Mathematical Optimization Model Research Articles

Electric Bus Scheduling and Timetabling, Fast Charging Infrastructure Planning, and Their Impact on the Grid: A Review

Transit agencies are increasingly embracing electric buses (EB) as an energy-efficient and emission-free alternative to the conventional bus fleets. They are rapidly replacing conventional buses with electric ones. As a result, emerging challenges of electrifying public transportation bus networks in cities should be addressed. Introducing electric buses to the bus transit system would affect the public transit operation planning steps. The steps are network design, timetabling, bus scheduling, and crew scheduling. Regarding the functional and operational differences between conventional buses and electric buses, such stages should be changed and optimized to enhance the level of service for the users while reducing operating costs for service providers. Many mathematical optimization models have been developed for conventional buses. However, such models would not fit the electric buses due to EBs’ limited traveling range and long charging time. Therefore, new mathematical models should be developed to consider the unique features of electric buses. We present a comprehensive literature review to critically review and classify the work done on these topics. This paper compares the studies that have been done in this field and highlight the missing links and gaps in the considered papers, and the potential future studies that could be done. The considered papers cover the integration of timetabling and vehicle scheduling, recharging scheduling planning, and fast charging infrastructure location planning and its impacts on the grid. The main goal of this research is to highlight the research gaps and potential directions for future studies in this domain to encourage more realistic and applicable models and solution approaches for fully electric bus transit systems.

Sustainable biodiesel supply chain model based on waste animal fat with subsidy and advertisement

The need for sustainable energy generation has grown in response to ascending levels of green house gases emissions and soaring energy demand. Biofuel is viewed as a viable alternative to non-renewable energy sources for energy generation. Animal fat, waste cooking oil, and vegetable oil are all examples of biomass that can be utilized to make biodiesel. In the midst of these sources’ animal fat is an acceptable choice due to its cheap cost and convenience of availability. The multi-objective mathematical optimization model is created to plan a sustainable supply chain for biodiesel made from waste animal fat. The proposed model minimizes the biodiesel supply chain cost, furthermore, minimizing the environmental impact while maximizing social impact. The demand for biodiesel is depending on advertisement costs and subsidies provided by the government. The advertisements promote biodiesel as an alternative to fossil fuels, and the government gives a subsidy for the collection of waste animal fat. The improved “augmented ϵ-constraint approach” is used to solve the proposed model. The multiple supply points for beef, mutton, and chicken fat, multi-collection and rendering plants, multiple biorefineries, and biodiesel depositories are designed. A numerical example is analyzed, and the consequences of a numerical experiment uncover that the transportation cost is 51.34% and installation cost of biodiesel production facilities accounts for 21.26% of the total cost, and the environmental installation impact of biodiesel production facilities accounts for 99.94% of total environmental impact. In the transportation sector, the heterogeneous fleet of trucks is employed to supply materials in the entire supply chain by which environmental transportation impacts account for 0.0005% of total environmental impacts. The social impact is examined by the social impact assessment method focused on life cycle assessment which is 1.363% for this model. The designed model can be appropriate to policymakers and investors engaged in the biodiesel industry.

Identification of arch dam mechanical parameters based on sensitivity analysis and Hooke–Jeeves algorithm optimization

To address the problem in which the mechanical parameters of a dam’s body and foundation are affected by a complex environment and changes during the service period, this study proposes an arch dam mechanical parameter inversion technique based on the sensitivity analysis of the Morris method and the Hooke–Jeeves algorithm. First, a Kriging mathematical model that reflects the nonlinear mapping relationship between the radial displacement of an arch dam and the mechanical parameters of an arch dam’s body and foundation is established. The sensitivity of the mechanical parameters of an arch dam and its foundation to the radial displacement of an arch dam is analyzed on the basis of the Morris method, and the mechanical parameters to be inverted are determined. Second, an optimization mathematical model based on the Kriging mathematical model is proposed to calculate the mechanical parameters of a dam’s body and foundation and the inversion of the displacement of an arch dam. The inversion problem of the mechanical parameters of a dam’s body and foundation is transformed into an optimization problem of the objective function. Finally, the Hooke–Jeeves algorithm is used to optimize the objective function, and the mechanical parameters of a dam’s body and foundation are inversely obtained. The case study shows that the relative errors of the mechanical parameters of the arch dam retrieved using the proposed method are all within 10%. Results indicate that the proposed parameter identification method is reasonable and effective. It provides a new idea for the parameter inversion of other hydraulic structures.

