Wireless Sensor Networks(WSNs)are one of the best technologies of the 21st century and have seen tremendous growth over the past decade.Much work has been put into its development in various aspects such as architectu...Wireless Sensor Networks(WSNs)are one of the best technologies of the 21st century and have seen tremendous growth over the past decade.Much work has been put into its development in various aspects such as architectural attention,routing protocols,location exploration,time exploration,etc.This research aims to optimize routing protocols and address the challenges arising from conflicting objectives in WSN environments,such as balancing energy consumption,ensuring routing reliability,distributing network load,and selecting the shortest path.Many optimization techniques have shown success in achieving one or two objectives but struggle to achieve the right balance between multiple conflicting objectives.To address this gap,this paper proposes an innovative approach that integrates Particle Swarm Optimization(PSO)with a fuzzy multi-objective framework.The proposed method uses fuzzy logic to effectively control multiple competing objectives to represent its major development beyond existing methods that only deal with one or two objectives.The search efficiency is improved by particle swarm optimization(PSO)which overcomes the large computational requirements that serve as a major drawback of existing methods.The PSO algorithm is adapted for WSNs to optimize routing paths based on fuzzy multi-objective fitness.The fuzzy logic framework uses predefined membership functions and rule-based reasoning to adjust routing decisions.These adjustments influence PSO’s velocity updates,ensuring continuous adaptation under varying network conditions.The proposed multi-objective PSO-fuzzy model is evaluated using NS-3 simulation.The results show that the proposed model is capable of improving the network lifetime by 15.2%–22.4%,increasing the stabilization time by 18.7%–25.5%,and increasing the residual energy by 8.9%–16.2% compared to the state-of-the-art techniques.The proposed model also achieves a 15%–24% reduction in load variance,demonstrating balanced routing and extended network lifetime.Furthermore,analysis using p-values obtained from multiple performance measures(p-values<0.05)showed that the proposed approach outperforms with a high level of confidence.The proposed multi-objective PSO-fuzzy model provides a robust and scalable solution to improve the performance of WSNs.It allows stable performance in networks with 100 to 300 nodes,under varying node densities,and across different base station placements.Computational complexity analysis has shown that the method fits well into large-scale WSNs and that the addition of fuzzy logic controls the power usage to make the system practical for real-world use.展开更多
Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may r...Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.展开更多
Vehicle Edge Computing(VEC)and Cloud Computing(CC)significantly enhance the processing efficiency of delay-sensitive and computation-intensive applications by offloading compute-intensive tasks from resource-constrain...Vehicle Edge Computing(VEC)and Cloud Computing(CC)significantly enhance the processing efficiency of delay-sensitive and computation-intensive applications by offloading compute-intensive tasks from resource-constrained onboard devices to nearby Roadside Unit(RSU),thereby achieving lower delay and energy consumption.However,due to the limited storage capacity and energy budget of RSUs,it is challenging to meet the demands of the highly dynamic Internet of Vehicles(IoV)environment.Therefore,determining reasonable service caching and computation offloading strategies is crucial.To address this,this paper proposes a joint service caching scheme for cloud-edge collaborative IoV computation offloading.By modeling the dynamic optimization problem using Markov Decision Processes(MDP),the scheme jointly optimizes task delay,energy consumption,load balancing,and privacy entropy to achieve better quality of service.Additionally,a dynamic adaptive multi-objective deep reinforcement learning algorithm is proposed.Each Double Deep Q-Network(DDQN)agent obtains rewards for different objectives based on distinct reward functions and dynamically updates the objective weights by learning the value changes between objectives using Radial Basis Function Networks(RBFN),thereby efficiently approximating the Pareto-optimal decisions for multiple objectives.Extensive experiments demonstrate that the proposed algorithm can better coordinate the three-tier computing resources of cloud,edge,and vehicles.Compared to existing algorithms,the proposed method reduces task delay and energy consumption by 10.64%and 5.1%,respectively.展开更多
To improve the efficiency of ship traffic in frequently traded sea areas and respond to the national“dual-carbon”strategy,a multi-objective ship route induction model is proposed.Considering the energy-saving and en...To improve the efficiency of ship traffic in frequently traded sea areas and respond to the national“dual-carbon”strategy,a multi-objective ship route induction model is proposed.Considering the energy-saving and environmental issues of ships,this study aims to improve the transportation efficiency of ships by providing a ship route induction method.Ship data from a certain bay during a defined period are collected,and an improved backpropagation neural network algorithm is used to forecast ship traffic.On the basis of the forecasted data and ship route induction objectives,dynamic programming of ship routes is performed.Experimental results show that the routes planned using this induction method reduce the combined cost by 17.55%compared with statically induced routes.This method has promising engineering applications in improving ship navigation efficiency,promoting energy conservation,and reducing emissions.展开更多
This paper presents a novel intelligent and effective method based on an improved ant colony optimization(ACO)algorithm to solve the multi-objective ship weather routing optimization problem,considering the navigation...This paper presents a novel intelligent and effective method based on an improved ant colony optimization(ACO)algorithm to solve the multi-objective ship weather routing optimization problem,considering the navigation safety,fuel consumption,and sailing time.Here the improvement of the ACO algorithm is mainly reflected in two aspects.First,to make the classical ACO algorithm more suitable for long-distance ship weather routing and plan a smoother route,the basic parameters of the algorithm are improved,and new control factors are introduced.Second,to improve the situation of too few Pareto non-dominated solutions generated by the algorithm for solving multi-objective problems,the related operations of crossover,recombination,and mutation in the genetic algorithm are introduced in the improved ACO algorithm.The final simulation results prove the effectiveness of the improved algorithm in solving multi-objective weather routing optimization problems.In addition,the black-box model method was used to study the ship fuel consumption during a voyage;the model was constructed based on an artificial neural network.The parameters of the neural network model were refined repeatedly through the historical navigation data of the test ship,and then the trained black-box model was used to predict the future fuel consumption of the test ship.Compared with other fuel consumption calculation methods,the black-box model method showed higher accuracy and applicability.展开更多
