Pareto Solutions Research Articles

Suppression of stimulated Brillouin scattering effect in 2 μm narrow linewidth Tm3+-doped fiber amplifier based on phase-modulated waveform design

In this paper, we investigate the optimal design of phase modulation waveforms using the theoretical model of Tm3+-doped fiber amplifiers. The proposed design suppresses the SBS effect in the 2 μm-band Tm3+-doped fiber amplifiers with the help of a reference point-based multi-device non-dominated sequential genetic algorithm (NSGA-III). At the same time, synthesis efficiency is ensured. Different from the previous use of conventional multi-objective genetic algorithms to suppress the SBS effect in narrow linewidth amplifiers in the 1 μm band, the maximum SBS threshold is 121 W at a signal linewidth of 496 MHz with a more uniform distribution of Pareto solutions under this scheme. The signal linewidth of 680.61 MHz increases the SBS threshold by almost 20 W and the operating speed by several times compared to a conventional multi-objective genetic algorithm at different modulation depths, modulation frequencies and modulation periods. The threshold enhancement factor of the SBS signal with optimal modulation is 2.12 times that of the sinusoidal signal with an extended bandwidth of 700 MHz. The 2 μm laser obtained by this scheme enables more accurate and longer distance ranges in coherent detection.

A voltage control method for distribution networks based on TCN and MPGA under cloud edge collaborative architecture

A distribution network voltage control method based on TCN and MPGA under cloud edge collaborative architecture is proposed to address the issues of heavy computational burden and inability to balance economic efficiency in traditional decentralized and centralized voltage control methods. Firstly, under the cloud edge collaboration architecture, the power prediction model based on time convolutional networks is trained in the cloud, and the edge predicts the load demand and new energy active output in each region based on the TCN Attention power prediction model issued by the cloud. Then, considering safety and economy comprehensively, with the goal of minimizing the daily network loss and voltage regulation cost in the distribution network, the Pareto solution set for the optimal operation point of each voltage regulation equipment in the entire distribution network was solved based on an improved multi population genetic algorithm at the distribution cloud main station. Finally, the optimal distribution network voltage control scheme is obtained based on the Pareto solution set. Based on the simulation system, experimental testing was conducted on the proposed method, and the results showed that its daily voltage regulation cost and network loss were 863.4 yuan and 43.73 MW h, respectively. The average absolute percentage error of the prediction model was 4.51 %, which was superior to other comparative methods.

Multi-objective dragonfly algorithm for optimizing a sustainable supply chain under resource sharing conditions

This research addresses optimizing production, inventory, location, and routing in a multi-level supply chain. In the studied supply chain, products are first sent to several distribution centers (DC) after production. Next, these products are delivered to several companies. Companies are divided into two independent groups considering sharing logistics resources. In this regard, vehicle routing optimization is applied for each group. For this purpose, a mixed-integer linear programming model has been developed. This model simultaneously minimizes total supply chain costs and total negative environmental impacts. A multi-objective dragonfly algorithm (MODA) has been developed to solve this model. Then, the implementation results are compared with the Non-Dominated Sorting Genetic Algorithm and Epsilon Constraint Method (EPC). Comparing the solution methods based on numerous test problems shows that the proposed MODA algorithm can be examined differently. The MODA algorithm has been able to have a significant advantage in providing solutions close to ideal points. Moreover, this algorithm has provided the most effective Pareto solutions in different test problems. However, the NSGA-II algorithm performs better regarding the spread of non-dominated solutions.

Integrated Emergency Vehicle Scheduling Model in Urban Emergency Rescue within a Time-Limited Period

Considering the uncertainty of urban emergency rescue time, it is difficult for emergency vehicles to maintain a 100% service level continuously. The biggest challenge is to minimize driving distance and costs when the number of vehicles available for deployment is uncertain. In this study, considering the limitation of emergency vehicles, a new integrated emergency vehicle scheduling model for large-scale urban emergency rescue was developed, which is able to tackle multiple emergency tasks at the same time, achieving the shortest path and the lowest cost. Then, the emergency scheduling was simulated in seven urban areas of H City in China to verify the applicability of the proposed model, during which a fast non-dominated sorting multi-objective genetic algorithm with elite strategy was used to solve this model. Moreover, the corresponding algorithm test was conducted to verify the feasibility of the Pareto solution and demonstrate its effectiveness. Moreover, the simulation results show that the used algorithm can reduce computing time by 14.27%, compared with the genetic algorithm. Finally, the optimal scheduling scheme was selected according to the decision-makers’ preferences. This study solved various emergency vehicle scheduling problems under uncertain emergency times, which was beneficial for multilateral cooperation emergency scheduling and provided decision support for emergency command departments for choosing the best emergency scheme.