Optimal Load Distribution of CHP Based on Combined Deep Learning and Genetic Algorithm

In an effort to address the load adjustment time in the thermal and electrical load distribution of thermal power plant units, we propose an optimal load distribution method based on load prediction among multiple units in thermal power plants. The proposed method utilizes optimization by attention to fine-tune a deep convolutional long-short-term memory network (CNN-LSTM-A) model for accurately predicting the heat supply load of two 30 MW extraction back pressure units. First, the inherent relationship between the heat supply load and thermal power plant unit parameters is qualitatively analyzed, and the influencing factors of the power load are screened based on a data-driven analysis. Then, a mathematical model for load distribution optimization is established by analyzing and fitting the unit’s energy consumption characteristic curves on the boiler and turbine sides. Subsequently, by using a randomly chosen operating point as an example, a genetic algorithm is used to optimize the distribution of thermal and electrical loads among the units. The results showed that the combined deep learning model has a high prediction accuracy, with a mean absolute percentage error (MAPE) of less than 1.3%. By predicting heat supply load variations, the preparedness for load adjustments is done in advance. At the same time, this helps reduce the real-time load adjustment response time while enhancing the unit load’s overall competitiveness. After that, the genetic algorithm optimizes the load distribution, and the overall steam consumption rate from power generation on the turbine side is reduced by 0.488 t/MWh. Consequently, the coal consumption rate of steam generation on the boiler side decreases by 0.197 kg (coal)/t (steam). These described changes can greatly increase the power plant’s revenue by CNY 6.2673 million per year. The thermal power plant used in this case study is in Zhejiang Province, China.

Retraction Notice to Mathematical model for quality cost optimization. [Robotics and Computer-Integrated Manufacturing. Vol. 24/6 (2008) pp 811-815

Retraction Notice to Mathematical model for quality cost optimization. [Robotics and Computer-Integrated Manufacturing. Vol. 24/6 (2008) pp 811-815

Research on a lightweight unmanned sightseeing vehicle frame based on multi-condition and multi-objective optimization

A design method for a lightweight unmanned sightseeing vehicle frame was proposed based on multi-condition and multi-objective optimization to improve the vehicle’s range and reduce its production cost. First, a finite element model of the frame is established, and its static and dynamic characteristics are analyzed. Then, the wall thickness of the middle beam of the frame was selected as the design variable, and its sensitivity was analyzed. Sample points were generated from the design variables using the Latin hypercube sampling method, and the corresponding response values of the sample points were calculated. A Kriging approximation model was established using the sample points and response values and replaced the actual model for optimization. Finally, a multi-condition and multi-objective optimization mathematical model of the frame was established with the minimum mass, maximum first-order natural frequency, and the minimum stresses under full load bending and torsion conditions as the objectives. The multi-objective genetic algorithm was used for the lightweight design by comparing the fuzzy matter element and analytic hierarchy process methods to select the optimal design and to verify the rationality of the final design scheme. The results show that this method results in an optimized frame meeting the strength requirements under various working conditions and reducing the frame mass by 5.4%.

Reliability analysis of boom of new lifting equipment based on improved wolf swarm algorithm

Aiming at the low accuracy or inability to solve the problem when the traditional reliability optimization method deals with the practical engineering reliability analysis problem, this paper proposes a structural reliability analysis method using the improved wolf swarm algorithm (IWSA). Firstly, the reliability optimization mathematical model is established with the minimum reliability index as the objective function and the limit state equation as the equality constraint. Then the augmented multiplier method is used to transform the constrained optimization mathematical model into an unconstrained optimization mathematical model. Finally, IWSA is used to solve the problem. The proposed method is applied to a numerical example and an engineering example. The computation results of the proposed method in solving the numerical example are compared with the Monte Carlo simulation (MCS), which verifies that the proposed method in this paper has good calculation accuracy. The maximum deformation under the working condition is used as the target to establish a limit state function, and the reliability index is obtained by the proposed method combining with the finite element analysis software, which provides a certain theoretical guiding significance for the reliability analysis of engineering structures.

Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel

In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology.

A Multi-Objective Optimisation Mathematical Model with Constraints Conducive to the Healthy Rhythm for Lighting Control Strategy

Studies have shown that illuminance and correlated colour temperature (CCT) are strongly correlated with body responses such as circadian rhythm, alertness, and mood. It is worth noting that these responses show a complex and variable coupling, which needs to be solved using accurate mathematical models for the regulation of indoor light parameters. Therefore, in this study, by weighing the evaluations of visual comfort, alertness, valence, and arousal of mood, a multi-objective optimisation mathematical model was developed with constraints conducive to the healthy rhythm. The problem was solved with the multi-objective evolutionary algorithm based on the decomposition differential evolution (MOEA/D-DE) algorithm. Taking educational space as the analysis goal, a dual-parameter setting strategy for illuminance and CCT covering four modes was proposed: focused learning, comfortable learning, soothing learning, and resting state, which could provide a scientific basis for the regulation of the lighting control system. The alertness during class time reached 3.01 compared to 2.34 during break time, showing a good light facilitation effect. The proposed mathematical model and analysis method also have the potential for application in the lighting design and control in other spaces to meet the era of intelligent, highly flexible, and sustainable buildings.

