Multi-objective Optimization Model Research Articles

Multi-objective Optimization for Green Delivery Routing Problems with Flexible Time Windows

ABSTRACT This paper presents a model and heuristic solution algorithms for the Green Vehicle Routing Problem with Flexible Time Windows. A scenario of new vehicle routing is analyzed in which customers are asked to provide alternative time windows to offer flexibility to help route planners find more fuel-efficient routes (“green delivery”). Customers can rank their preferred time windows as first, second, and third. The optimization model aims to reduce tour costs, promote electromobility over fossil fuels, such as diesel, and meet customer preferences when possible and affordable. The study incorporates a multi-objective optimization model with three objectives, which are overall cost, use of fossil fuel, and customer satisfaction. For the new problem, a set of realistic benchmark problems is created and four mainstream solvers are applied for the Pareto front approximation: NSGA-II, NSGA-III, MOEA/D, and SMS-EMOA. These algorithms are compared in terms of their effectiveness in achieving the objectives of minimizing travel costs, promoting electromobility, and meeting customer preferences. The study uses five different problems of single-vehicle route planning. Two major findings are that the selection of the metaheuristic can make a big difference in terms of algorithm performance. The resulting 3-D Pareto fronts reveal the nature of this new class of problems: Interestingly, in the new model with flexible time windows, most users can still be delivered in their most preferred time windows with only small concessions to the other objectives. However, using only one time window per user can lead to an increasingly drastic cost and fossil fuel consumption.

Multi-objective arterial coordination control method based on induction control and vehicle speed guidance

The fixed green wave speed and staged statistical flow used in arterial signal coordination are not adaptable to the fluctuations in vehicle travel speed and traffic flow on roads, resulting in a mismatch between the signal scheme and the optimal green wave speed and traffic flow demand. This discrepancy negatively impacts the efficiency of intersection traffic. In traditional signal control systems, the cycle and green light timing are typically set independently. However, such a setting method poses problems in practical operation. In this paper, we combine vehicle arrival and vehicle location information, and consider the interaction of speed guidance and dynamic signal optimization to construct a model. This study is developed along the following steps: in the vehicle-road coordination environment, based on the MAXBAND model, a global coordination scheme is obtained, incorporating the speed guidance method; then, based on the vehicle saturation of the inlet lane of the arterial intersection, a multi-objective optimization model for arterial signal coordination under vehicle speed guidance is established based on global coordination with the maximum green wave bandwidth and the minimum delay of arterial vehicles, the minimum number of arterial stops and the minimum delay in the minor direction road as the optimization objectives. Based on global coordination, adopting an integrated control mechanism of cycle and green light timing allows for dynamic adjustments according to real-time traffic conditions. The improved multi-objective particle swarm algorithm is chosen to solve the model, and the simulation environment is built based on the COM interface of VISSIM software and C# platform. Three adjacent intersections of Ganjiang Middle Road in Nanchang are selected as case studies, and the methods in this paper are compared with the current timing scheme, the MAXBAND method and the optimization scheme under speed guidance only, respectively. The results show that the model proposed in this paper achieves significant optimization effects on the indicators of arterial delay, arterial stopping times and the delay of minor roads.

NC process information mining based optimization method of roughing tool sequence selection for pocket features

The appropriate and intelligent selection of roughing tool sequence for pocket features is essential to improve the efficiency of NC machining. However, there exist few researches exploring how to discover and utilize the valuable NC process information imbedded in 3D CAD models. In this paper, a NC process information mining based optimization method of roughing tool sequence selection for pocket features is presented. Firstly, the medial axis transform (MAT) is introduced to represent the tool paths of a pocket feature, and corresponding parameters of MAT are calculated. Secondly, considering the restrictions of tool movements during machining, the mapping mechanism between geometry and NC process is elaborated based on MAT to reveal the association of 3D CAD models and NC machining. The deeper information for NC process planning is mined to reflect the machining procedure feasibly. Then, the multi-objective optimization model is constructed by considering material removal amount and cutting consistency synthetically. Moreover, the precedence and distances between roughing tools are formulated in a Candidate Tools Graph (CTG). Finally, a hybrid ant colony algorithm (ACA) and simulated annealing (SA) approach based on CTG is proposed to generate the global optimal roughing tool sequence. In the experiment, various pocket features are conducted to illustrate the application effectiveness of the proposed method. The experimental results show that our method can achieve highly satisfactory results and outperforms other approaches.