Application of Improved Frog Leaping Algorithm in Multi objective Optimization of Engineering Project Management

The development of information has promoted the development of various industries, and the development of industries will inevitably lead to intensified competition, including the construction industry. To enhance the competitiveness of construction enterprises in the industry, a multi-objective optimization model for construction project management has been proposed. At the same time, carbon emission was included as one of the optimization objectives in the experiment. This can also align the construction industry with the concept of modern green development. A non-dominated sorting genetic algorithm with elite strategy was proposed to improve the hybrid frog leaping algorithm, and the improved hybrid frog leaping algorithm was used to solve multi-objective optimization problems. The improved hybrid frog leaping algorithm performed better in solving multi-objective optimization problems. The improved hybrid frog leaping algorithm found a total of 132 Pareto solution sets, while the non-dominated sorting genetic algorithm with elite strategy only found 23 Pareto solution sets. And the solution set of the improved hybrid frog leaping algorithm is closer to the optimal position. The optimized duration and cost of the improved hybrid frog leaping algorithm are lower, with an optimal duration of 135 days and a minimum cost of $20,000. A multi-objective optimization model for engineering project management incorporating carbon emissions was successfully constructed in the study, and the multi-objective optimization problem was solved.

Formulation and heuristic method for urban cold-chain logistics systems with path flexibility – The case of China

The focus of this paper is on achieving a win-win situation regarding the economic, environmental, and social impacts of the cold chain logistics terminal distribution system. This paper proposes three multi-objective models to investigate the above effects by incorporating soft time windows, heterogeneous fleets, and path flexibility, with defining the objectives of examining logistics costs, fuel consumption, carbon emissions, quality damage to perishable commodities, and customer satisfaction using six evaluation functions. To solve the proposed models, an efficient optimization framework is developed by combining domain operators with versatile multi-objective evolutionary algorithms (MOEA) to obtain Pareto solutions. Extensive experiments are conducted to test the validity of the concerned model and algorithms. The results demonstrate that: (1) the proposed algorithm is effective in solving the proposed model; (2) the proposed multi-path strategy can effectively improve the performance of cold-chain logistics systems compared to single-path strategies; (3) evaluation functions that assess customer satisfaction greatly affect the performance of cold-chain logistics systems; and (4) the trade-off relationship between the objectives should be investigated to define the model. The paper also provides valuable managerial insights for improving the efficiency and sustainability of cold-chain logistics operations.

Multi-objective optimization for reciprocating expansion engine used in compressed air energy storage (CAES) systems

Instability poses a significant challenge for renewable energies such as solar and wind power. Addressing this issue involves generating compressed air and implementing storage solutions (CAES). Reciprocating engines emerge as a viable option for the recovery of compressed air, offering a potential solution to mitigate the instability associated with solar and wind energy sources. The current research initially identified the parameters influencing engine performance. Subsequently, the engine's performance was assessed at input pressures of 10, 8, and 6 bar. The optimization process was then carried out using the Pareto solution as a multi-objective optimization method, complemented by the TOPSIS method. These parameters included the engine speed, piston diameter, piston stroke, inlet port diameter, and outlet port diameter. The results show the optimum engine speed at 6 & 10 bar is 1500 rpm and at 8 bar was 1750 rpm. Also, piston diameter at 6, 8 and 10 bar are obtained 12, 10 and 10 cm, respectively. Furthermore, the power generation at input pressures of 6, 8, and 10 bar was determined to be 15.86 kW, 14.02 kW, and 16.01 kW, respectively.

