Improved Non-dominated Sorting Genetic algorithm-II Research Articles

Multi-objective hybrid job-shop scheduling with multiprocessor task (HJSMT) problem with cooperative effect

In order to solve the problem of discrete manufacturing customization and personalized production scheduling, considering the influence of manual labor on processing time, we propose a multi-objective Hybrid Job-shop Scheduling with Multiprocessor Task(HJSMT) problem with cooperative effect model. Based on the actual production, two optimization objectives are set, i. e. minimizing the maximum completion time and the total tardiness. Firstly, considering the situation where workers’ cooperation reduces job processing time, the cooperative effect of workers co-processing is considered by referring to the learning effect curve in the model. Subsequently, we develop an Improved Non-dominated Sorting Genetic Algorithm-II (INSGA-II) to solve the multi-objective HJSMT problem by improving Precedence Operation Crossover (POX) and Multiple Mutations (MM) operations. Finally, the scheduling results and the C values are compared with other algorithms to verify the effectiveness of the algorithm. Simultaneously, the multi-objective HJSMT problem with the cooperative effect is solved by the INSGA-II algorithm, and the experimental results also demonstrate the superior performance of the algorithm.

A new on-line combustion optimization approach for ultra-supercritical coal-fired boiler to improve boiler efficiency, reduce NOx emission and enhance operating safety

To take into account the economy, environment protection and operating safety of the boiler in the combustion optimization process, a new on-line combustion optimization approach for boiler is proposed. The historical combustion data collected from DCS of the coal-fired power plant is preprocessed at first. Then improved biogeography optimization-based long short-term memory neural network (IBBO-LSTM) and similarity measurement method are designed to construct the adaptive dynamic combustion model for boiler with boiler efficiency, NOx emission and the temperature of water wall as outputs respectively. After that improved non-dominated sorting genetic algorithm-Ⅱ (INSGA-Ⅱ) is designed to generate a series of boiler combustion optimization solutions under different running load offline, and improved multi-level fuzzy comprehensive evaluation (IDHGF) is designed to retain the combustion optimization solutions with higher running safety. Meanwhile, the retained optimization solutions are integrated into an optimization cases base. Thereafter, case-based reasoning based on safety enhancement mechanism (CBRSEM) is designed to achieve the online combustion optimization for boiler. Finally, to confirm the effectiveness of the combination of IBBO-LSTM, INSGA-Ⅱ, IDHGF and CBRSEM, different online optimization methods (IBBO-LSTM-INSGA-Ⅱ, IBBO-LSTM-INSGA-Ⅱ-IDHGF, IBBO-LSTM-NSGA-Ⅱ-DHGF-CBR, IBBO-LSTM-NSGA-Ⅱ-IDHGF-CBR, IBBO-LSTM-NSGA-Ⅱ-DHGF-CBRSEM, IBBO-LSTM-NSGA-Ⅱ-IDHGF-CBRSEM, IBBO-LSTM-INSGA-Ⅱ-DHGF-CBR, IBBO-LSTM-INSGA-Ⅱ-IDHGF-CBR) are adopted to optimize a given combustion case. The proposed on-line combustion optimization approach for boiler received satisfied combustion optimization results that the growing for boiler efficiency was 0.653%, and the reduced concentration for NOx emission reached 22.891 mg/m3, and the operating safety raised from 5.592 to 6.913. In conclusion, IBBO-LSTM-INSGA-Ⅱ-IDHGF-CBRSEM can online offer the combustion optimization strategy to the boiler operators to improve boiler efficiency, reduce NOx emission and enhance the running safety of boiler, so that it is suitable for online application.

