch. We also developed a mathematical optimization model using statistical and operations management techniques combined with logistics expertise for a location decision. First, the appropriateness of each service point as a candidate transshipment facility is evaluated from internal and external perspectives by applying multiple centrality assessment from complex network theory and fuzzy Technique for Order Preference by Similarity to an Ideal Solution, respectively. Second, 16 candidate transshipment facilities are selected by combining these two ways. Then, a multi-objective integer programming model is built to obtain the optimal number, locations of transshipment facilities, and the corresponding service points covered by each transshipment facility. Using this multi-methodologic approach, we show that the optimized two-level network is economically feasible and simply applicable, with the total cost and average delivery time reduced by 18.41% and 6 h, respectively. This article is of practical significance and provides an important reference for optimizing ground express service networks for other large cities.

A Method for Dynamic Insertion Order Scheduling in Flexible Job Shops Based on Digital Twins

Various production disturbances occurring in the flexible job shop production process may affect the production of the workshop, some of which may lead to the prolongation of production completion time. Therefore, a flexible job shop dynamic scheduling method based on digital twins is proposed and a dynamic scheduling framework is constructed. Compared with the traditional workshop, the digital twin-based flexible job shop can upload the relevant production data of the physical workshop to the data management center in real time, and after fusion processing the data can work cooperatively with the upper application system. Taking the dynamic disturbance of rush order insertion as an example, the dynamic scheduling of insertion order is realized based on the dynamic scheduling framework, and then the production efficiency is improved. To achieve the shortest completion time, a mathematical model for dynamic scheduling optimization is established and a genetic algorithm (GA) is applied to solve the model. Finally, a practical case is applied to show that the completion time of this algorithm is reduced by 35%, which verifies the feasibility of the proposed dynamic scheduling method.

Design and Optimization of Coal to Hydrogen System Coupled with Non-Nominal Operation of Thermal Power Unit

In an actual thermal power plant, deep peak shaving will cause thermal power units to run under non-nominal conditions for an extended period, resulting in serious problems such as increased equipment wearing, low equipment utilization efficiency and decreased benefits. To this end, in this work, both the design and optimization method for a coal to hydrogen system which is coupled with the expected non-nominal operation of thermal power units are proposed. Aiming towards maximum profit in the context of thermal power plants, a mathematical optimization model for a coal to hydrogen system based on the multi-period operating conditions of thermal power plants is established. The corresponding optimal design scheme of the coal to hydrogen system is determined using variable operating conditions. The superiority of the integrated system compared with an independent system is explored and the feasibility of the proposed method is verified by using the case study of an actual thermal power plant. The results show that compared with the independent system, the economic benefits of the integrated system can increase by 13.56%, where the sale of hydrogen in the coal to hydrogen system accounts for 60.3% of the total benefit. The main expenditure associated with the system is the purchase cost of feedstock coal, accounting for 91.8%. Since the required power and medium-pressure steam in the coal to hydrogen process are provided by thermal power units, the minimum operating load of the thermal power plant in the integrated system increases from 40% to 60.1%, which significantly improves the utilization efficiency and service life of the generator units. In addition, the proposed integration scheme of the system is simple and controllable, which can contribute to the maintenance of the safe and stable operation of power generation and hydrogen production processes. These results are expected to provide the necessary methodological guidance for the integration and optimization of coal-fired power plants and coal to hydrogen systems.

An optimization approach for parameter selection in natural history of breast cancer in China

Breast cancer is one of the most common cancers for females. In order to propose efficient screening strategies and evaluate the effect, one fundamental and important step is to choose proper parameters, i.e., transition rates, in the natural history model of breast cancer in China. There are two challenges to choosing reasonable transition rates. Firstly, the transition rates used in other countries may be not applicable to China, due to the cancer epidemiology. Secondly, little screening sample data are available, making the traditional statistical based approaches such as maximum likelihood methods fail. In this paper, we propose an optimization approach for parameter selection in the natural history of breast cancer in China. A mathematical optimization model is established based on the published statistical data. A coordinate descent algorithm is proposed to solve the resulting box-constrained and highly nonlinear problem, whose objective function does not have an explicit form. Finally, the best matching method is proposed to estimate the distributions of each transition rate. Our approach provides solid foundations to further propose reasonable screening strategies for breast cancer in China and analyze the economic burden of breast cancer.