Multi-objective configuration and evaluation of dynamic virtual inertia from DFIG based wind farm for frequency regulation

Modern power systems are gradually evolving into low-inertia systems due to the integration of high penetration of renewable energy and power electronic equipment. For the natural inertia on the rotor, doubly-fed induction generator (DFIG) based wind farms are expected to provide inertia support for systems. The paper proposed an analytical model of DFIG with df/dt inertia control for studying frequency dynamics, and investigates the optimal design of virtual inertia from wind farms, as well as its equivalent inertia contribution to system. The inertia response differences between DFIG and synchronous generator (SG) are discussed and analyzed for the first time, and then to accurately describe the frequency response with low cost, an analytical model of DFIG with inertia control is developed considering wind turbine aerodynamic characteristics. The explicit expression of virtual inertia provided by DFIG is derived according to the kinetic energy equilibrium, and the key factors that dominate the magnitude of virtual inertia are illustrated. Based on the system frequency response model including wind farms, taking the system frequency nadir (SFN) and the time of reaching nadir (ToN) as targets, a multi-objective optimal configuration model of virtual inertia is constructed and solved through MOPSO. The time domain simulations of a generic two machine four bus system and modified IEEE 9-bus test system are both performed in MATLAB/Simulink, the accuracy and efficiency of our proposed DFIG model on system frequency dynamics research are demonstrated, the pareto frontiers of virtual inertia configuration under different working conditions are optimized and analyzed as well as the impacts of different parameters on inertia evaluation.

A multi-objective optimization model for the location of cold chain logistics distribution center based on trust domain optimization algorithm

Cold chain transportation refers to a logistics method that transports fresh, perishable, and perishable items from the place of production, processing or warehouse to the place of consumption under certain temperature conditions. As consumers have higher and higher requirements for food safety and quality, the cold chain logistics industry has also developed rapidly. However, the high cost of cold chain logistics, the difficulty of technology, the difficulty of ensuring service quality and other problems have also arisen, and how to optimize cold chain transportation has become a hot issue in the cold chain logistics industry. Cold chain transportation optimization refers to the premise of ensuring the quality and safety of goods, through reasonable transportation paths, transportation methods, temperature control and other measures, to minimize the cost of cold chain transportation, improve efficiency and service quality. In order to achieve the optimization of cold chain transportation, it is necessary to establish a reliable cold chain logistics distribution center to ensure the safety and quality of goods during transportation. In order to solve the problem of location selection of cold chain logistics distribution center, this paper first defines the service reliability and calculation method of cold chain distribution center. Then, the location model of the cold chain logistics distribution center and the trust domain optimization algorithm model were established. The model aims to minimize the total cost, while considering multiple factors such as transportation distance, temperature control, facility construction, etc., to ensure the reliability and operational efficiency of the cold chain logistics distribution center. Finally, this paper introduces an example for calculation to prove the feasibility and universality of the model in the location problem of cold chain logistics distribution center. Through the calculation of examples, it can be seen that the model can effectively reduce the cost of cold chain transportation and improve the service quality and efficiency of cold chain logistics distribution center. In summary, this paper proposes a reliable location model and trust domain optimization algorithm model for cold chain logistics distribution centers to solve the challenges faced by the cold chain logistics industry. This model can provide guidance for cold chain logistics companies to gain a greater advantage in a highly competitive market.