Dual-service integrated scheduling of manufacturing and logistics for multiple tasks in cloud manufacturing

To meet the frequent transportation requirements between distributed manufacturing services (MSs), logistics services (LSs) have played an essential role in cloud manufacturing. However, previous studies on service scheduling focused on MSs and simply treated the logistics process as a linear relationship with distance. In fact, the resulting scheduling scheme for MSs is prone to deterioration in practical implementation when the dynamic nature of LSs is neglected. Therefore, this paper presents a multi-objective model for dual-service integrated scheduling of manufacturing and logistics (DISML) and proposes an improved non-dominated sorting genetic algorithm-II (INSGA-II) to solve it. The integration of manufacturing and logistics processes introduces complex constraints, making it challenging to properly represent the solution. To address this challenge, a novel three-layer encoding approach is designed and its feasibility is demonstrated through directed graphs. Additionally, several problem-dependent heuristics are developed to enhance solving efficiency. Experimental results show that INSGA-II outperforms other algorithms in terms of IGD and C metric in 96% and 83% of instances, respectively. The results also demonstrate the advantages of the DISML mode over the decentralized scheduling mode in terms of solution quality and efficiency. Our proposed model and the results presented here provide managers with a new tool to help them schedule MSs and LSs more effectively, thereby improving production efficiency, reducing costs and unexpected delays in execution.

A knowledge-driven multiobjective algorithm for distributed hybrid flowshop with group and carryover setup in glass manufacturing systems

The distributed hybrid flow shop problem (DHFSP) exists widely in real workshop production processes. Its process optimization has important academic significance and application value, and has become one of the research hotspots in the field of production scheduling. In this study, a multiobjective DHFS problem with carryover setup time and group constraints (DHFGSP) is considered with the background of glass processing, and the objectives are the completion time and time of use price. First, a mathematical programming model is established according to the processing flow of glass production. Second, an improved nondominated sorting genetic algorithm-II (INSGAII) is adopted to optimize the problem. Third, the evolutionary strategies based on problem knowledge are developed, and a local search strategy based on critical factories is designed. Finally, the proposed algorithm is compared with several of the most advanced multiobjective algorithms, which shows that INSGA-II has better performance for solving DHFGSP.

Joint optimization of integrated mixed maintenance and distributed two-stage hybrid flow-shop production for multi-site maintenance requirements

Similar to the synergy of machines and workers in the production process, a perfect operation and maintenance (O&M) service can be implemented only when spare parts and service workers are available at the same time. Considering the production of spare parts and the limited number of workers, a collaborative optimization problem of spare parts production and worker arrangement driven by O&M is proposed in this paper. Specifically, in view of the characteristics that distributed hybrid flow-shops are often encountered in the industrial environment and one O&M activity can be completed by one worker or two workers jointly, spare parts are produced in distributed two-stage hybrid flow shop, and worker service adopts a mixed mode of one worker and two workers. To obtain a satisfactory joint optimization scheme of spare parts and workers, this paper first establishes a mixed integer programming model with dual objectives: the total weighted earliness/tardiness penalty and the number of lost orders. Then, an improved Non-dominated Sorting Genetic Algorithm-II (INSGA-II) is proposed to solve it. In INSGA-II, an initialization rule, an initialization optimization strategy and three local search operators are designed. Next, to give full play to the best performance of the algorithm, the key parameters are set by a full factor experiment. Finally, extensive experiments are carried out to verify that INSGA-II has good advantages in solving the problem studied.

A multi-objective optimization method for hydraulically interconnected suspension system

To enhance the ride comfort and roll stability of the special vehicle, this study concentrates on the inherent parameters optimization of the hydraulically interconnected suspension (HIS) system. A road-tire-HIS-body model of a special vehicle is established based on the AMESim/Simulink co-simulation platform. Then the sensitivity of the HIS system is analyzed to determine the design variables to be optimized through the AMESim/Simulink/Isight co-simulation. Two objectives including improving the ride comfort and roll stability of the vehicle are proposed. In order to enhance the population diversity and accelerate the convergence velocity, the improved non-dominated sorting genetic algorithm II (NSGA-II) based on orthogonal experimental design method is used for multi-objective optimization problem of the HIS system. The numerical simulations indicate that the improved NSGA-II (INSGA-II) can generate better distributed Pareto solutions than traditional NSGA-II. Furthermore, simulation results indicate that both of the ride comfort and roll stability of the vehicle are improved based on the HIS system optimized by INSGA-II than NSGA-II. Compared with the NSGA-II method, the vehicle ride comfort and roll stability of HIS system optimized by INSGA-II are increased by 17.62% and 8.56% in sinusoidal conditions, respectively.