Knowledge Equivalence in Digital Twins of Intelligent Systems

A digital twin contains up-to-date data-driven models of the physical world being studied and can use simulation to optimise the physical world. However, the analysis made by the digital twin is valid and reliable only when the model is equivalent to the physical world. Maintaining such an equivalent model is challenging, especially when the physical systems being modelled are intelligent and autonomous. The paper focuses in particular on digital twin models of intelligent systems where the systems are knowledge-aware but with limited capability. The digital twin improves the acting of the physical system at a meta-level by accumulating more knowledge in the simulated environment. The modelling of such an intelligent physical system requires replicating the knowledge-awareness capability in the virtual space. Novel equivalence maintaining techniques are needed, especially in synchronising the knowledge between the model and the physical system. This paper proposes the notion of knowledge equivalence and an equivalence maintaining approach by knowledge comparison and updates. A quantitative analysis of the proposed approach confirms that compared to state equivalence, knowledge equivalence maintenance can tolerate deviation thus reducing unnecessary updates and achieve more Pareto efficient solutions for the trade-off between update overhead and simulation reliability.

Network structure guided multi-objective optimization approach for key entity identification

Multi-objective key entity identification problems have attracted the attention of researchers due to their potential real-world applications, which single-objective approaches simply cannot provide. However, existing multi-objective optimization models seldom consider the heterogeneous propagation costs of key entities. In addition, most multi-objective algorithms are directly used to solve these models, leading to poor performance since they easily fall into local optimal solutions and cause isolated points on the Pareto frontier. This study aims to address the multi-objective key entity identification problem by maximizing the propagation scale while simultaneously minimizing the heterogeneous propagation costs to obtain a more realistic model. A network structure guided approach was designed to solve the formulated model. This consisted of two new strategies, i.e., the best candidate selection strategy and the layered crossover operator strategy, to enhance candidates during the evolution process and to obtain more complete Pareto solutions. Finally, experiments conducted using synthetic and real-world networks show that the proposed approach improves upon five commonly studied multi-objective algorithms and achieves superior performance compared to similar approaches on the Pareto frontier across a number of metrics.

Green Vessel Scheduling with Weather Impact and Emission Control Area Consideration

Emissions of maritime transport have been a critical research topic with the substantial growth in the global shipping industry, encompassing both the expansion of the world fleet and the increased distances it has been covering recently. The International Maritime Organization (IMO) has enforced some regulations to mitigate ship Greenhouse Gas (GHG) emissions, which affect vessels’ operational practice, and further affect service reliability. In this paper, some compliance methods (two-speed strategy, fuel switching, and LNG) against Emission Control Areas (ECAs) at the operational level are examined regarding if and how they impact the liner shipping schedule and service reliability; meanwhile, uncertain weather conditions and port times, as the main uncertain factors, are also involved. Then, a bi-objective fuzzy programming model is formulated and solved by the augmented ε-constraint approach, which generates a set of Pareto solutions by balancing the economic and environmental sustainability. Some findings can be concluded through the experimental results, including that, firstly, to meet uncertain weather conditions at sea requires strong robustness; secondly, ECA regulations can negatively affect the liner shipping service level; moreover, slow steaming is an immediate and effective measure to reduce GHG emissions; and, furthermore, ship routing choice could have a significant influence on ship emissions and service reliability.

Vessel voyage schedule planning for maritime ore transportation

This paper introduces a vessel voyage schedule planning problem for maritime ore transportation arising from a real-world project in Boffa, Guinea. In this problem, delay of vessel arrivals at the loading port often occurs which interrupts the ore loading operation and further impacts the yearly throughput of ore transportation, which dues to variable weather conditions at sea and changing loading/discharging time at ports. Thus, factors regarding the uncertainty of vessel voyages must be considered in order to ensure continuous vessel arrivals and uninterrupted loading operations at the original port, leading to an increase in the overall productivity of the project. And at the same time, since every voyage entails an increase in costs, cost control is necessary to be accounted for, so there is also a need to consider minimizing operating costs. In this study, to address the uncertainty in voyage duration, a chance-constrained model is introduced to obtain sailing schedules as well as the associated costs within a given confidence level. And then, for the multi-objective requirements, we develop a multi-objective planning model and the actual system operating capacity limitation constraints are considered. After that, considering that the multi-objective model cannot be solved by the solver directly, the weighting method is introduced. Afterwards, since the direct solving of the model is rather time-consuming, valid cuts are designed to accelerate it. Finally, considering that the Pareto solutions of multi-objective problems are numerous, a nondominated sorting genetic algorithm II (NSGA-II) is launched with the aim of providing more solutions to the manager in a shorter time. In terms of experiments, each of the aforementioned issues and proposed remedies are verified. The results confirm the effectiveness of the valid cuts and NSGA-II, and demonstrate that the obtained vessel voyage schedule is more robust and outperforms manual decisions.