Designing a green-resilient closed-loop supply chain to preserve business continuity under interrelated disruptions (a case study of the automotive battery industry)

Improving profitability, implementing the recycling cycle to reduce resource consumption, and managing interrelated disturbances to maintain business continuity are important issues for supply chain management. Accordingly, this study proposes a multi-objective optimization model to design a green-resilient closed-loop supply chain considering pricing decisions under multiple interrelated disturbances. Herein, the fuzzy c-means clustering method is employed to lessen probable scenarios and cluster main suppliers and target markets to reduce mathematical complexity. The multi-objective model is solved by adopting the improved augmented ε-constraint method to achieve the minimum total cost, total environmental impact, and network non-resiliency. The mixed uncertainty is coped with by developing a novel robust optimization method. Finally, an automotive battery manufacturing industry case study is applied to the model. The results reveal that the mutual effects of disturbances intensify the deterioration of objective functions. Also, the dynamic pricing of products reduces the financial vulnerability of the supply chain.

Optimizing the Three-Dimensional Multi-Objective of Feeder Bus Routes Considering the Timetable

To optimize the evacuation process of rail transit passenger flows, the influence of the feeder bus network on bus demand is pivotal. This study first examines the transportation mode preferences of rail transit station passengers and addresses the feeder bus network’s optimization challenge within a three-dimensional framework, incorporating an elastic mechanism. Consequently, a strategic planning model is developed. Subsequently, a multi-objective optimization model is constructed to simultaneously increase passenger numbers and decrease both travel time costs and bus operational expenses. Due to the NP-hard nature of this optimization problem, we introduce an enhanced non-dominated sorting genetic algorithm, INSGA-II. This algorithm integrates innovative encoding and decoding rules, adaptive parameter adjustment strategies, and a combination of crowding distance and distribution entropy mechanisms alongside an external elite archive strategy to enhance population convergence and local search capabilities. The efficacy of the proposed model and algorithm is corroborated through simulations employing standard test functions and instances. The results demonstrate that the INSGA-II algorithm closely approximates the true Pareto front, attaining Pareto optimal solutions that are uniformly distributed. Additionally, an increase in the fleet size correlates with greater passenger volumes and higher operational costs, yet it substantially lowers the average travel cost per customer. An optimal fleet size of 11 vehicles is identified. Moreover, expanding feeder bus routes enhances passenger counts by 18.03%, raises operational costs by 32.33%, and cuts passenger travel time expenses by 21.23%. These findings necessitate revisions to the bus timetable. Therefore, for a bus network with elastic demand, it is essential to holistically optimize the actual passenger flow demand, fleet size, bus schedules, and departure frequencies.

Multi-objective optimization and evaluation of hybrid combined cooling, heating and power system considering thermal energy storage

Introducing thermal energy storage (TES) and solar energy effectively reduces fossil fuel consumption and greenhouse gas emissions in combined cooling, heating, and power (CCHP) systems. This study establishes a two-layer optimization framework to obtain the optimal configuration of the CCHP system coupling solar and thermal energy storage. The outer layer uses component sizes as decision variables to optimize the system's annual economic economy, annual carbon dioxide emissions, and annual primary energy consumption; the inner layer uses equipment output as decision variables to optimize the operation and maintenance costs. Firstly, the representative typical scenes were obtained using the k-means algorithm to reduce the computational complexity. Then, the multi-objective chaos optimization (MOCGO) algorithm is combined with mixed-integer linear programming (MILP) to obtain the established optimization model's configuration scheme and optimal operating strategy. TOPSIS is to rank the best Pareto solutions. Finally, a large hotel is a case study. The optimization results indicate that the proposed two-layer optimization model can achieve the optimal configuration scheme and scheduling strategy for hybrid CCHP. Compared to the rule-based multi-objective one-layer optimization model, the proposed two-layer optimization model can achieve maximum improvements of 30.63 %, 37.94 %, and 38.16 % in economic, energy, and environmental performance. Compared with the rule-based single-objective one-layer optimization model, the proposed two-layer optimization model can achieve maximum improvements of 34.95 %, 35.81 %, and 37.55 % in economic, energy, and environmental performance, respectively. In addition, TES can substantially increase the optimal performance of the two-layer optimization model.