A Decision-Support Model for the Generation of Marine Green Tide Disaster Emergency Disposal Plans

Green tide is a harmful marine ecological phenomenon caused by the explosive proliferation or high aggregation of some macroalgae, and can cause significant impacts on ecological environments and economies. An effective emergency disposal plan can significantly improve disposal capacity and reduce total costs. At present, the formulation of emergency disposal plans for green tide disasters usually depends on subjective experience. The primary purpose of this paper is to develop a decision-support model based on intelligent algorithms to optimize the type and number of resources when making emergency disposal plans so as to improve the reliability and efficiency of decision making. In order to simulate the decision-making environment more realistically, the drift motion of green tide is considered in this model. Two intelligent algorithms, the Genetic Algorithm (GA) and the improved Non-Dominated Sorting Genetic Algorithm-II (IMNSGA-II), are used to solve the model and find appropriate emergency disposal plans. Finally, a case study on the green tide disaster that occurred in Qingdao (Yellow Sea, China) is conducted to demonstrate the effectiveness and optimization of the proposed model. Through the model proposed in this paper, the overall response time and cost can be reduced in green tide disaster emergency operations.

Electric Vehicle Charging Station Location-Routing Problem with Time Windows and Resource Sharing

Electric vehicles (EVs) are widely applied in logistics companies’ urban logistics distribution, as fuel prices increase and environmental awareness grows. This study introduces an EV charging station (CS) location-routing problem with time windows and resource sharing (EVCS-LRPTWRS). Resource sharing, among multiple depots within multiple service periods is proposed to adjust the transportation resource configuration for a sustainable logistics development. Solving the EVCS-LRPTWRS involves a periodic CS location selection and a multi-depot multi-period EV routing optimization. A bi-objective nonlinear programming model is proposed to formulate the EVCS-LRPTWRS with a minimum total operating cost and number of EVs. A hybrid algorithm combining the Gaussian mixture clustering algorithm (GMCA) with the improved nondominated sorting genetic algorithm-II (INSGA-II) is designed to address the EVCS-LRPTWRS. The GMCA is employed to assign customers to appropriate depots in various service periods in order to reduce the computational complexity. The INSGA-II is adopted to obtain the Pareto optimal solutions by using the CS insertion operation to select CS locations and integrating the elite retention mechanism to ensure a stable and excellent performance. The superiority of the hybrid algorithm is proven by comparison with the other three algorithms (i.e., multi-objective genetic algorithm, multi-objective particle swarm optimization, and multi-objective ant colony optimization). An empirical study of the EVCS-LRPTWRS in Chongqing City, China is conducted. Then, four types of service period divisions and three scenarios of resource sharing modes are further analyzed and discussed. The empirical results demonstrate the validity and practicability of the proposed solution method in realizing a sustainable operation in EV distribution networks.

Two-Echelon Multidepot Logistics Network Design with Resource Sharing

Resource sharing within a logistics network offers an effective way to solve problems resulting from inefficient and costly operations of individual logistics facilities. However, the existing analysis of resource sharing and profit allocation is still limited. Therefore, this study aims to model resource sharing in two-echelon delivery and pickup logistics networks to improve the overall efficiency and decrease the total network operating cost. A bi-objective integer programming model is first proposed for two-echelon collaborative multidepot pickup and delivery problems with time windows (2E-CMDPDTW) to seek the minimization of operating costs and number of vehicles. Integrating a customer clustering algorithm, a greedy algorithm, and an improved nondominated sorting genetic algorithm-II (Im-NSGA-II), a hybrid method is then designed to handle the 2E-CMDPDTW model. The customer clustering and the greedy algorithms are employed to generate locally optimized initial solutions to accelerate the calculating velocity and guarantee the diversity of feasible solutions. The Im-NSGA-II combines the order crossover operation and the polynomial mutation process to find the optimal solution of the 2E-CMDPDTW. The comparative results show that the proposed hybrid method outperforms the NSGA-II and the multiobjective genetic algorithm. Furthermore, a Shapley value method is used for allocating total profits of established alliances and finding an optimal coalition sequence of the logistics facilities joining alliances based on the strictly monotonic path strategy. Finally, a case study of 2E-CMDPDTW in Chongqing China is conducted to validate the feasibility. Results indicate that this study contributes to long-term partnerships between logistics facilities within multi-echelon logistics networks in practice and contributes to the long-term sustainability of urban logistics pickup and delivery networks’ development.