Explicit reliability incorporated switches planning of smart distribution system with high flexibility

Different types of switches play different roles in the fault management procedure in particular context of smart grid, which have different impact on system reliability. The motivation behind this paper is to develop an explicit reliability assessment method adapting to flexible deployment of circuit breakers (CBs), remote-controlled switches (RCSs), and manual switches (MSs), which can be further integrated into switch planning models analytically. The peculiar of this paper is to use the propagation constraints of fictitious power flows to model three stages of fault management procedures. Based on the fictitious power flows, the placement and action for CBs, RCSs, and MSs are modeled in detail as linear constraints, considering power flow constraints in fault management procedure. Therefore, this MILP model can be easily integrated into an exact mathematical optimization model. Finally, the proposed method is tested in 37, 85, 137, 417 node distribution network systems to verify the efficiency of the algorithm. Besides, the necessity of considering flexible location of three types of switches and its application on switch planning are verified.

A mathematical optimization model using red deer algorithm for resource discovery in CloudIoT

AbstractThe Internet of Things (IoT) and cloud computing are new concepts in revolutionized communication and information technologies. Different technologies, for example, transportation and healthcare, can benefit from Cloud of Things (CloudIoT) for mobile and fixed resource applications with great promises. Fixed and mobile resources are very important items in the CloudIoT paradigm because of the need for an appropriate discovery mechanism. In the present study, a mathematical optimization model is proposed for the minimization of bandwidth, cost, and response time of CloudIoT platforms with a special focus on the role of mobile and fixed resources in resource discovery. Additionally, this study presents a heuristic resource discovery algorithm using a mathematical optimization model (RDMOM). The mixed‐integer non‐linear programming is used to design the discovery mechanism. Furthermore, the optimization problem is solved using the red deer algorithm. Finally, the simulation results show a significant reduction in the latency, resource efficiency, and energy consumption, as well as an improvement in availability and success ratio, compared to previous algorithms. The RDMOM algorithm significantly improves the success ratio, energy consumption, resource efficiency, availability, and latency, respectively, by 18%, 21%, 24%, 17%, and 21% in comparison to other algorithms.

Resource Allocation in DT-Assisted Internet of Vehicles via Edge Intelligent Cooperation

Applications in the Internet of Vehicles (IoV) are usually accompanied by ultralow network response latency requirement. A promising approach to meet this demand is combining the IoV with mobile edge computing and enabling edge devices to share their communication, computation, and caching (3C) resources via edge intelligent cooperation. However, the allocation of 3C resources supported by artificial intelligence (AI) demands a huge number of training data and strong computing ability which is impossible to achieve on resource-limited on board unit (OBU) or road side unit (RSU). In this article, we propose a digital twin (DT) supported edge intelligent cooperation scheme, which empowers the optimal 3C resource allocation and edge intelligent cooperation possible. We focus on the response delay minimization in order to meet the requirement of latency-sensitive applications in the IoV. Specifically, mathematical expressions of the network response time are formulated according to modeling the workflow of the edge server as an M/M/1/N/FCFS queuing process. Especially, we conduct a detailed analysis of the deviations in 3C resource between the physical world and the DT space, based on which we further discuss the impact of these deviations in offloading decision. Furthermore, a mathematical optimization model aiming at minimizing the latency is formulated. In view of its complexity, we apply a deep deterministic policy gradient algorithm to solve it by modeling the cooperation process between edge nodes as a Markov decision process. Finally, we carry out simulations to demonstrate that our algorithm outperforms the existing schemes in terms of network response latency.