Multi-Objective Optimization of Tasks Scheduling Problem for Overlapping Multiple Tower Cranes

The scheduling of tower crane operations is a complex process. Overlapping areas between tower cranes often lead to increased collision possibilities, resulting in additional tower crane operation complexity. Single objectives related to time or economic aspects were always considered in dealing with this issue, which neglected other objectives and the relationships between different objectives. Therefore, this article proposes a novel method for the schedule of prefabricated component lifting tasks on the construction site, integrating the multi-objective optimization model with the decision-making method with the aim of minimizing energy consumption costs and minimizing the amplitude of the costs among multiple tower cranes. A non-dominated sorting genetic algorithm-III (NSGA-III) written in Python is used as the multi-objective optimization algorithm—which considers the selection of tasks for each tower crane and the order of lifting for each tower crane and technique for order preference by similarity to an ideal solution (TOPSIS), and is applied as the decision-making method for ranking the Pareto front. Then, a green construction production and education integration training building construction project located in Jinan, China is used as the case study to verify that the method is practical and reasonable. The results show that conflicts can be effectively avoided, energy consumption costs reduced, and equipment utilization increased by rationally distributing lifting tasks among multiple overlapping tower cranes. And among the top 11 solutions, the lifting tasks and priorities for tower crane 1 are close to the same. In contrast, the task lifting for tower crane 2 was assigned based on the balance of the energy consumption costs of the two tower cranes. The discovery of this article is helpful to eliminate collisions, interference, and frequent start and stop of several tower cranes, so as to realize the safe, stable, and efficient operation of the construction site.

Multi-objective optimization scheduling method considering flexible load integration for distribution network

In response to a series of issues in the distribution network, such as inadequate and inflexible utilization of flexible loads, delayed response to demand participation, and the uncertainty of new energy source output, a differentiated objective-based method for optimizing distribution network operations is proposed. Firstly, flexible loads are categorized, and corresponding mathematical models are established. Secondly, by employing chance-constrained programming to account for the uncertainty in new energy source output, a multi-objective optimization model is developed to reduce distribution network economic costs, decrease network losses, and enhance power supply reliability. Subsequently, an improved NSGA-III algorithm is introduced to address the multi-objective model. Finally, an 11-node distribution network is used as a case study, and three different algorithms are comprehensively compared. This confirms the rationality of the optimized scheduling scheme proposed in this paper.

Managing the water-agriculture-environment-energy nexus: Trade-offs and synergies in an arid area of Northwest China

Water is a stabilizer for production and life in the arid areas. According to research shared by the Pacific Institute and The Guardian, there were 228 incidents of water conflict globally in 2022. Therefore, comprehensive measures are necessary to achieve regional water security. This objective can be achieved by the application of interdisciplinary and professional approaches through establishing a dynamic equilibrium of the different water consumers, and trade-offs and synergies for water allocation between them. A multi-objective optimization model is proposed for managing the water-agriculture-energy-environment (WAEE) nexus in water-scarce areas. Real and integer-encoded multi-objective evolutionary algorithms (EMCMO) were applied to solving management models. Multiple objectives, such as the maximization of economic benefits from agriculture and hydropower generation, the minimization of ecological water shortages for local plants, and the minimization of environmental risks influenced by land use and food supply, were defined in the model. The model was applied to the Yanqi Basin, an important agriculture and energy producer in Xinjiang province, Northwest China. The results indicated that (1) the four-dimensional Pareto solution set has the advantage of presenting the WAEE nexus, highlighting the trade-offs and synergies between high-value crops, surface water, and groundwater, ecological water demand, hydropower generation and total nitrogen and phosphorus loading (TNP); (2) An excessive increase in the agricultural economy will increase TNP loading and agricultural non-point source pollution; (3) Optimization of WAFE for local ecosystem restoration. Optimization in a wet year, reduced agricultural economic benefits by 0.20%, and agricultural TNP loading by 13.19% while increasing ecological water by 58.33%, and hydropower generation by 3.98%; in a normal year, reduced agricultural economic benefits by 6.62%, agricultural TNP loading by 13.19% while increasing ecological water by 46.43%, and hydropower generation by 0.79%; in a dry year, reduced agricultural economic benefits by 17.19%, agricultural TNP loading by 9.72%, and hydropower generation by 16.18% while increasing ecological water by 42.86%. The trade-offs and synergies of the WAEE nexus also apply to other similar water-scarce areas.