Reinforcement Learning-Based Rumor Blocking Approach in Directed Social Networks

Social network platforms (such as Facebook, Wechat, and Weibo) can help people build relationships, transmit information, and make daily communication more convenient. However, in recent times, the rapid spread of misinformation and rumors has been causing public panic. Especially, during the epidemic, the severity of the crisis has been further exacerbated. Therefore, in this article, we study the influence minimization problem and propose a practical framework to address the rumor propagation problem. At first, we formulate the influence minimization problem as the mathematical optimization model. Then, we leverage the multistage competitive linear threshold model to reflect the activation status of network nodes. We propose a practical framework, called CCSQ, to select the seed nodes, which consists of community detection, candidate seed nodes, and the seeding algorithm with the Q-learning method. In particular, we construct the action, reward, and state of the Q-learning-based seeding algorithm to adaptively generate the seed nodes. Experimental results show that the proposed approach achieves smaller rumor propagation than the baseline algorithms.

A jerk-limited heuristic feedrate scheduling method based on particle swarm optimization for a 5-DOF hybrid robot

Compared with machine tools, five degrees-of-freedom (DOFs) hybrid robots have been widely concerned in the manufacturing of large complex surface parts due to their characteristics of high flexibility and large workspace. It is of great significance to schedule the time-optimal feedrate that satisfies the high-order constraints (e.g., jerk or jounce) in the toolpath and joint systems to achieve the high-precision and high-efficiency machining of the robot. To overcome the complexity of five-axis feedrate scheduling and improve the optimality of machining time, this paper proposes a jerk-limited heuristic feedrate scheduling (HFS) method with near-optimal time. Firstly, the analytical equations between all constraints and the parametric feedrate are derived, and the mathematical model for control points optimization of the parametric feedrate profile expressed by a B-spline curve is established. Then, combined with the global search particle swarm optimization (GSPSO) algorithm, a proposed moving window planning method optimizes a small number of control points so that the feedrate curve has enough rising space. Subsequently, to obtain the near time-optimal feedrate, the local search PSO (LSPSO) algorithm within the moving window is developed to locally adjust the non-uniformly inserted control points. Compared with the existing methods, the HFS method is beneficial to further optimize the machining time with a faster computation speed, and ensure the stability of the robot machining. Finally, simulations and experiments on the developed TriMule-800 hybrid robot verify the effectiveness of this method.

Optimizing FANET Lifetime for 5G Softwarized Network Provisioning

Recently, Flying Ad Hoc Networks (FANET) have been proposed to empower 5G networks to support complex missions and provide ubiquitous connectivity to heterogeneous devices. However, it is needed to cope with the limited UAV capabilities (e.g. limited available energy to supply engines and computing elements, limited computing capabilities), as well as with the need to provide network and application services as foreseen in highly dynamic and time varying 5G ecosystems. This paper presents for the first time a comprehensive framework that integrates a FANET with a 5G network, with the aim of providing services that can be even chained with each other. This model is comprehensive in the sense that it takes into account physical constraints of the devices, as well as features and requirements of traffic flows. For this framework, the paper proposes a mathematical optimization model, allowing Virtual Function (VF) placement and chaining, aimed at minimizing energy consumption and service unsatisfaction probabilities of the FANET as a whole without employing heuristics for the solution of the problem. Two placement strategies named MLP and WMP are introduced and compared with the standard placement strategy named NoShP. An extensive numerical analysis shows that MLP and WMP allow us to well catch network dynamics and to reduce the number of virtual functions needed while decreasing the power consumption, so increasing UAV flight time and network lifetime.