Improving Performance of Distributed Collaborative Beamforming in Mobile Wireless Sensor Networks: A Multiobjective Optimization Method

Mobile wireless sensor networks (MWSNs) are resource constrained, and have limited energy and transmission range. Distributed collaborative beamforming (DCB) in MWSNs based on a virtual node antenna array (VNAA) can increase the transmission distance and enhance the energy efficiency of a single sensor node. To achieve a lower maximum sidelobe level (SLL), sensor nodes can move to optimal locations with optimal excitation current weights for DCB. However, this leads to an extra motion energy consumption. In this article, we construct a multiobjective optimization framework (MOF) to jointly optimize the maximum SLL, transmission power, and motion energy consumption of the DCB nodes in MWSNs. Moreover, an improved nondominated sorting genetic algorithm-II (INSGA-II) and a distributed parallel INSGA-II (DPINSGA-II) are proposed for solving the formulated MOF. In addition, a simple but practical DCB scheduling mechanism is proposed. The simulation results show that the maximum SLL, transmission power, and motion energy consumption of the VNAA can be effectively optimized by the proposed algorithms.

Collaborative two-echelon multicenter vehicle routing optimization based on state–space–time network representation

Collaboration among service providers in a logistics network can greatly increase their operation efficiencies and reduce transportation emissions. This study proposes, formulates and solves a collaborative two-echelon multicenter vehicle routing problem based on a state–space–time (CTMCVRP-SST) network to facilitate collaboration and resource sharing in a multiperiod state–space–time (SST) logistics network. The CTMCVRP-SST aims to facilitate collaboration in logistics networks by leveraging the spatial-temporal properties of logistics demands and resources to optimize the distribution of logistics resources in space and time to meet logistics demands. A three-component solution framework is proposed to solve CTMCVRP-SST. First, a bi-objective linear programming model based on resource sharing in a multiperiod SST network is formulated to minimize the number of vehicles and the total cost of the collaborative operation. Second, an integrated algorithm consisting of SST-based dynamic programming (DP), improved K-means clustering and improved non-dominated sorting genetic algorithm-II (Im-NSGAII) is developed to obtain optimal routes. Third, a cost gap allocation model is employed to design a collaborative mechanism that encourages cooperation among logistics service providers. Using this solution framework, the coalition sequences (i.e., the order of each logistics provider joining a collaborative coalition) are designed and the stability of the coalitions based on profit allocations is studied. Results show that the proposed algorithm outperforms existing algorithms in minimizing the total cost with all other constraints being the same. An empirical case study of a logistics network in Chongqing suggests that the proposed collaboration mechanism with SST network representation can reduce costs, improve transportation efficiency, and contribute to efficient and sustainable logistics network operations.