Multi-objective Quantum Annealing approach for solving flexible job shop scheduling in manufacturing

Flexible Job Shop Scheduling (FJSSP) is a challenging optimization problem with multiple conflicting objectives used to model and compute real-world process scheduling tasks. In order for a manufacturing system to remain competitive, it is necessary to compute such optimization problems quickly and efficiently. The limitations of conventional optimization methods frequently stem from a delicate balance between solution quality and computation time. Consequently, a pressing need for solution algorithms arises that can effectively transcend these limitations. This paper presents a novel Quantum Annealing-based solving algorithm (QASA) for computing FJSSP, leveraging the power of Quantum Annealing combined with classical techniques. The proposed approach aims to optimize a multi-criterial FJSSP considering makespan, total workload, and job priority simultaneously. QASA employs a Hamiltonian formulation with Lagrange parameters to integrate the problem's constraints and objectives. By assigning appropriate weights to the objectives, the method allows the prioritization of certain objectives over others. To handle the computational complexity of large FJSSP instances, the problem is decomposed into smaller subproblems, and a decision logic based on bottleneck factors is employed to select critical jobs for computation combined with variable pruning techniques. To evaluate the effectiveness of the proposed approach, experiments are conducted on benchmark problems, considering makespan, total workload, and priority objectives. Therefore, QASA combining tabu search, simulated annealing, and Quantum Annealing is used for efficient computation and is compared with a classical solving algorithm (CSA) combining tabu search and simulated annealing. The results demonstrate that QASA outperforms CSA in terms of solution quality, as measured by set coverage and hypervolume ratio metrics. Furthermore, computational efficiency analysis reveals that QASA achieves superior Pareto solutions compared to the classical approach, with a reasonable increase in computation time.

Deep learning-based field-guided optimization method

TEAM Problem 35, a benchmark problem in the optimization of electrical equipment, is a multi-objective, multi-variable optimization problem involving uniform field optimization. This paper proposes a novel guided optimization algorithm to address this problem and achieve optimal magnetic field regulation. First, the deep learning method is used to predict the magnetic field of the solenoid; second, the generated magnetic field cloud map is screened to extract the magnetic field information of the more optimal solution with uniform magnetic field distribution by calculating the variance of the generated magnetic field map; finally, the magnetic field features are combined with the particle swarm optimization algorithm; specifically, the variance of the calculated magnetic field map is added to the objective function of the optimization algorithm to strengthen the optimization process. This integration improves the convergence speed of the optimization process and ensures the continuity and stability of the obtained Pareto solutions. To optimize the solenoid, this paper considers the uniformity of magnetic field distribution and power loss as the primary optimization objectives. The radius of the coil is chosen as the design variable. The optimization results are compared with those obtained by conventional optimization algorithms, demonstrating superior optimization performance.

Research on multi-objective flow shop scheduling optimization in supply chain environment based on Fuzzy Relevance Entropy Method

For the multi-objective flow shop scheduling problem in the supply chain environment, this paper proposes the Fuzzy Relevance Entropy method (FREM) to solve the adaptive value assignment problem in the multi-objective optimization process of the supply chain environment by combining Fuzzy Information Entropy Theory (FIET) and Degree of Membership Function (DMF). Firstly, the uncertainty of each sub-objective of the ideal solution and Pareto solution of the objective is extracted using the Degree of Membership Function. Secondly, each solution is mapped into an affiliation degree fuzzy set and the information contained in the fuzzy set is reprocessed using Fuzzy Information Entropy Theory. Finally, the amount of information contained in the ideal solution solved by the Pareto method is used to guide the evolution of the Particle Swarm Optimization (PSO) algorithm, thus avoiding the traditional multi-objective optimization process of assigning weights to solve the fitness link. This paper combines both the Fuzzy Relevance Entropy method and the Stochastic Weight method with Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms to address the five-objective flow shop scheduling problem in the supply chain environment. Experimental results demonstrate that the proposed Fuzzy Relevance Entropy method effectively solves the multi-objective flow shop scheduling problem in the supply chain environment and achieves better optimization results compared to the Stochastic Weight method.