The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency...The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.展开更多
Maritime transportation has become an important part of the international trade system.To promote its sustainable de-velopment,it is necessary to reduce the fuel consumption of ships,decrease navigation risks,and shor...Maritime transportation has become an important part of the international trade system.To promote its sustainable de-velopment,it is necessary to reduce the fuel consumption of ships,decrease navigation risks,and shorten the navigation time.Ac-cordingly,planning a multi-objective route for ships is an effective way to achieve these goals.In this paper,we propose a multi-ob-jective optimal ship weather routing system framework.Based on this framework,a ship route model,ship fuel consumption model,and navigation risk model are established,and a non-dominated sorting and multi-objective ship weather routing algorithm based on particle swarm optimization is proposed.To fasten the convergence of the algorithm and improve the diversity of route solutions,a mutation operation and an elite selection operation are introduced in the algorithm.Based on the Pareto optimal front and Pareto optimal solution set obtained by the algorithm,a recommended route selection criterion is designed.Finally,two sets of simulated navigation simulation experiments on a container ship are conducted.The experimental results show that the proposed multi-objective optimal weather routing system can be used to plan a ship route with low navigation risk,short navigation time,and low fuel consumption,fulfilling the safety,efficiency,and economic goals.展开更多
Tourism development in emerging destinations requires balancing economic benefits with ecological sustainability.In this study,we investigate the case of multi-attraction tourism planning in Qujing City,where the dual...Tourism development in emerging destinations requires balancing economic benefits with ecological sustainability.In this study,we investigate the case of multi-attraction tourism planning in Qujing City,where the dual challenge lies in maximizing economic-experiential value while minimizing congestion-eco-logical stress.We formulate this problem as a bi-objective optimization model,integrating attraction revenues,visitor preferences,route costs,and site capacities into a unified framework.To solve the model,we employ NSGA-II en-hanced with customized crossover and mutation operators specifically designed for route structures and visitor allocations.These operators enable efficient exploration of feasible solutions while maintaining capacity and time-window constraints.Extensive experiments across different scales of scenic scenarios demonstrate that our method consistently outperforms greedy and randomized baselines in terms of hypervolume and sustainability indicators.The results highlight the effectiveness of incorporating problem-specific operators into evo-lutionary algorithms and provide practical insights for sustainable tourism man-agement in Qujing and other similar destinations.展开更多
The vehicle routing and scheduling (VRS) problem with multi-objective and multi-constraint is analyzed, considering the complexity of the modern logistics in city economy and daily life based on the system engineering...The vehicle routing and scheduling (VRS) problem with multi-objective and multi-constraint is analyzed, considering the complexity of the modern logistics in city economy and daily life based on the system engineering. The objective and constraint includes loading, the dispatch and arrival time, transportation conditions,total cost,etc. An information model and a mathematical model are built,and a method based on knowledge and biologic immunity is put forward for optimizing and evaluating the programs dimensions in vehicle routing and scheduling with multi-objective and multi-constraints. The proposed model and method are illustrated in a case study concerning a transport network, and the result shows that more optimization solutions can be easily obtained and the method is efficient and feasible. Comparing with the standard GA and the standard GA without time constraint,the computational time of the algorithm is less in this paper. And the probability of gaining optimal solution is bigger and the result is better under the condition of multi-constraint.展开更多
The overall healthcare system has been prioritized within development top lists worldwide.Since many national populations are aging,combined with the availability of sophisticated medical treatments,healthcare expendi...The overall healthcare system has been prioritized within development top lists worldwide.Since many national populations are aging,combined with the availability of sophisticated medical treatments,healthcare expenditures are rapidly growing.Blood banks are a major component of any healthcare system,which store and provide the blood products needed for organ transplants,emergency medical treatments,and routine surgeries.Timely delivery of blood products is vital,especially in emergency settings.Hence,blood delivery process parameters such as safety and speed have received attention in the literature,as well as other parameters such as delivery cost.In this paper,delivery time and cost are modeled mathematically and marked as objective functions requiring simultaneous optimization.A solution is proposed based on Deep Reinforcement Learning(DRL)to address the formulated delivery functions as Multi-objective Optimization Problems(MOPs).The basic concept of the solution is to decompose the MOP into a scalar optimization sub-problems set,where each one of these sub-problems is modeled as a separate Neural Network(NN).The overall model parameters for each sub-problem are optimized based on a neighborhood parameter transfer and DRL training algorithm.The optimization step for the subproblems is undertaken collaboratively to optimize the overall model.Paretooptimal solutions can be directly obtained using the trained NN.Specifically,the multi-objective blood bank delivery problem is addressed in this research.Onemajor technical advantage of this approach is that once the trainedmodel is available,it can be scaled without the need formodel retraining.The scoring can be obtained directly using a straightforward computation of the NN layers in a limited time.The proposed technique provides a set of technical strength points such as the ability to generalize and solve rapidly compared to othermulti-objective optimizationmethods.The model was trained and tested on 5 major hospitals in Saudi Arabia’s Riyadh region,and the simulation results indicated that time and cost decreased by 35%and 30%,respectively.In particular,the proposed model outperformed other state-of-the-art MOP solutions such as Genetic Algorithms and Simulated Annealing.展开更多