An expert system for highway construction: Multi-objective optimization using enhanced particle swarm for optimal equipment management

Expert systems play a crucial role in decision-making across various industries. This study introduces a novel expert system employing a tailored multi-objective optimization (MOO) model to address the intricate demands of highway projects. Integrating an advanced Enhanced Particle Swarm Optimization (IPSO) strategy, our model emphasizes key operations like excavation, hauling, grading, and compaction. Considering factors such as equipment count, velocity, and capacity, the system provides a comprehensive set of optimal solutions and reveals the Pareto frontier. In benchmarking our Improved Particle Swarm Optimization (IPSO) model against established methods, such as Genetic Algorithms (GA) by various researchers and the Guided Population Archive Whale Optimization Algorithm (GPAWOA), our approach significantly excelled. Our model demonstrated a 35.4%-time reduction and a 39.1% cost reduction while enhancing operational quality—starkly contrasting the modest improvements seen with other methods. This showcases the IPSO model's robustness in optimizing construction equipment utilization beyond current standards. Functioning as a decision-support tool, the expert system aids stakeholders in selecting optimal equipment setups, considering diverse attributes from equipment specifications to speed and volume. This application is exemplified through a real-world highway construction case study. The Case Study showcases the proposed model's remarkable impact, yielding a 35.4% time saving and a 16.8% cost decrease with Optimal Solution (I). In contrast, Optimal Solution (III) required 144.6% more time yet reduced costs by 39.1%. Furthermore, Optimal Solution (II) achieved a 4.6%-time reduction and a 32.4% cost decrease, demonstrating the system's versatility in managing constraints and optimizing decision-making processes across various project stages.

A multi-objective optimization model for medical waste recycling network design under uncertainties

Transporting medical waste (MW) generated by medical institutions (MIs) is a process that poses potential threats to the environment and public safety. Therefore, it is vital to find a safe and efficient way to transport this type of waste to disposal centers (DCs). However, there are challenges in the transportation of MW due to random factors such as the generation of waste in an unpredictable manner and unforeseen travel times. In this paper, we propose a bi-level optimization model to minimize site selection costs, transportation costs, time-window penalties costs, and transportation risks under uncertainties. The concepts of “loading reliability”, “travel time reliability” and “transportation risk” are adopted in the proposed optimization model. The simulated annealing algorithm (SA) is employed to address the optimal location problem (Upper level), which involves minimizing the construction cost, transportation cost (DC-CP-DC), and transportation risk (estimated using Bayesian method). To tackle the capacity-constrained vehicle routing problem considering transportation risk and time window penalties (Lower level), we propose an improved genetic algorithm named harmony search algorithm (IHSGA). Subsequently, the results from the lower level are looped back to the upper level, fostering mutual influence between the two stages. We demonstrate the effectiveness and correctness of the proposed model and algorithm using S city in China as an illustrative example. Furthermore, a series of sensitivity analyses were conducted to examine the impact of various factors. The findings highlight the pivotal roles of both travel time reliability and loading reliability in designing the medical waste recycling network. In comparison to the general Genetic Algorithm (GA) and CPLEX solver, the modified IHSGA presented in this paper exhibits superior performance.

A two-stage decision model for sustainable-resilient supplier selection and order allocation under uncertain environment

PurposeThe paper aims to propose an innovative two-stage decision model to address the sustainable-resilient supplier selection and order allocation (SSOA) problem in the single-valued neutrosophic (SVN) environment.Design/methodology/approachFirst, the sustainable and resilient performances of suppliers are evaluated by the proposed integrated SVN-base-criterion method (BCM)-an acronym in Portuguese of interactive and multi-criteria decision-making (TODIM) method, with consideration of the uncertainty in the decision-making process. Then, a novel multi-objective optimization model is formulated, and the best sustainable-resilient order allocation solution is found using the U-NSGA-III algorithm and TOPSIS method. Finally, based on a real-life case in the automotive manufacturing industry, experiments are conducted to demonstrate the application of the proposed two-stage decision model.FindingsThe paper provides an effective decision tool for the SSOA process in an uncertain environment. The proposed SVN-BCM-TODIM approach can effectively handle the uncertainties from the decision-maker’s confidence degree and incomplete decision information and evaluate suppliers’ performance in different dimensions while avoiding the compensatory effect between criteria. Moreover, the proposed order allocation model proposes an original way to improve sustainable-resilient procurement values.Originality/valueThe paper provides a supplier selection process that can effectively integrate sustainability and resilience evaluation in an uncertain environment and develops a sustainable-resilient procurement optimization model.