Study on the Influence of Special Vehicle Locking Mechanism on Protective Performance

In order to study the influence of various structural dimensions of the suspension floor locking mechanism on the vehicle protection performance of the special vehicle suspension floor, the finite element simulation analysis and structural optimization design of the locking mechanism are carried out. The starting load of the locking mechanism based on the occupant damage threshold was determined, the dynamic tensile loading system of the locking mechanism was designed, the accuracy of the design scheme and the finite element model was verified, and the experimental design was carried out using Latin hypercube sampling. In addition, the sensitivity analysis was carried out, the relationship between the structural size of the locking mechanism and the protective performance of the vehicle was clarified, the optimal mathematical model of the locking mechanism was established, and the Pareto solution set of the optimization model was obtained through the multi-objective genetic algorithm. The optimal design scheme of the locking mechanism was obtained by using the linear multi-criterion decision method, and the accuracy of the optimal scheme was verified by the simulation.

Optimization of Interface layout of electrical equipment using Heuristic Algorithm

Facility Layout Problem(FLP) is a major matter in the process of human-machine interface(HMI) design, which has a direct impact on how well operators perform their duties. Electrical equipment, which controls the power system, has a direct impact on how safely the system operates. The current optimization techniques prioritize improving the equipment’s performance characteristics at the expense of user aspects. This work aims to apply heuristic algorithms that introduce cognitive psychology and adopt the layout principle as a constraint condition to solve this problem. The improved analytic hierarchy process (AHP) is used to conduct the optimal design practice of the HMI of electrical switching equipment, develop the optimization mathematical model, and quantify the subjective and objective layout principles. Comparing the optimization results reveals that the genetic algorithm’s optimization impact is superior and the ant colony algorithm’s iterative pace is faster. The HMI’s optimized design based on a heuristic algorithm can improve the usability of interface operation, and has a certain reference for the optimization design of HMI of electrical equipment.

Topology optimization of robotic arm for gas drainage pipeline installation

By means of finite element analysis and topology optimization methods, the structural optimization and lightweight design of the robotic arm for the installation of gas drainage pipelines are realized, so that it can realize more complex actions under the premise of ensuring stability. SolidWorks 3D modeling and Ansys Workbench analysis software are used to build models of the robotic arm and perform static analysis. The structural design is optimized through the deformation and stress distribution when grasping the maximum weight. The topology optimization mathematical model of the variable density method and the SIMP (Simplified Isotropic Material with Penalization) interpolation model was constructed, and the topology optimization of the robotic arm was performed in the Shape Optimization module in Ansys Workbench. On this basis, the structure after topology optimization is analyzed and studied. The results show that compared with before topology optimization, the mass of the manipulator is reduced by 29.65%, and the maximum deformation and maximum stress are both reduced by 10%, which confirms the feasibility of lightweight design and structural optimization of the manipulator.

Numerical optimization of pacing strategy in cross-country skiing based on Gauss pseudo-spectral method

In cross-country skiing competitions, the choice of pacing strategy is of decisive significance to athletes' performance. A reasonable pacing strategy is essential for athletes to improve their performance. In this paper, the mathematical models of cross-country skiing simulation and pacing optimization are established, including motion model, athlete power output model, and optimization model. The actual competition data of a Chinese athlete in Guyangshu 1.5 km track was compared with the model simulation results. The whole process time error is less than 3%, which verifies the accuracy of the motion and power output model. Gauss pseudo-spectral method is applied to the optimization model. By changing the distribution of athletes' power output, the racing time is minimized under the condition that the total energy output remains unchanged. Compared with the pacing strategy before optimization, the optimized racing time was shortened by 12.6 s, which verifies the effectiveness of the optimization model. Optimized results show that in the first significant uphill section, a recommendation is to use a more conservative strategy, while in the latter half of uphill sections the power output should be increased.