In the distributed networks,many applications send information from a source node to multiple destination nodes.To support these applications requirements,the paper presents a multi-objective algorithm based on ant co...In the distributed networks,many applications send information from a source node to multiple destination nodes.To support these applications requirements,the paper presents a multi-objective algorithm based on ant colonies to construct a multicast tree for data transmission in a computer network.The proposed algorithm simultaneously optimizes total weight(cost,delay and hop)of the multicast tree.Experimental results prove the proposed algorithm outperforms a recently published Multi-objective Multicast Algorithm specially designed for solving the multicast routing problem.Also,it is able to find a better solution with fast convergence speed and high reliability.展开更多
A Mobile Ad hoc Network(MANET)is a group of low-power con-sumption of wireless mobile nodes that configure a wireless network without the assistance of any existing infrastructure/centralized organization.The primary a...A Mobile Ad hoc Network(MANET)is a group of low-power con-sumption of wireless mobile nodes that configure a wireless network without the assistance of any existing infrastructure/centralized organization.The primary aim of MANETs is to extendflexibility into the self-directed,mobile,and wireless domain,in which a cluster of autonomous nodes forms a MANET routing system.An Intrusion Detection System(IDS)is a tool that examines a network for mal-icious behavior/policy violations.A network monitoring system is often used to report/gather any suspicious attacks/violations.An IDS is a software program or hardware system that monitors network/security traffic for malicious attacks,sending out alerts whenever it detects malicious nodes.The impact of Dynamic Source Routing(DSR)in MANETs challenging blackhole attack is investigated in this research article.The Cluster Trust Adaptive Acknowledgement(CTAA)method is used to identify unauthorised and malfunctioning nodes in a MANET environment.MANET system is active and provides successful delivery of a data packet,which implements Kalman Filters(KF)to anticipate node trustworthiness.Furthermore,KF is used to eliminate synchronisation errors that arise during the sending and receiving data.In order to provide an energy-efficient solution and to minimize network traffic,route optimization in MANET by using Multi-Objective Particle Swarm Optimization(MOPSO)technique to determine the optimal num-ber of clustered MANET along with energy dissipation in nodes.According to the researchfindings,the proposed CTAA-MPSO achieves a Packet Delivery Ratio(PDR)of 3.3%.In MANET,the PDR of CTAA-MPSO improves CTAA-PSO by 3.5%at 30%malware.展开更多
In wireless sensor network(WSN),the gateways which are placed far away from the base station(BS)forward the collected data to the BS through the gateways which are nearer to the BS.This leads to more energy consumptio...In wireless sensor network(WSN),the gateways which are placed far away from the base station(BS)forward the collected data to the BS through the gateways which are nearer to the BS.This leads to more energy consumption because the gateways nearer to the BS manages heavy traffic load.So,to over-come this issue,loads around the gateways are to be balanced by presenting energy efficient clustering approach.Besides,to enhance the lifetime of the net-work,optimal routing path is to be established between the source node and BS.For energy efficient load balancing and routing,multi objective based beetle swarm optimization(BSO)algorithm is presented in this paper.Using this algo-rithm,optimal clustering and routing are performed depend on the objective func-tions routingfitness and clusteringfitness.This approach leads to decrease the power consumption.Simulation results show that the performance of the pro-posed BSO based clustering and routing scheme attains better results than that of the existing algorithms in terms of energy consumption,delivery ratio,through-put and network lifetime.Namely,the proposed scheme increases throughput to 72%and network lifetime to 37%as well as it reduces delay to 37%than the existing optimization algorithms based clustering and routing schemes.展开更多
Unmanned aerial vehicle(UAV)was introduced as a novel traffic device to collect road traffic information and its cruise route planning problem was considered.Firstly,a multi-objective optimization model was proposed a...Unmanned aerial vehicle(UAV)was introduced as a novel traffic device to collect road traffic information and its cruise route planning problem was considered.Firstly,a multi-objective optimization model was proposed aiming at minimizing the total cruise distance and the number of UAVs used,which used UAV maximum cruise distance,the number of UAVs available and time window of each monitored target as constraints.Then,a novel multi-objective evolutionary algorithm was proposed.Next,a case study with three time window scenarios was implemented.The results show that both the total cruise distance and the number of UAVs used continue to increase with the time window constraint becoming narrower.Compared with the initial optimal solutions,the optimal total cruise distance and the number of UAVs used fall by an average of 30.93% and 31.74%,respectively.Finally,some concerns using UAV to collect road traffic information were discussed.展开更多
The multi-objective particle swarm optimization algorithm(MOPSO)is widely used to solve multi-objective optimization problems.In the article,amulti-objective particle swarm optimization algorithmbased on decomposition...The multi-objective particle swarm optimization algorithm(MOPSO)is widely used to solve multi-objective optimization problems.In the article,amulti-objective particle swarm optimization algorithmbased on decomposition and multi-selection strategy is proposed to improve the search efficiency.First,two update strategies based on decomposition are used to update the evolving population and external archive,respectively.Second,a multiselection strategy is designed.The first strategy is for the subspace without a non-dominated solution.Among the neighbor particles,the particle with the smallest penalty-based boundary intersection value is selected as the global optimal solution and the particle far away fromthe search particle and the global optimal solution is selected as the personal optimal solution to enhance global search.The second strategy is for the subspace with a non-dominated solution.In the neighbor particles,two particles are randomly selected,one as the global optimal solution and the other as the personal optimal solution,to enhance local search.The third strategy is for Pareto optimal front(PF)discontinuity,which is identified by the cumulative number of iterations of the subspace without non-dominated solutions.In the subsequent iteration,a new probability distribution is used to select from the remaining subspaces to search.Third,an adaptive inertia weight update strategy based on the dominated degree is designed to further improve the search efficiency.Finally,the proposed algorithmis compared with fivemulti-objective particle swarm optimization algorithms and five multi-objective evolutionary algorithms on 22 test problems.The results show that the proposed algorithm has better performance.展开更多
Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions ...Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.展开更多