The Green Flexible Job-Shop Scheduling Problem Considering Cost, Carbon Emissions, and Customer Satisfaction under Time-of-Use Electricity Pricing

Exploration of the green flexible job-shop scheduling problem is essential for enterprises aiming for sustainable practices, including energy conservation, emissions reduction, and enhanced economic and social benefits. While existing research has predominantly focused on carbon emissions or energy consumption as green scheduling objectives, this paper addresses the broader scope by incorporating the impact of variable energy prices on energy cost. Through the introduction of an energy cost model based on time-of-use electricity pricing, the study formulates a multi-objective optimization model for green flexible job-shop scheduling. The objectives include minimizing cost, reducing carbon emissions, and maximizing customer satisfaction. To prevent premature convergence and maintain population diversity, an enhanced genetic algorithm is employed for solving. The validation of the algorithm’s effectiveness is demonstrated through specific examples, providing decision results for optimal scheduling under various weight combinations. The research outcomes hold substantial practical value as they can significantly reduce energy expenses, lower carbon emissions, and elevate customer satisfaction while safeguarding production efficiency. This contributes to enhancing the market competitiveness and green brand image of businesses.

Consideration of Carbon Emissions in Multi-Trip Delivery Optimization of Unmanned Vehicles

In order to achieve the goal of low-carbon, efficient delivery using unmanned vehicles, a multi-objective optimization model considering carbon emissions in the problem of optimizing multi-route delivery for unmanned vehicles is proposed. An improved genetic algorithm (IGA) is designed for solving this problem. This study takes into account constraints such as the maximum service duration for delivery, the number of vehicles, and the approved loading capacity of the vehicles, with the objective of minimizing the startup cost, transportation cost, fuel cost, and environmental cost in terms of the carbon dioxide emissions of unmanned vehicles. A combination encoding method based on the integer of the number of trips, the number of vehicles, and the number of customers is used. The inclusion of a simulated annealing algorithm and an elite selection strategy in the design of the IGA enhances the quality and efficiency of the algorithm. The international dataset Solomon RC 208 is used to verify the effectiveness of the model and the algorithm in small-, medium-, and large-scale cases by comparing them with the genetic algorithm (GA) and simulated annealing algorithm (SA). The research results show that the proposed model is applicable to the problem of optimizing the multi-route delivery of unmanned vehicles while considering carbon emissions. Compared with the GA and SA, the IGA demonstrates faster convergence speed and higher optimization efficiency. Additionally, as the problem’s scale increases, the average total cost deviation rate changes significantly, and better delivery solutions for unmanned vehicles are obtained with the IGA. Furthermore, the selection of delivery routes for unmanned vehicles primarily depends on their startup costs and transportation distance, and the choice of different vehicle types has an impact on delivery duration, total distance, and the average number of trips. The delivery strategy that considers carbon emissions shows a 22.6% difference in its total cost compared to the strategy that does not consider carbon emissions. The model and algorithms proposed in this study provide optimization solutions for achieving low-carbon and efficient delivery using unmanned vehicles, aiming to reduce their environmental impact and costs. They also contribute to the development and application of unmanned vehicle technology in the delivery field.