Optimization of the Adaptability of the Fuel Cell Vehicle Waste Heat Utilization Subsystem to Extreme Cold Environments

In extremely cold environments, the fuel cell vehicle (FCV) waste heat utilization subsystem can only exchange a small amount of proton exchange membrane fuel cell (PEMFC) waste heat into the warm air circuit for cab heating, which has poor adaptability to extremely cold environments. The first step in this study was to build a test bench for the waste heat utilization subsystem of fuel cell vehicles. Secondly, the PEMFC heating capacity and liquid–liquid exchanger heat transfer capacity were analyzed using experimental data to assess the ability of FCV waste heat utilization subsystems with different rated powers to adapt to extremely cold environments. Then, the optimization mathematical model of the liquid–liquid exchanger was established, and the heat transfer performance of the liquid–liquid exchanger was orthogonally optimized based on the Taguchi method. Finally, the optimized liquid–liquid exchanger was installed in the waste heat utilization subsystem for experimental tests. The results show that when the ambient temperature is −20 °C, −25 °C or −30 °C, in the optimized waste heat utilization subsystem, the inlet and outlet temperatures of the PEMFC are reduced, and the power consumption of the positive temperature coefficient (PTC) is reduced by 57.6% and 48% and 34.3%, respectively, improving the utilization rate of PEMFC waste heat, and thereby improving the adaptability of FCV in extremely cold environments.

Optimal industrial flexibility scheduling based on generic data format

The energy transition into a modern power system requires energy flexibility. Demand Response (DR) is one promising option for providing this flexibility. With the highest share of final energy consumption, the industry has the potential to offer DR and contribute to the energy transition by adjusting its energy demand. This paper proposes a mathematical optimization model that uses a generic data model for flexibility description. The optimization model supports industrial companies to select when (i.e., at which time), where (i.e., in which market), and how (i.e., the schedule) they should market their flexibility potential to optimize profit. We evaluate the optimization model under several synthetic use cases developed upon the learnings over several workshops and bilateral discussions with industrial partners from the paper and aluminum industry. The results of the optimization model evaluation suggest the model can fulfill its purpose under different use cases even with complex use cases such as various loads and storages. However, the optimization model computation time grows as the complexity of use cases grows.

Optimizing the quality level of raw materials based on material flow cost accounting in a production system with rework

The concept of Material Flow Cost Accounting (MFCA) was developed by a German textile company in late 1980s through their projects for environmental management. The major objectives of MFCA are to increase transparency of material flow and energy usage along with their environmental and financial impacts. MFCA traces a variety of measures from material productivity metrics to crucial environmental indexes. Most of the existing researches on MFCA focus on conceptual models. A major research gap is the lack of mathematical optimization models which use the MFCA logic to support managerial decisions. This is the first known study in which a comprehensive mathematical optimization model has been developed based on MFCA cost logic, i.e., positive and negative costs. The model is named MFCABOM (MFCA-Based Optimization Model) in this paper. In addition, we have incorporated the quality cost of raw materials into the MFCABOM. The MFCABOM determines the optimal quality level of raw materials in a production system with rework. A numerical example has been solved and discussed to assess the performance and validity of the MFCABOM. The results show that the MFCABOM can strongly support production managers in selecting the optimal quality level of raw materials based on MFCA cost logic.

COVID-19 safe campus evaluation for universities by a hybrid interval type-2 fuzzy decision-making model.

The fight against the COVID-19 pandemic, which has affected the whole world in recent years and has had devastating effects on all segments of society, has been one of the most important priorities. The Turkish Standards Institution has determined a checklist to contribute to developing safe and clean environments in higher education institutions in Turkey and to follow-up on infection control measures. However, this study is only a checklist that makes it necessary for decision-makers to make a subjective evaluation during the evaluation process, while the need to develop a more effective, systematic framework that takes into account the importance levels of multiple criteria has emerged. Therefore, this study applies the best-worst method under interval type-2 fuzzy set concept (IT2F-BWM) to determine the importance levels of criteria affecting the “COVID-19 safe campus” evaluation of universities in the context of global pandemic. A three-level hierarchy consisting of three main criteria, 11 sub-criteria, and 58 sub-criteria has been created for this aim. Considering the hierarchy, the most important sub-criterion was determined as periodic disinfection. The high contribution of the interval-valued type-2 fuzzy sets in expressing the uncertainty in the decision-makers’ evaluations and the fact that BWM provides criterion weights with a mathematical optimization model that produces less pairwise comparisons and higher consistency are the main factors in choosing this approach. Simple additive weighting (SAW) has also been injected into the IT2F-BWM to determine the safety level of any university campus regarding COVID-19. Thus, decision-makers will be better prepared for the devastating effects of the pandemic by first improving the factors that are relatively important in the fight against the pandemic. In addition, a threshold value will be determined by considering all criteria, and it will prepare the ground for a road map for campuses. A case study is employed to apply the proposed model, and a comparison study is also presented with the Bayesian BWM to validate the results of the criteria weights.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11356-022-22796-1.