This paper introduces the Surrogate-assisted Multi-objective Grey Wolf Optimizer(SMOGWO)as a novel methodology for addressing the complex problem of empty-heavy train allocation,with a focus on line utilization balanc...This paper introduces the Surrogate-assisted Multi-objective Grey Wolf Optimizer(SMOGWO)as a novel methodology for addressing the complex problem of empty-heavy train allocation,with a focus on line utilization balance.By integrating surrogate models to approximate the objective functions,SMOGWO significantly improves the efficiency and accuracy of the optimization process.The effectiveness of this approach is evaluated using the CEC2009 multi-objective test function suite,where SMOGWO achieves a superiority rate of 76.67%compared to other leading multi-objective algorithms.Furthermore,the practical applicability of SMOGWO is demonstrated through a case study on empty and heavy train allocation,which validates its ability to balance line capacity,minimize transportation costs,and optimize the technical combination of heavy trains.The research highlights SMOGWO's potential as a robust solution for optimization challenges in railway transportation,offering valuable contributions toward enhancing operational efficiency and promoting sustainable development in the sector.展开更多
In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimizatio...In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.展开更多
Low Earth orbit(LEO)satellite networks exhibit distinct characteristics,e.g.,limited resources of individual satellite nodes and dynamic network topology,which have brought many challenges for routing algorithms.To sa...Low Earth orbit(LEO)satellite networks exhibit distinct characteristics,e.g.,limited resources of individual satellite nodes and dynamic network topology,which have brought many challenges for routing algorithms.To satisfy quality of service(QoS)requirements of various users,it is critical to research efficient routing strategies to fully utilize satellite resources.This paper proposes a multi-QoS information optimized routing algorithm based on reinforcement learning for LEO satellite networks,which guarantees high level assurance demand services to be prioritized under limited satellite resources while considering the load balancing performance of the satellite networks for low level assurance demand services to ensure the full and effective utilization of satellite resources.An auxiliary path search algorithm is proposed to accelerate the convergence of satellite routing algorithm.Simulation results show that the generated routing strategy can timely process and fully meet the QoS demands of high assurance services while effectively improving the load balancing performance of the link.展开更多
In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the ...In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the complexity of transportation costs and demand,this study presents a novel method that offers flexible routing alternatives to manage these complexities.When real-world variables such as fluctuating costs,variable capacity,and unpredictable demand are considered,traditional transshipment models often prove inadequate.To overcome these challenges,we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers.This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters.To overcome these challenges,we develop an innovative,fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters,offering more flexible and adaptive decision-making in multi-objective transshipment problems.The proposed model also presents alternative route options,giving decisionmakers a range of choices to satisfy multiple requirements,including reducing costs,improving service quality,and expediting delivery.Through extensive numerical experiments,we demonstrate that the model can achieve greater adaptability,efficiency,and flexibility than standard approaches.This multi-path structure provides additional flexibility to adapt to dynamic network conditions.Using ranking strategies,we compared our multi-objective transshipment model with existing methods.The results indicate that,while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value,thus reducing their efficiency,our model produces solutions close to the ideal value,thereby facilitating better decision making.By combining dynamic routing alternatives with a fully fuzzybased approach,this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings.In this paper,we utilize LINGO 18 software to solve the provided numerical example,demonstrating the effectiveness of the proposed method.展开更多
基金funded by Deanship of Graduate studies and Scientific Research at Jouf University under grant No.(DGSSR-2023-2-02038).
文摘Wireless Sensor Networks(WSNs)are one of the best technologies of the 21st century and have seen tremendous growth over the past decade.Much work has been put into its development in various aspects such as architectural attention,routing protocols,location exploration,time exploration,etc.This research aims to optimize routing protocols and address the challenges arising from conflicting objectives in WSN environments,such as balancing energy consumption,ensuring routing reliability,distributing network load,and selecting the shortest path.Many optimization techniques have shown success in achieving one or two objectives but struggle to achieve the right balance between multiple conflicting objectives.To address this gap,this paper proposes an innovative approach that integrates Particle Swarm Optimization(PSO)with a fuzzy multi-objective framework.The proposed method uses fuzzy logic to effectively control multiple competing objectives to represent its major development beyond existing methods that only deal with one or two objectives.The search efficiency is improved by particle swarm optimization(PSO)which overcomes the large computational requirements that serve as a major drawback of existing methods.The PSO algorithm is adapted for WSNs to optimize routing paths based on fuzzy multi-objective fitness.The fuzzy logic framework uses predefined membership functions and rule-based reasoning to adjust routing decisions.These adjustments influence PSO’s velocity updates,ensuring continuous adaptation under varying network conditions.The proposed multi-objective PSO-fuzzy model is evaluated using NS-3 simulation.The results show that the proposed model is capable of improving the network lifetime by 15.2%–22.4%,increasing the stabilization time by 18.7%–25.5%,and increasing the residual energy by 8.9%–16.2% compared to the state-of-the-art techniques.The proposed model also achieves a 15%–24% reduction in load variance,demonstrating balanced routing and extended network lifetime.Furthermore,analysis using p-values obtained from multiple performance measures(p-values<0.05)showed that the proposed approach outperforms with a high level of confidence.The proposed multi-objective PSO-fuzzy model provides a robust and scalable solution to improve the performance of WSNs.It allows stable performance in networks with 100 to 300 nodes,under varying node densities,and across different base station placements.Computational complexity analysis has shown that the method fits well into large-scale WSNs and that the addition of fuzzy logic controls the power usage to make the system practical for real-world use.