Multi-objective optimization study of regional integrated energy systems coupled with renewable energy, energy storage, and inter-station energy sharing

Globally, countries have established timelines and technological pathways towards achieving "carbon neutrality". Regional integrated energy systems, as an efficient and clean mode of energy provision, are particularly suitable for supplying various forms of energy to building users. However, due to the complexity of their structure and multiple energy flow couplings, regional integrated energy systems face challenges in system optimization, warranting further exploration in design optimization and benefit analysis. Therefore, a regional integrated energy system was established, integrating renewable energy, energy storage, and power/thermal sharing between stations. A multi-objective optimization model for the regional integrated energy system was established, targeting economic benefits, carbon reduction, and reliability. Overall benefits of the internal energy stations in the regional integrated energy system were meticulously analyzed, considering system benefits, inter-station energy sharing, and energy storage. Research findings indicate, the regional integrated energy system constructed in this study exhibited superior energy-saving, carbon reduction, and independence, compared to other integrated energy systems. For the proposed system, the annual total cost was 38.41 CNY/m2, primary energy consumption stood at 16.26 kWh/m2, carbon emission was recorded at 4.33 kg/m2, and the system interaction power measured 9.99 kWh/m2. Final, this study provides theoretical support for the application and promotion of regional integrated energy systems.

Multi-objective structural optimization and degradation model of magnesium alloy ureteral stent

BackgroundMg alloys have attractive properties, including biocompatibility, biodegradability, and ideal mechanical properties. Moreover, Mg alloys are regarded as one of the promising candidates for manufacturing ureteral stents. This study proposed a multi-objective optimization method based on the Kriging surrogate model, NSGA-Ⅲ, and finite element analysis to improve the degradation performance of Mg alloy ureteral stents. MethodsThe finite element model for the degradation of Mg alloy ureteral stents has been established to compare the degradation performance of the stents under different parameters. Latin hypercube sampling was adopted to generate train sample points in the design space. Meanwhile, the Kriging surrogate model was constructed between strut parameters and stent degradation behavior. The NSGA-Ⅲ was utilized to determine the optimal solution in the global design space. ResultsThe optimized stent achieved 5.52 ​× ​degradation uniformity (M), 10 ​× ​degradation time (DT), and 4 ​× ​work time (FT). The errors between the Kriging surrogate model and the finite element calculation results were less than 6%. ConclusionThe optimized stent achieved better degradation performance. The degradation behavior of stents was dependent on the design parameters. The multi-objective optimization method based on the Kriging surrogate model and finite element analysis was effective in stent design optimization problems.

A country-level multi-objective optimization model for a sustainable steel supply chain

Steel supply chains have been pushed to consider environmental and social aspects, other than financial, however, in the context of Operational Research, the few papers proposing mathematical formulations and algorithms tackle only few dimensions of the problem. This study proposes a solution for sustainable steel production by formulating a multi-objective, multi-level, multi-modal, multi-product, and multi-period model and also devising an evolutionary algorithm for the problem. The results provide a Pareto front mapping the conflicting nature of economic, environmental and social objectives; show how changes in the production technology and transportation mode impact the objectives, and how locations with social vulnerability influence the decision of where and when to locate facilities. This paper provides a broad-ranging formulation and the results show its potential to help decision makers of the steel supply chain to make decisions considering not only economic factors.

Research on Case Reasoning Multi-attribute Group Decision-making Method Based on Hesitant Fuzzy Set

In this study, a hesitant fuzzy set-based case-based reasoning integration method is proposed for the multi-attribute group decision-making problem with unknown attribute weights and mixed forms of attribute values. First, from two perspectives, traditional distance measure and information theory, a multi-objective optimization model is constructed using the distance similarity measure and information entropy of each type of attributes to determine the attribute weights. Secondly, considering the hybrid and nonlinear characteristics of case data, based on the principle of symmetric interaction entropy and TOPSIS method, a global similarity measure based on symmetric interaction entropy is proposed and a case inference algorithm suitable for hesitant fuzzy environment is designed. Finally, by analyzing the arithmetic cases of the target case in the case base, the most similar historical cases to the target case are retrieved to determine the decision-making scheme, and the practicality and feasibility of the decision-making method are verified. The results show that considering hesitant fuzzy theory for case-based reasoning research will help improve the accuracy and reliability of decision-making and provide more effective support for multi-attribute group decision management.