Optimal Siting and Sizing of Distributed Generation Based on Improved Nondominated Sorting Genetic Algorithm II

With the development of distributed generation technology, the problem of distributed generation (DG) planning become one of the important subjects. This paper proposes an Improved non-dominated sorting genetic algorithm-II (INSGA-II) for solving the optimal siting and sizing of DG units. Firstly, the multi-objective optimization model is established by considering the energy-saving benefit, line loss, and voltage deviation values. In addition, relay protection constraints are introduced on the basis of node voltage, branch current, and capacity constraints. Secondly, the violation constrained index and improved mutation operator are proposed to increase the population diversity of non-dominated sorting genetic algorithm-II (NSGA-II), and the uniformity of the solution set of the potential crowding distance improvement algorithm is introduced. In order to verify the performance of the proposed INSGA-II algorithm, NSGA-II and multiple objective particle swarm optimization algorithms are used to perform various examples in IEEE 33-, 69-, and 118-bus systems. The convergence metric and spacing metric are used as the performance evaluation criteria. Finally, static and dynamic distribution network planning with the integrated DG are performed separately. The results of the various experiments show the proposed algorithm is effective for the siting and sizing of DG units in a distribution network. Most importantly, it also can achieve desirable economic efficiency and safer voltage level.

Collaborative Mechanism for Pickup and Delivery Problems with Heterogeneous Vehicles under Time Windows

The sustainability and complexity of logistics networks come from the temporally and spatially uneven distributions of freight demand and supply. Operation strategies without considering the sustainability and complexity could dramatically increase the economic and environmental costs of logistics operations. This paper explores how the unevenly distributed demand and supply can be optimally matched through collaborations, and formulates and solves a Collaborative Pickup and Delivery Problem under Time Windows (CPDPTW) to optimize the structures of logistics networks and improve city sustainability and liverability. The CPDPTW is a three-stage framework. First, a multi-objective linear optimization model that minimizes the number of vehicles and the total cost of logistics operation is developed. Second, a composite algorithm consisting of improved k-means clustering, Demand-and-Time-based Dijkstra Algorithm (DTDA) and Improved Non-dominated Sorting Genetic Algorithm-II (INSGA-II) is devised to solve the optimization model. The clustering algorithm helps to identify the feasible initial solution to INSGA-II. Third, a method based on improved Shapley value model is proposed to obtain the collaborative alliance strategy that achieves the optimal profit allocation strategy. The proposed composite algorithm outperforms existing algorithms in minimizing terms of the total cost and number of electro-tricycles. An empirical case of Chongqing is employed to demonstrate the efficiency of the proposed mechanism for achieving optimality for logistics networks and realizing a win-win situation between suppliers and consumers.

Multi-Objective Optimal Operations Based on Improved NSGA-II for Hanjiang to Wei River Water Diversion Project, China

It is important to investigate the laws of reservoir multi-objective optimization operations, because it can obtain the best benefits from inter-basin water transfer projects to mitigate water shortage in intake areas. Given the multifaceted demands of the Hanjiang to Wei River Water Diversion Project, China (referred hereafter as “the Project”), an easy-to-operate multi-objective optimal model based on simulation is built and applied to search the multi-objective optimization operation rules between power generation and energy consumption. The Project includes two reservoirs connected by a water transfer tunnel. One is Huangjinxia, located in the mainstream of Hanjiang with abundant inflow but no regulation ability, and the other is Sanhekou, located in the tributary of Hanjiang with multi-year regulation ability but less water. The layout of the Project increases the difficulty of reservoir joint optimization operations. Therefore, an improved Non-dominated Sorting Genetic Algorithm-II (I-NSGA-II) with a feasible search space is proposed to solve the model based on long-term series data. The results show that: (1) The validated simulation model is helpful to obtain Pareto front curves to reveal the rules between power generation and energy consumption. (2) Choosing a reasonable search step size to build a feasible search space based on simulation results for the I-NSGA-II can help find more optimized solutions. Considering the influence of the initial populations of the algorithm and limited computing ability of computers, the qualified rate of Pareto points solved by I-NSGA-II are superior to NSGA-II. (3) According to the characteristics of the Project, water transfer ratio threshold value of two reservoirs are quantified for maximize economic benefits. Moreover, the flood season is a critical operation period for the Project, in which both reservoirs should supply more water to intake areas to ensure the energy balanced of the entire system. The findings provide an easy-to-operate multi-objective operation model with the I-NSGA-II that can easily be applied in optimal management of inter-basin water transfer projects by relevant authorities.