文摘Community detection is one of the most fundamental applications in understanding the structure of complicated networks.Furthermore,it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships.Networking structures are highly sensitive in social networks,requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks.In addition,they miss out on accurately identifying clusters.Since single-objective optimization cannot always generate accurate and comprehensive results,as multi-objective optimization can.Therefore,we utilized two objective functions that enable strong connections between communities and weak connections between them.In this study,we utilized the intra function,which has proven effective in state-of-the-art research studies.We proposed a new inter-function that has demonstrated its effectiveness by making the objective of detecting external connections between communities is to make them more distinct and sparse.Furthermore,we proposed a Multi-Objective community strength enhancement algorithm(MOCSE).The proposed algorithm is based on the framework of the Multi-Objective Evolutionary Algorithm with Decomposition(MOEA/D),integrated with a new heuristic mutation strategy,community strength enhancement(CSE).The results demonstrate that the model is effective in accurately identifying community structures while also being computationally efficient.The performance measures used to evaluate the MOEA/D algorithm in our work are normalized mutual information(NMI)and modularity(Q).It was tested using five state-of-the-art algorithms on social networks,comprising real datasets(Zachary,Dolphin,Football,Krebs,SFI,Jazz,and Netscience),as well as twenty synthetic datasets.These results provide the robustness and practical value of the proposed algorithm in multi-objective community identification.
基金supported by Key Science and Technology Program of Henan Province,China(Grant Nos.242102210147,242102210027)Fujian Province Young and Middle aged Teacher Education Research Project(Science and Technology Category)(No.JZ240101)(Corresponding author:Dong Yuan).
文摘Vehicle Edge Computing(VEC)and Cloud Computing(CC)significantly enhance the processing efficiency of delay-sensitive and computation-intensive applications by offloading compute-intensive tasks from resource-constrained onboard devices to nearby Roadside Unit(RSU),thereby achieving lower delay and energy consumption.However,due to the limited storage capacity and energy budget of RSUs,it is challenging to meet the demands of the highly dynamic Internet of Vehicles(IoV)environment.Therefore,determining reasonable service caching and computation offloading strategies is crucial.To address this,this paper proposes a joint service caching scheme for cloud-edge collaborative IoV computation offloading.By modeling the dynamic optimization problem using Markov Decision Processes(MDP),the scheme jointly optimizes task delay,energy consumption,load balancing,and privacy entropy to achieve better quality of service.Additionally,a dynamic adaptive multi-objective deep reinforcement learning algorithm is proposed.Each Double Deep Q-Network(DDQN)agent obtains rewards for different objectives based on distinct reward functions and dynamically updates the objective weights by learning the value changes between objectives using Radial Basis Function Networks(RBFN),thereby efficiently approximating the Pareto-optimal decisions for multiple objectives.Extensive experiments demonstrate that the proposed algorithm can better coordinate the three-tier computing resources of cloud,edge,and vehicles.Compared to existing algorithms,the proposed method reduces task delay and energy consumption by 10.64%and 5.1%,respectively.
基金Supported by the National Key R&D Program of China project (2017YFC0805309)the National Natural Science Foundation of China (60602020)。
文摘To improve the efficiency of ship traffic in frequently traded sea areas and respond to the national“dual-carbon”strategy,a multi-objective ship route induction model is proposed.Considering the energy-saving and environmental issues of ships,this study aims to improve the transportation efficiency of ships by providing a ship route induction method.Ship data from a certain bay during a defined period are collected,and an improved backpropagation neural network algorithm is used to forecast ship traffic.On the basis of the forecasted data and ship route induction objectives,dynamic programming of ship routes is performed.Experimental results show that the routes planned using this induction method reduce the combined cost by 17.55%compared with statically induced routes.This method has promising engineering applications in improving ship navigation efficiency,promoting energy conservation,and reducing emissions.
基金funded by the Russian Foundation for Basic Research(RFBR)(No.17-07-00361a)。
文摘This paper presents a novel intelligent and effective method based on an improved ant colony optimization(ACO)algorithm to solve the multi-objective ship weather routing optimization problem,considering the navigation safety,fuel consumption,and sailing time.Here the improvement of the ACO algorithm is mainly reflected in two aspects.First,to make the classical ACO algorithm more suitable for long-distance ship weather routing and plan a smoother route,the basic parameters of the algorithm are improved,and new control factors are introduced.Second,to improve the situation of too few Pareto non-dominated solutions generated by the algorithm for solving multi-objective problems,the related operations of crossover,recombination,and mutation in the genetic algorithm are introduced in the improved ACO algorithm.The final simulation results prove the effectiveness of the improved algorithm in solving multi-objective weather routing optimization problems.In addition,the black-box model method was used to study the ship fuel consumption during a voyage;the model was constructed based on an artificial neural network.The parameters of the neural network model were refined repeatedly through the historical navigation data of the test ship,and then the trained black-box model was used to predict the future fuel consumption of the test ship.Compared with other fuel consumption calculation methods,the black-box model method showed higher accuracy and applicability.