Automated Sortie Scheduling Optimization for Fixed-Wing Unmanned Carrier Aircraft and Unmanned Carrier Helicopter Mixed Fleet Based on Offshore Platform

Optimizing naval aircraft deck sortie scheduling is important for improving the sortie efficiency of naval aircraft groups. It is also an important link in realizing the automated scheduling of aircraft carriers. Firstly, a single-aircraft surface transit path library was constructed. This paper used the improved A* algorithm and the optimal control deck path planning algorithm to construct the transit path library between the deck parking position and take-off position, or between warmable and non-warmable parking positions. Secondly, a mathematical optimization model was constructed for the sortie scheduling of a mixed fleet of fixed-wing carrier aircraft and carrier helicopters. The model took the maximum sortie time of the fleet and taxiing time of the fleet of fixed-wing aircraft as the optimization objectives, and considered the process flow, spatial, and resource constraints. Thirdly, a discretized improved whale optimization algorithm (IWOA) was designed to solve the problem. To improve the optimization-seeking capability of the algorithm, we discretized the algorithm, optimized its coding method, and introduced pre-constraints, learning factors, parameter improvements, and population restart. Finally, we set up various cases and proposed a new strategy for simulation experiments: these simulations verified the validity of the model, the excellent optimization performance of the IWOA, and the superiority of the sortie strategy. The research in this study will help to implement automated aircraft carrier scheduling.

A station location-allocation optimization problem in star-star pipeline network layout

The oil and gas field surface gathering pipeline network is an important hub for transporting oil and gas products outward, and its optimal design is crucial to reducing the construction cost of the pipeline system. Star-star topology is often applied to the layout of surface gathering pipeline networks in oil and gas fields. However, the optimization of star-star topology is often carried out under the constraint of the fixed station type, which may easily lead to a waste of station capacity and increase investment or make the optimization results meaningless. In this article, a mixed integer linear programming mathematical model for the overall optimization of star-star pipeline network layout considering the station location-allocation problem is constructed in discrete space with coupled station type constraints, and the branch-and-bound method is used to obtain the global optimal solution. Three cases verify the feasibility and effectiveness of the model and algorithm. The results show that the maximum avoided capacity waste is 20 × 104 m3/d and the maximum investment can be reduced by 8961.6 × 104 Yuan, which shows that the proposed model can effectively improve the economy and rationality of the pipeline system, and has important guiding significance for the construction of oil and gas fields.

Optimal design of an autonomous underwater helicopter's shape based on combinatorial optimization strategy

In this study, the shape of the autonomous underwater helicopter (AUH) was optimized. AUH is a new type of disc autonomous underwater vehicle with good maneuverability and flexibility. In this paper, an optimization mathematical model is established, which takes the resistance coefficient as the optimization objective and the internal volume and the actual engineering demand as the constraints. The optimization mathematical model of AUH is solved by using two combinatorial optimization strategies. Two combinatorial optimization strategies use experimental design algorithm and multi Island genetic algorithm (MIGA) as global search algorithm, and sequential quadratic programming algorithm as local search algorithm. And based on the back propagation (BP) neural network, the sample points are trained and fitted, and the cloud map of the resistance coefficient distribution in the design space is obtained. The optimization results show that compared with the initial resistance coefficient, the first optimal solution reduces by 9.14%, and the second optimal solution reduces by 9.53%. So the resistance performance of AUH is significantly improved, which proves the feasibility of the method proposed in this paper. This provides theoretical support for the shape optimization design of AUH, which will improve the motion performance of AUH in practical engineering applications.

A Discrete-Event Mathematical Model for Resource Allocation Optimization: A Case Study of Vehicle Scheduling in a Signal-Free Intersection

In industrial applications, many systems present serious productivity problems due to limited resources. Generally, the dynamics of resource allocation are inherently discrete-event driven, such as the buffer allocation in production line systems. In this paper, we develop a discrete-event mathematical model for resource allocation optimization. In this work, we consider two crucial optimization objectives, e.g., deadlock-free and efficiency, that originate from the customer’s actual requirements. The main aim is to develop a resource allocation scheme for fulfilling the production process (without deadlock) while ensuring that the cost of the process is minimized. As a case study, we consider the vehicle scheduling problem in a signal-free intersection. The intersection is divided into several disjoint spatial traffic resources, and vehicles need to occupy different traffic resources for passing through the intersection. Thus, the traffic control problem at the signal-free intersection is transformed into a scheduling problem with limited resource constraints. An online control approach is developed to schedule vehicles to go through the intersection safely and efficiently by optimizing the resource allocation order. Simulation results demonstrate the efficiency and robustness of the proposed model and optimization approach.