An efficient many-objective optimization algorithm for computation offloading in heterogeneous vehicular edge computing network

Vehicular Edge Computing (VEC) provides flexible distributed computing paradigm for vehicular network through computation offloading. With the advent of a growing of modern vehicle applications, the challenge for VEC network to fulfill the expansive demands from various suppliers, users and environments is increasingly prominent. This paper formulates a many-objective computation offloading problem in heterogeneous VEC network aiming to fulfill the diversified optimization requirements, including minimizing the task completion time, energy consumption and resource costs as well as load balance. A many-objective optimization algorithm named MaOITGO-CO is proposed to solve the formulated problem based on ITGO (Invasive Tumor Growth Optimization) by simulating the growth patterns of tumor cells. Specifically, considering the characteristics of computation offloading in VEC scenarios such as mobility, real-time requirements and the variety of tasks and resources, four types of tumor cells are equipped with different search strategies to enhance the search effectiveness and efficiency. The simulation results show that the proposed approach can provide high quality Pareto solutions for computation offloading problem, which outperforms other widely used algorithms in terms of convergency and diversity. Furthermore, the results of scalability experiments validate the availability of MaOITGO-CO when the problem is extended to different scales of both tasks and computing resources.

Multi-objective optimization of thermal modules in high heat flux laptops

The thermal module, as an important cooling pathway for chips, is a major factor affecting the performance of laptops. However, thermal analysis and optimization of the whole thermal module of a laptop is absent. Moreover, cost is also a major consideration in the design of a laptop’s thermal module. In this study, based on the thermal module of a high heat flux prototype laptop, we constructed an efficient thermal resistance network model and a cost model to evaluate the impact of different components. Furthermore, we employed NSGA-II (non-dominated sorting genetic algorithm II) to enhance the thermal module's heat dissipation capacity while minimizing cost. By obtaining Pareto solutions that provided optimal thermal resistances for the components in the thermal module, we then utilized LINMAP (linear programming technique for multidimensional analysis of preference) as a decision-making method to determine the best compromise solution. The best compromise solution focuses on reducing the thermal resistances of the thermal interface material on the high heat flux APU side, the shared heat pipe, and heatsinks to enhance the heat dissipation capacity of the thermal module. To control cost, sacrifices were made in the heat transfer performances of the thermal interface material on the GPU side and the independent heat pipes. Comparing the best compromise solution with the prototype, the cooling capacity is improved by 24% and cost is reduced by 9%. The efficient model coupled with optimization method may provide a new theoretical guideline for the laptop designers.

Modeling and solving the multi-objective energy-efficient production planning and scheduling with imperfect maintenance activities

PurposeThe purpose of this study is to propose a new mathematical model that integrates strategic decision-making with tactical-operational decision-making in order to optimize production and scheduling decisions.Design/methodology/approachThis study presents a multi-objective optimization framework to make production planning, scheduling and maintenance decisions. An epsilon-constraint method is used to solve small instances of the model, while new hybrid optimization algorithms, including multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm, multi-objective harmony search and improved multi-objective harmony search (IMOHS) are developed to address the high complexity of large-scale problems.FindingsThe computational results demonstrate that the metaheuristic algorithms are effective in obtaining economic solutions within a reasonable computational time. In particular, the results show that the IMOHS algorithm is able to provide optimal Pareto solutions for the proposed model compared to the other three algorithms.Originality/valueThis study presents a new mathematical model that simultaneously determines green production planning and scheduling decisions by minimizing the sum of the total cost, makespan, lateness and energy consumption criteria. Integrating production and scheduling of a shop floor is critical for achieving optimal operational performance in production planning. To the best of the authors' knowledge, the integration of production planning and maintenance has not been adequately addressed.