基金Project(50775089)supported by the National Natural Science Foundation of ChinaProject(2007AA04Z190,2009AA043301)supported by the National High Technology Research and Development Program of ChinaProject(2005CB724100)supported by the National Basic Research Program of China
文摘The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.
基金the Russian Foundation for Basic Research(RFBR)(No.20-07-00531).
文摘Maritime transportation has become an important part of the international trade system.To promote its sustainable de-velopment,it is necessary to reduce the fuel consumption of ships,decrease navigation risks,and shorten the navigation time.Ac-cordingly,planning a multi-objective route for ships is an effective way to achieve these goals.In this paper,we propose a multi-ob-jective optimal ship weather routing system framework.Based on this framework,a ship route model,ship fuel consumption model,and navigation risk model are established,and a non-dominated sorting and multi-objective ship weather routing algorithm based on particle swarm optimization is proposed.To fasten the convergence of the algorithm and improve the diversity of route solutions,a mutation operation and an elite selection operation are introduced in the algorithm.Based on the Pareto optimal front and Pareto optimal solution set obtained by the algorithm,a recommended route selection criterion is designed.Finally,two sets of simulated navigation simulation experiments on a container ship are conducted.The experimental results show that the proposed multi-objective optimal weather routing system can be used to plan a ship route with low navigation risk,short navigation time,and low fuel consumption,fulfilling the safety,efficiency,and economic goals.
基金supported by Qujing Social Science Federation-Qujing Normal University Philosophy and Social Sciences Joint Special Project(ZSLH2023YB05).
文摘Tourism development in emerging destinations requires balancing economic benefits with ecological sustainability.In this study,we investigate the case of multi-attraction tourism planning in Qujing City,where the dual challenge lies in maximizing economic-experiential value while minimizing congestion-eco-logical stress.We formulate this problem as a bi-objective optimization model,integrating attraction revenues,visitor preferences,route costs,and site capacities into a unified framework.To solve the model,we employ NSGA-II en-hanced with customized crossover and mutation operators specifically designed for route structures and visitor allocations.These operators enable efficient exploration of feasible solutions while maintaining capacity and time-window constraints.Extensive experiments across different scales of scenic scenarios demonstrate that our method consistently outperforms greedy and randomized baselines in terms of hypervolume and sustainability indicators.The results highlight the effectiveness of incorporating problem-specific operators into evo-lutionary algorithms and provide practical insights for sustainable tourism man-agement in Qujing and other similar destinations.
基金National natural science foundation (No:70371040)
文摘The vehicle routing and scheduling (VRS) problem with multi-objective and multi-constraint is analyzed, considering the complexity of the modern logistics in city economy and daily life based on the system engineering. The objective and constraint includes loading, the dispatch and arrival time, transportation conditions,total cost,etc. An information model and a mathematical model are built,and a method based on knowledge and biologic immunity is put forward for optimizing and evaluating the programs dimensions in vehicle routing and scheduling with multi-objective and multi-constraints. The proposed model and method are illustrated in a case study concerning a transport network, and the result shows that more optimization solutions can be easily obtained and the method is efficient and feasible. Comparing with the standard GA and the standard GA without time constraint,the computational time of the algorithm is less in this paper. And the probability of gaining optimal solution is bigger and the result is better under the condition of multi-constraint.
文摘The overall healthcare system has been prioritized within development top lists worldwide.Since many national populations are aging,combined with the availability of sophisticated medical treatments,healthcare expenditures are rapidly growing.Blood banks are a major component of any healthcare system,which store and provide the blood products needed for organ transplants,emergency medical treatments,and routine surgeries.Timely delivery of blood products is vital,especially in emergency settings.Hence,blood delivery process parameters such as safety and speed have received attention in the literature,as well as other parameters such as delivery cost.In this paper,delivery time and cost are modeled mathematically and marked as objective functions requiring simultaneous optimization.A solution is proposed based on Deep Reinforcement Learning(DRL)to address the formulated delivery functions as Multi-objective Optimization Problems(MOPs).The basic concept of the solution is to decompose the MOP into a scalar optimization sub-problems set,where each one of these sub-problems is modeled as a separate Neural Network(NN).The overall model parameters for each sub-problem are optimized based on a neighborhood parameter transfer and DRL training algorithm.The optimization step for the subproblems is undertaken collaboratively to optimize the overall model.Paretooptimal solutions can be directly obtained using the trained NN.Specifically,the multi-objective blood bank delivery problem is addressed in this research.Onemajor technical advantage of this approach is that once the trainedmodel is available,it can be scaled without the need formodel retraining.The scoring can be obtained directly using a straightforward computation of the NN layers in a limited time.The proposed technique provides a set of technical strength points such as the ability to generalize and solve rapidly compared to othermulti-objective optimizationmethods.The model was trained and tested on 5 major hospitals in Saudi Arabia’s Riyadh region,and the simulation results indicated that time and cost decreased by 35%and 30%,respectively.In particular,the proposed model outperformed other state-of-the-art MOP solutions such as Genetic Algorithms and Simulated Annealing.