Multi-objective optimization method for spectrum allocation in cognitive heterogeneous wireless networks

In a multi-heterogeneous network dense deployment and convergence environment, the cognitive radio technology dynamically utilizes the idle spectrum resources of each primary network, which can effectively improve the data transmission rate and system capacity, and is also a key technology of the next generation wireless communication network. However, how to efficiently and reasonably select the network and allocate idle spectrum resources to meet the low cost and large traffic demand of users is a difficult problem in the case of dynamic coupling with multiple heterogeneous primary networks overlapping coverage and diversified user requirements. In this paper, with the goal of maximizing the total bandwidth and minimizing the total cost, a multi-objective optimization mathematical model for network selection and idle spectrum allocation is established in the context of comprehensive consideration of the difference of spectrum resource attributes of different primary networks in the network domain and the diversification of secondary user requirements in the user domain, and the complexity of the problem is analyzed. Based on this, two kinds of technical paths to solve the complex network selection and spectrum allocation problem are applied in this paper. The first is the simplification method. By analyzing the relationship between optimization objectives and constraints, simplification method simplifies the objective function and constraints of the mathematical model and transforms the complex allocation problem into a standard form of the 01 programming problem. The second is the intelligent optimization algorithm. By improving the traditional multi-objective optimization algorithm Non-dominated Sorting Genetic Algorithm II (NSGA-II), an improved NSGA-II(INSGA-II) method is proposed, which combines the interference constraints of the primary network and the service quality requirements of the secondary users into the objective value evaluation of NSGA-II algorithm, while making the decision selection on the optimal solution set to select a compromise solution. Finally, the performance of this two methods is compared and analyzed through experiments. The experimental results show that the simplified method has higher efficiency advantages, and the INSGA-II algorithm can often meet the user’s service requirements at a lower cost, especially the cost priority strategy.

Economic and environmental evaluations in the two-echelon collaborative multiple centers vehicle routing optimization

Abstract The two-echelon collaborative multiple centers vehicle routing problem (2E-CMCVRP) integrates collaboration mechanism and the vehicle routing problem. Combining k-means clustering algorithm and an improved Non-dominated Sorting Genetic Algorithm-II (Im-NSGA-II), this paper proposes a three-phase approach to simultaneously minimize the aggregate operating cost and reduce carbon dioxide emission. To ensure the initial population's quality, the sweep algorithm is integrated as modification of the standard NSGA-II. The chromosome population consists of multiple depots and corresponding customer nodes independently assessed to find local solutions, and latterly combined to yield suboptimal routes. The nodes scan principle of the sweep algorithm is employed to enforce optimization constraints, and the non-dominated sorting of the population efficiently improves the solution search accuracy. Further, the Minimum Cost-Remaining Savings (MCRS) method is used to determine appropriate profit distribution schemes, and the selection of the optimal sequential coalition is executed on the basis of the strictly monotonic path principle. Computational comparisons on benchmark instances indicate the superiority of Im-NSGA-II over NSGA-II and MOGA, and an empirical study in Chongqing, China confirms the practicability of our solution approach. The evaluation of MCRS solution's stability displays outperformance over other methods including the Shapley value model, CGA and GQP, and suitable coalition sequences are selected and assessed to improve the efficiency of logistics network optimization as well as the achievement of environment-friendly objectives.

An Improved Non-dominated Sorting Genetic Algorithm-II (INSGA-II) applied to the design of DNA codewords

DNA codewords design is critical for many research fields, from DNA computing, to DNA hybridization arrays, to DNA nanotechnology. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Since DNA codewords design can be regarded as a multi-objective optimization problem, and nondominated sorting genetic algorithm II (NSGA-II) has been demonstrated as one of the most efficient algorithms for multi-objective optimization problems, in this paper, we proposed an improved nondominated sorting genetic algorithm II (INSGA-II) for the design of DNA codewords. The novelty of our method is that introduced the constraints to the non-dominated sorting process. The performance of our method is compared with other DNA codewords design methods, and the experiment results in silico showed that the INSGA-II has a higher convergence speed and better population diversity than those of other algorithms, and can provide reliable and effective codewords for the controllable DNA computing.