Methodology for predicting dynamic response of multi-layer aluminum foam protected RC slabs under blast loading

Multi-layer aluminum foam with varying density distribution has been proven to exhibit significant blast alleviation capabilities under blast loads. Using the equivalent multiple degree of freedom (MDOF) method and rigid-perfectly-plastic-locking (RPPL) model, an analytical model for multi-layer aluminum foam protected RC (MF-RC) slabs is developed to predict displacement and energy properties. Studies on MF-RC slabs show that multi-layer aluminum foam with greater energy absorption causes more damage to RC slabs, revealing the limitations of the energy assessment method. RC slab displacement is used as a comprehensive assessment parameter for multi-layer aluminum foam using the pressure-impulse (P–I) diagram approach. Calculations and analyses of assessment indicators for different foam density distributions of triple-layer foam are carried out to compare their mitigation capacities under blast. Moreover, the multi-layer feedforward neural network (MFNN) is used as the surrogate model of the MDOF module, and an optimum Pareto solution between energy absorption and structural damage prevention is obtained using the non-dominated sorting genetic algorithm II (NSGA-II).

An efficient mixed-variable generation operator for integrated energy system configuration optimization

Energy consumption has skyrocketed as society has progressed, resulting in energy crises and environmental issues. New energy technologies are being developed to address these challenges, and technologies such as the cogeneration of electricity, heating, and cooling are being used to improve energy utilization. The configuration of an energy system has a critical impact on the economics of the system, its ability to supply energy, etc. This study establishes a multiobjective mixed-variable configuration optimization model for a comprehensive combined cooling, heating, and power energy system. The model considers equipment types (categorical variables), equipment quantities (integer variables), and critical parameters (real variables) as optimization variables, where economic performance, the proportion of renewable energy, supply shortage, and dependence on the external power grid are considered unoptimized objectives. This is a multiobjective and mixed-variable problem, and the combination of the two properties poses an excellent challenge for evolutionary algorithms in optimizing the model. Therefore, we propose an efficient generating operator based on a fully connected weighted neural network, called the FCWN operator. This operator overcomes the challenge of the discrete variable space and broken neighborhood relationships in mixed-variable problems. During the algorithm search process, search history information is used to update the fully connected weight network for distribution estimation of the variable space. Offspring are generated based on the fully connected network to improve the algorithm’s search efficiency. In the experimental section, we construct a model with 20 variables and conduct simulation-based configuration optimization for scenarios with 3, 5, and 8 available equipment types. The final obtained Pareto frontier solution set is evaluated using the hypervolume metric, a widely used multiobjective evaluation metric. The Wilcoxon rank sum test on the experimental results shows that the proposed algorithm has better results than other state-of-the-art algorithms at a 95% confidence level.

Parallelization of AMALGAM algorithm for a multi-objective optimization of a hydrological model

A calibration procedure is essential step to achieve a realistic model simulation particularly in hydrological model which simulates water cycle in the basin. This process is always faced with challenges due to selection of objective function and highly time-consuming. This study aimed to take advantage of parallel processing to accelerate the computations involved with simulation process of hydrologic model linked with the multi-objective optimization algorithm of AMALGAM for multi-site calibration of SWAT hydrologic model parameters. In order to illustrate how meaningful SWAT model calibration trade-off between the four objective functions involved in AMALGAM optimization program, the Pareto solution sets were provided. Furthermore, it is implemented a group of model runs with a number of cores involved (from one to eight) to demonstrate and evaluate the running of parallelized AMALGAM with taking advantages of “spmd” method to decrease the running time of the SWAT model. The results revealed the robustness of the method in reducing computational time of the parameter calibration significantly. This strategy with 4-objective functions focuses on high streamflow (Nash–Sutcliffe coefficient), low streamflow (Box–Cox transformed root–mean–square error), water balance (runoff coefficient error), and flashiness (slope of the flow duration curve error) provided an efficient tool to decide about the best simulation based on the investigated objective functions. This study also provides a strong basis for multi-objective optimization of hydrological and water quality models and its general analytical framework could be applied to other parts of the world.