文摘In the distributed networks,many applications send information from a source node to multiple destination nodes.To support these applications requirements,the paper presents a multi-objective algorithm based on ant colonies to construct a multicast tree for data transmission in a computer network.The proposed algorithm simultaneously optimizes total weight(cost,delay and hop)of the multicast tree.Experimental results prove the proposed algorithm outperforms a recently published Multi-objective Multicast Algorithm specially designed for solving the multicast routing problem.Also,it is able to find a better solution with fast convergence speed and high reliability.
文摘A Mobile Ad hoc Network(MANET)is a group of low-power con-sumption of wireless mobile nodes that configure a wireless network without the assistance of any existing infrastructure/centralized organization.The primary aim of MANETs is to extendflexibility into the self-directed,mobile,and wireless domain,in which a cluster of autonomous nodes forms a MANET routing system.An Intrusion Detection System(IDS)is a tool that examines a network for mal-icious behavior/policy violations.A network monitoring system is often used to report/gather any suspicious attacks/violations.An IDS is a software program or hardware system that monitors network/security traffic for malicious attacks,sending out alerts whenever it detects malicious nodes.The impact of Dynamic Source Routing(DSR)in MANETs challenging blackhole attack is investigated in this research article.The Cluster Trust Adaptive Acknowledgement(CTAA)method is used to identify unauthorised and malfunctioning nodes in a MANET environment.MANET system is active and provides successful delivery of a data packet,which implements Kalman Filters(KF)to anticipate node trustworthiness.Furthermore,KF is used to eliminate synchronisation errors that arise during the sending and receiving data.In order to provide an energy-efficient solution and to minimize network traffic,route optimization in MANET by using Multi-Objective Particle Swarm Optimization(MOPSO)technique to determine the optimal num-ber of clustered MANET along with energy dissipation in nodes.According to the researchfindings,the proposed CTAA-MPSO achieves a Packet Delivery Ratio(PDR)of 3.3%.In MANET,the PDR of CTAA-MPSO improves CTAA-PSO by 3.5%at 30%malware.
文摘In wireless sensor network(WSN),the gateways which are placed far away from the base station(BS)forward the collected data to the BS through the gateways which are nearer to the BS.This leads to more energy consumption because the gateways nearer to the BS manages heavy traffic load.So,to over-come this issue,loads around the gateways are to be balanced by presenting energy efficient clustering approach.Besides,to enhance the lifetime of the net-work,optimal routing path is to be established between the source node and BS.For energy efficient load balancing and routing,multi objective based beetle swarm optimization(BSO)algorithm is presented in this paper.Using this algo-rithm,optimal clustering and routing are performed depend on the objective func-tions routingfitness and clusteringfitness.This approach leads to decrease the power consumption.Simulation results show that the performance of the pro-posed BSO based clustering and routing scheme attains better results than that of the existing algorithms in terms of energy consumption,delivery ratio,through-put and network lifetime.Namely,the proposed scheme increases throughput to 72%and network lifetime to 37%as well as it reduces delay to 37%than the existing optimization algorithms based clustering and routing schemes.
基金Project(2009AA11Z220)supported by the National High Technology Research and Development Program of China
文摘Unmanned aerial vehicle(UAV)was introduced as a novel traffic device to collect road traffic information and its cruise route planning problem was considered.Firstly,a multi-objective optimization model was proposed aiming at minimizing the total cruise distance and the number of UAVs used,which used UAV maximum cruise distance,the number of UAVs available and time window of each monitored target as constraints.Then,a novel multi-objective evolutionary algorithm was proposed.Next,a case study with three time window scenarios was implemented.The results show that both the total cruise distance and the number of UAVs used continue to increase with the time window constraint becoming narrower.Compared with the initial optimal solutions,the optimal total cruise distance and the number of UAVs used fall by an average of 30.93% and 31.74%,respectively.Finally,some concerns using UAV to collect road traffic information were discussed.
基金supported by National Natural Science Foundations of China(nos.12271326,62102304,61806120,61502290,61672334,61673251)China Postdoctoral Science Foundation(no.2015M582606)+2 种基金Industrial Research Project of Science and Technology in Shaanxi Province(nos.2015GY016,2017JQ6063)Fundamental Research Fund for the Central Universities(no.GK202003071)Natural Science Basic Research Plan in Shaanxi Province of China(no.2022JM-354).
文摘The multi-objective particle swarm optimization algorithm(MOPSO)is widely used to solve multi-objective optimization problems.In the article,amulti-objective particle swarm optimization algorithmbased on decomposition and multi-selection strategy is proposed to improve the search efficiency.First,two update strategies based on decomposition are used to update the evolving population and external archive,respectively.Second,a multiselection strategy is designed.The first strategy is for the subspace without a non-dominated solution.Among the neighbor particles,the particle with the smallest penalty-based boundary intersection value is selected as the global optimal solution and the particle far away fromthe search particle and the global optimal solution is selected as the personal optimal solution to enhance global search.The second strategy is for the subspace with a non-dominated solution.In the neighbor particles,two particles are randomly selected,one as the global optimal solution and the other as the personal optimal solution,to enhance local search.The third strategy is for Pareto optimal front(PF)discontinuity,which is identified by the cumulative number of iterations of the subspace without non-dominated solutions.In the subsequent iteration,a new probability distribution is used to select from the remaining subspaces to search.Third,an adaptive inertia weight update strategy based on the dominated degree is designed to further improve the search efficiency.Finally,the proposed algorithmis compared with fivemulti-objective particle swarm optimization algorithms and five multi-objective evolutionary algorithms on 22 test problems.The results show that the proposed algorithm has better performance.