Application of fuzzy decision-making based on INSGA-II to designing PV–wind hybrid system

This paper addresses the attuned design of wind and photovoltaic (PV) hybrid generation system to supply office buildings. The main target of this design is to minimize the annualized cost of the hybrid system, environmental cost related to pollutant gas emissions avoided due to the use of the hybrid generation system, and index of loss of power supply probability. System costs consist of investment, replacement, operation, and maintenance cost of each component. The problem of design is formulated as a multi-objective optimization issue and solved by improved non-dominated sorting genetic algorithm-II (INSGA-II). The presented technique intends to offer the optimal number of system devices such that the economic and environmental profits achieved during the systems operational lifetime period are maximized. Optimizations of decision variables are the optimal number of photovoltaic modules, wind turbines, inverters, charge controllers, and storage batteries. A decision-making methodology based on fuzzy decision-making (FDM) is applied for finding the best compromise solution from the set of Pareto-optimal solutions obtained by INSGA-II technique. Two frameworks are considered for the design procedure of hybrid generation system. In the first framework, a two-objective optimization problem is developed based on system cost and environmental cost. The second framework is formulated based on three objective functions: system cost; environmental cost; and reliability index. The proposed method has been conducted on four office buildings in city of Ardabil. The comparative analysis shows the efficiency of the proposed method.

INSGA-II implementation for optimal placement and design of flux-lock type superconducting fault current limiter with tap changer for improving distribution system reliability

Improved non-dominated sorting genetic algorithm-II (INSGA-II) implementation for the assignment of the optimal location and tap changer adjustment related to flux-lock type superconducting fault current limiter with tap changer (TC-FLSFCL) is presented in this paper. TC-FLSFCL is a flexible SFCL that has preference over previous SFCLs. In this type of SFCL the current limiting characteristics are improved and the fault current limiting level during a fault period can be adjusted by controlling the current in the third winding, which also makes the magnetic field apply to the high-Tc superconducting (HTSC) element. Three objective functions, based on reliability index, reduction of fault current, and number of installed TC-FLSFCL, are systematized and improved non-dominated sorting genetic algorithm-II (INSGA-II) style is then formed in the search for the best location and tuning of the tap changer of TC-FLSFCL to meet the fitness requirements. A decisionmaking procedure based on the technique for order preference by similarity to ideal solution (TOPSIS) is used for finding the best compromise solution from the set of Pareto-solutions obtained by INSGA-II. In a distribution network as bus 4 of Roy Billinton test system (RBTS), comparative analysis of the results obtained from the application of the resistive SFCL (RSFCL) and TC-FLSFCL is presented. The results show that optimal placement of TC-FLSFCL compared with RSFCL can improve reliability index and fault current reduction index with a less number.

Optimal Placement and Sizing of Distributed Generation via an Improved Nondominated Sorting Genetic Algorithm II

An improved nondominated sorting genetic algorithm–II (INSGA-II) has been proposed for optimal planning of multiple distributed generation (DG) units in this paper. First, multiobjective functions that take minimum line loss, minimum voltage deviation, and maximal voltage stability margin into consideration have been formed. Then, using the proposed INSGA-II algorithm to solve the multiobjective planning problem has been described in detail. The improved sorting strategy and the novel truncation strategy based on hierarchical agglomerative clustering are utilized to keep the diversity of population. In order to strengthen the global optimal searching capability, the mutation and recombination strategies in differential evolution are introduced to replace the original one. In addition, a tradeoff method based on fuzzy set theory is used to obtain the best compromise solution from the Pareto-optimal set. Finally, several experiments have been made on the IEEE 33-bus test case and multiple actual test cases with the consideration of multiple DG units. The feasibility and effectiveness of the proposed algorithm for optimal placement and sizing of DG in distribution systems have been proved.