Reducing external container trucks’ turnaround time in ports: A data-driven approach under truck appointment systems

A longer turnaround time of container trucks in ports are commonly related to a higher energy cost and more carbon emissions, hindering the green development goal of ports. In this context, the implementation of Truck appointment system (TAS) is widely recognized as a very effective way to reduce external container trucks’ total turnaround time in ports. However, the number of appointment quotas allocated for each time window are the key to determine the efficiency of a TAS. This study proposed a data-driven approach to address the appointment quota optimization problem, which combined data mining technologies with mathematical optimization modeling methods, and an empirical study in YT port, China was given. Specifically, the smart gate data of the port were mined to explore the causal relationship between the number of truck arrivals at each time window and their total turnaround time within the port. The results exhibited a non-deterministic quadratic function relationship, and the range of changes regarding total turnaround time were measured by boundary functions obtained through a stepwise approaching algorithm. Considering the obtained causal relationship and its uncertainties, a robust optimization model was built to find the optimal appointment quota plan by minimizing the total turnaround time of external container trucks and the total deviations from the trucks’ preferred arrival time in the worst case. A numerical experiment was designed to examine the validity of the proposed data-driven approach, and compare the effectiveness of the proposed approach with a conventional stochastic optimization method. The results indicated the proposed approach was more effective on reducing the external container trucks’ total turnaround time in ports under a Truck appointment system.

A Coordination Optimization Method for Load Shedding Considering Distribution Network Reconfiguration

Load shedding control is an emergency control measure to maintain the frequency stability of the power system. Most of the existing load shedding methods use the extensive form of directly cutting off the outlet of the substation, featuring low control accuracy and high control cost. A network reconfiguration technique can adjust the topology of the distribution network and offers more optimization space for load shedding control. Therefore, this paper proposes a reconfiguration–load shedding coordination optimization scheme to reduce the power loss caused by load shedding control. In the proposed method, a load shedding mathematical optimization model based on distribution network reconfiguration is first established. The tie switches and segment switches in the distribution network are used to perform the reconfiguration of the distribution network, and the load switches are adopted to realize the load shedding. To improve the solving efficiency of the model, a solving strategy that combined a minimum spanning tree algorithm with an improved genetic algorithm is trailed to address the nonlinear and nonconvex terms. The application of the proposed method and model are finally verified via the IEEE 33 bus system, and the advantages in reducing the loss cost and the number of outage users are accordingly proven.

An economic view on rerouting railway wagons in a single wagonload network to avoid congestion

SummaryIt is expected that in the process of meeting the climate policy goals, more transport will take place by rail. Single wagonload transport plays a crucial role as a direct competitor to road-based transport. The aim of this contribution is an evaluation of capacity correlated effects in a railway wagon routing network.MethodsFor this purpose, we developed a mathematical optimisation model. In order to be able to identify the effects and impacts of congestion we created several scenarios and evaluated each of them individually.FindingsBy conducting computational experiments we were able to identify various effects and draw conclusions about the impact. This work contributes to the optimisation of the most costefficient short-term rerouting of railway wagons in single wagonload transport.

A Mathematical Modeling Approach for Power Flow and State Estimation Analysis in Electric Power Systems through AMPL

This paper presents a mathematical modeling approach by which to solve the power flow and state estimation problems in electric power systems through a mathematical programming language (AMPL). The main purpose of this work is to show the advantages of representing these problems through mathematical optimization models in AMPL, which is a modeling language extensively used in a wide range of research applications. The proposed mathematical optimization models allow for dealing with particular issues in that they are not usually considered in the classical approach for power flow and state estimation, such as solving the power flow problem considering reactive power limits in generation buses, as well as the treatment of errors in state estimation analysis. Furthermore, the linearized mathematical optimization models for both problems at hand are also presented and discussed. Several tests were carried out to validate the proposed optimization models, evidencing the applicability of the proposed approach.