基金partially supported by the National Natural Science Foundation of China(41930644,61972439)the Collaborative Innovation Project of Anhui Province(GXXT-2022-093)the Key Program in the Youth Elite Support Plan in Universities of Anhui Province(gxyqZD2019010)。
文摘Tourism route planning is widely applied in the smart tourism field.The Pareto-optimal front obtained by the traditional multi-objective evolutionary algorithm exhibits long tails,sharp peaks and disconnected regions problems,which leads to uneven distribution and weak diversity of optimization solutions of tourism routes.Inspired by these limitations,we propose a multi-objective evolutionary algorithm for tourism route recommendation(MOTRR)with two-stage and Pareto layering based on decomposition.The method decomposes the multiobjective problem into several subproblems,and improves the distribution of solutions through a two-stage method.The crowding degree mechanism between extreme and intermediate populations is used in the two-stage method.The neighborhood is determined according to the weight of the subproblem for crossover mutation.Finally,Pareto layering is used to improve the updating efficiency and population diversity of the solution.The two-stage method is combined with the Pareto layering structure,which not only maintains the distribution and diversity of the algorithm,but also avoids the same solutions.Compared with several classical benchmark algorithms,the experimental results demonstrate competitive advantages on five test functions,hypervolume(HV)and inverted generational distance(IGD)metrics.Using the experimental results of real scenic spot datasets from two famous tourism social networking sites with vast amounts of users and large-scale online comments in Beijing,our proposed algorithm shows better distribution.It proves that the tourism routes recommended by our proposed algorithm have better distribution and diversity,so that the recommended routes can better meet the personalized needs of tourists.
基金supported by the National Natural Science Foundation of China(Project No.5217232152102391)+2 种基金Sichuan Province Science and Technology Innovation Talent Project(2024JDRC0020)China Shenhua Energy Company Limited Technology Project(GJNY-22-7/2300-K1220053)Key science and technology projects in the transportation industry of the Ministry of Transport(2022-ZD7-132).
文摘This paper introduces the Surrogate-assisted Multi-objective Grey Wolf Optimizer(SMOGWO)as a novel methodology for addressing the complex problem of empty-heavy train allocation,with a focus on line utilization balance.By integrating surrogate models to approximate the objective functions,SMOGWO significantly improves the efficiency and accuracy of the optimization process.The effectiveness of this approach is evaluated using the CEC2009 multi-objective test function suite,where SMOGWO achieves a superiority rate of 76.67%compared to other leading multi-objective algorithms.Furthermore,the practical applicability of SMOGWO is demonstrated through a case study on empty and heavy train allocation,which validates its ability to balance line capacity,minimize transportation costs,and optimize the technical combination of heavy trains.The research highlights SMOGWO's potential as a robust solution for optimization challenges in railway transportation,offering valuable contributions toward enhancing operational efficiency and promoting sustainable development in the sector.
基金sponsored by R&D Program of Beijing Municipal Education Commission(KM202410009013).
文摘In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.
基金National Key Research and Development Program(2021YFB2900604)。
文摘Low Earth orbit(LEO)satellite networks exhibit distinct characteristics,e.g.,limited resources of individual satellite nodes and dynamic network topology,which have brought many challenges for routing algorithms.To satisfy quality of service(QoS)requirements of various users,it is critical to research efficient routing strategies to fully utilize satellite resources.This paper proposes a multi-QoS information optimized routing algorithm based on reinforcement learning for LEO satellite networks,which guarantees high level assurance demand services to be prioritized under limited satellite resources while considering the load balancing performance of the satellite networks for low level assurance demand services to ensure the full and effective utilization of satellite resources.An auxiliary path search algorithm is proposed to accelerate the convergence of satellite routing algorithm.Simulation results show that the generated routing strategy can timely process and fully meet the QoS demands of high assurance services while effectively improving the load balancing performance of the link.
基金the financial support of the European Union under the REFRESH-Research Excellence for Region Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition and has been done in connection with project Students Grant Competition SP2025/062"specific research on progressive and sustainable production technologies"and SP2025/063"specific research on innovative and progressive manufacturing technologies"financed by the Ministry of Education,Youth and Sports and Faculty of Mechanical Engineering VSB-TUOThe authors would like to extend their sincere appreciation to Researchers Supporting Project number(RSP2025R472)King Saud University,Riyadh,Saudi Arabia.
文摘In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the complexity of transportation costs and demand,this study presents a novel method that offers flexible routing alternatives to manage these complexities.When real-world variables such as fluctuating costs,variable capacity,and unpredictable demand are considered,traditional transshipment models often prove inadequate.To overcome these challenges,we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers.This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters.To overcome these challenges,we develop an innovative,fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters,offering more flexible and adaptive decision-making in multi-objective transshipment problems.The proposed model also presents alternative route options,giving decisionmakers a range of choices to satisfy multiple requirements,including reducing costs,improving service quality,and expediting delivery.Through extensive numerical experiments,we demonstrate that the model can achieve greater adaptability,efficiency,and flexibility than standard approaches.This multi-path structure provides additional flexibility to adapt to dynamic network conditions.Using ranking strategies,we compared our multi-objective transshipment model with existing methods.The results indicate that,while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value,thus reducing their efficiency,our model produces solutions close to the ideal value,thereby facilitating better decision making.By combining dynamic routing alternatives with a fully fuzzybased approach,this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings.In this paper,we utilize LINGO 18 software to solve the provided numerical example,demonstrating the effectiveness of the proposed method.