Development of a Quality-Based Model for Software Architecture Optimization: A Case Study of Monolith and Microservice Architectures

Various architectures can be applied in software design. The aim of this research is to examine a typical implementation of Jakarta EE monolithic and microservice software architectures in the context of software quality attributes. Software quality standards are used to define quality models, as well as quality characteristics and sub-characteristics, i.e., software quality attributes. This paper evaluates monolithic and microservice architectures in the context of Coupling, Testability, Security, Complexity, Deployability, and Availability quality attributes. The performed examinations yielded a quality-based mixed integer goal programming mathematical model for software architecture optimization. The model incorporates various software metrics and considers their maximal, minimal or targeted values, as well as upper and lower deviations. The objective is the sum of all deviations, which should be minimal. Considering the presented model, a solution which incorporated multiple monoliths and microservices was defined. This way, the internal structure of the software is defined in a consistent and symmetrical context, while the external software behavior remains unchanged. In addition, an intersection point of monolithic and microservice software architectures, where software metrics obtain the same values, was introduced. Within the intersection point, either one of the architectures can be applied. With the exception of some metrics, an increase in the number of features leads to a value increase of software metrics in microservice software architecture, whilst these values are constant in monolithic software architecture. An increase in the number of features indicated a quality attribute’s importance for the software system should be examined and an appropriate architecture should be selected accordingly. Finally, practical recommendations regarding software architectures in terms of software quality were given. Since each software system needs to meet non-functional in addition to functional requirements, a quality-driven software engineering can be established.

Mathematical optimization models for reallocating and sharing health equipment in pandemic situations

In this paper we provide a mathematical programming based decision tool to optimally reallocate and share equipment between different units to efficiently equip hospitals in pandemic emergency situations under lack of resources. The approach is motivated by the COVID-19 pandemic in which many Heath National Systems were not able to satisfy the demand of ventilators, sanitary individual protection equipment or different human resources. Our tool is based in two main principles: (1) Part of the stock of equipment at a unit that is not needed (in near future) could be shared to other units; and (2) extra stock to be shared among the units in a region can be efficiently distributed taking into account the demand of the units. The decisions are taken with the aim of minimizing certain measures of the non-covered demand in a region where units are structured in a given network. The mathematical programming models that we provide are stochastic and multiperiod with different robust objective functions. Since the proposed models are computationally hard to solve, we provide a divide-et-conquer math-heuristic approach. We report the results of applying our approach to the COVID-19 case in different regions of Spain, highlighting some interesting conclusions of our analysis, such as the great increase of treated patients if the proposed redistribution tool is applied.

Multiphysics Field Topology Optimization Design of Main Support Structure of High-Temperature Superconducting Magnets

The high-temperature superconducting magnet (HTS) is one of the core technologies of a superconducting maglev. The effects of multiphysics fields including electromagnetic, mechanical, and thermal should be taken into consideration in design. Traditional design methods rely on the initial configuration and the engineer's experience and only consider the design for the heat conduction performance or the structure strength, which often significantly increases the weight. To solve the above problems, based on COMSOL Multiphysics software, the mathematical model of topology optimization of the main support was established with electromagnetic force and thermal stress as the input loads. The objective functions were assigned to total strain energy and heat leakage, combined with stress value and volume fraction constraint conditions. The solid isotropic material with penalization (SIMP) method was used to carry out the topological analysis of multiphysics. Finally, the innovative structure of main support is obtained. Through finite element analysis of multiphysics fields, the heat leakage, the max Von-Mises stress, and weight were taken as evaluation indexes to compare the optimal structure performance. The results show that the method adopted in this paper can reduce the heat leakage by 61.7% while reducing the weight of the main support by 85%, and the max Von-Mises stress does not exceed the yield limit of the material. The work of this paper provides a theoretical foundation for the engineering design of the heat conduction structure of a HTS magnet.

A Genetic Algorithm Model for Human Resource Management Optimization in the Internet Marketing Era

In the context of the Internet marketing era, rational use of big data for quantitative analysis of human resource management can effectively help each unit better understand the industry talent and analyze the development trend of the industry. Personnel competency is the key factor affecting job performance. The renewable resources in the resource constrained project scheduling problem are transformed into human resources with competency differences through a series of scientific and reasonable methods. A human resource constrained project scheduling problem model emphasizing competency differences is constructed. The most prominent advantage of this model lies in the selection of indicators that can objectively and reasonably evaluate the competency of personnel, and the rigorous and scientific relationship is provided. The complex multiproject double-objective minimization problem of the total construction period and total cost is transformed into a comprehensive index single-objective maximization problem. Then, a mathematical optimization model is established and solved by a genetic algorithm. Finally, the effectiveness of the algorithm is shown by comparing numerical experiments with other algorithms.