Set Of Non-dominated Solutions Research Articles

Optimal planning of hybrid electric-hydrogen energy storage systems via multi-objective particle swarm optimization

Abstract: In recent years, hydrogen is rapidly developing because it is environmentally friendly and sustainable. In this case, hydrogen energy storage systems (HESSs) can be widely used in the distribution network. The application of hybrid electric-hydrogen energy storage systems can solve the adverse effects caused by renewable energy access to the distribution network. In order to ensure the rationality and effectiveness of energy storage systems (ESSs) configuration, economic indicators of battery energy storage systems (BESSs) and hydrogen energy storage systems, power loss, and voltage fluctuation are chosen as the fitness function in this paper. Meanwhile, multi-objective particle swarm optimization (MOPSO) is used to solve Pareto non-dominated set of energy storage systems’ optimal configuration scheme, in which the technique for order preference by similarity to ideal solution (TOPSIS) based on information entropy weight (IEW) is used select the optimal solution in Pareto non-dominated solution set. Based on the extended IEEE-33 system and IEEE-69 system, the rationality of energy storage systems configuration scheme under 20% and 35% renewable energy penetration rate is analyzed. The simulation results show that the power loss can be reduced by 7.9%–22.8% and the voltage fluctuation can be reduced by 40.0%–71% when the renewable energy penetration rate is 20% and 35% respectively in IEEE-33 and 69 nodes systems. Therefore, it can be concluded that the locations and capacities of energy storage systems obtained by multi-objective particle swarm optimization can improve the distribution network stability and economy after accessing renewable generation.

A semi-desirable location and sizing model for hydrogen fuel storage areas: A case study for Istanbul

Due to their sustainable nature and high energy efficiency, hydrogen fuel vehicles (HFVs) gradually replace gasoline internal combustion engine vehicles. The increasing number of HFVs brings out the need for installing hydrogen fuel storage areas (HFSAs) that serve as local suppliers for the fuel retail stations. In this study, we consider the HFSA locating and sizing problem for the Anatolian side of Istanbul and pose it as a bi-objective semi-desirable facility location problem which incorporates both social and transshipment costs as push and pull objectives. Next, by adopting a weighted goal programming framework, we minimize the total weighted unwanted deviations from each goal for years between 2021 and 2030 while accounting for several organizational and governmental rules. Our modelling approach is also supported by a structured demand prediction methodology which accounts for the HFV market penetration rates and other parameters such as predicted population, number of HFVs on road, etc. Having two conflicting objectives, we adopt a posteriori approach and generate a representative set of non-dominated solutions to provide decision support to planners and investors. Finally, we perform a sensitivity analysis to account for the uncertainty in the hydrogen fuel demands of districts by defining an uncertainty set for the demand of each district. Sensitivity analysis reveals how and how much change in the district demands modify the most preferred solution.

MaOMFO: Many-objective moth flame optimizer using reference-point based non-dominated sorting mechanism for global optimization problems

Many-objective optimization (MaO) deals with a large number of conflicting objectives in optimization problems to acquire a reliable set of appropriate non-dominated solutions near the true Pareto front, and for the same, a unique mechanism is essential. Numerous papers have reported multi-objective evolutionary algorithms to explain the absence of convergence and diversity variety in many-objective optimization problems. One of the most encouraging methodologies utilizes many reference points to segregate the solutions and guide the search procedure. The above-said methodology is integrated into the basic version of the Moth Flame Optimization (MFO) algorithm for the first time in this paper. The proposed Many-Objective Moth Flame Optimization (MaOMFO) utilizes a set of reference points progressively decided by the hunt procedure of the moth flame. It permits the calculation to combine with the Pareto front yet synchronize the decent variety of the Pareto front. MaOMFO is employed to solve a wide range of unconstrained and constrained benchmark functions and compared with other competitive algorithms, such as non-dominated sorting genetic algorithm, multi-objective evolutionary algorithm based on dominance and decomposition, and novel multi-objective particle swarm optimization using different performance metrics. The results demonstrate the superiority of the algorithm as a new many-objective algorithm for complex many-objective optimization problems.

Directional Pareto Front and Its Estimation to Encourage Multi-Objective Decision-Making

This work introduces the following concepts of directional and estimated directional Pareto front to encourage multi-objective decision making, especially when the Pareto front exists in limited regions in the objective space. The general output of multi-objective optimization is a set of non-dominated solutions to approximate the Pareto front. When the Pareto front exists in limited regions, few solutions are obtained and presented to the decision maker. The limited output representing the objective value trade-off is a barrier to multi-objective decision making. The directional Pareto front introduced in this study is a superset of the Pareto front and supplements the objective value trade-off between the Pareto fronts. The estimated directional Pareto front is a response surface that represents the directional Pareto front using a limited number of points, which are objective vectors of the obtained solutions. The experimental results show that the directional Pareto front and the estimated front provide an objective value trade-off even in areas where the Pareto front does not exist and enhances the explanation of the objective space of the target problem.

Elements of simulated annealing in Pareto front search

Determination of the Pareto front of location problem solutions represents one of the very complex and computational time demanding tasks, when solved by exact means of mathematical programming. This paper is motivated by possible application of the metaheuristic simulated annealing to the process of obtaining a close approximation of the Pareto front by a set of non-dominated solutions of the p-location problem. Contrary to the other approaches, the suggested method is based on minimization of non-dominated solution set area, which directly describes quality of the approximation. Elements of the simulated annealing method are used for random breaking some limits imposed on local characteristics of the improving process. The presented results of the numerical experiments give an insight to relations among the simulated annealing parameters and optimization process efficiency.

Multi-Strategy Dynamic Evolution-Based Improved MOEA/D Algorithm for Solving Multi-Objective Fuzzy Flexible Job Shop Scheduling Problem

A scheduling model was developed to optimize the maximum completion time, total machine load, and maximum machine load for the fuzzy flexible job shop problem with uncertain processing times. To solve this problem, a multi-strategy dynamic evolution-based improved multi-objective evolutionary algorithm based on decomposition(IMOEA/D) was proposed. In order to enhance the quality of the non-dominated solution set and improve the algorithm efficiency. The algorithm firstly employs a strategy based on minimum processing time and workload, along with a non-dominated solution prioritization mechanism to generate the initial population. Secondly, three evolutionary strategies are incorporated, and their probabilities are dynamically adjusted with the increase of evolution generations. Finally, a variable neighborhood search method is introduced to improve the search performance of the algorithm. The effectiveness of the proposed algorithm was demonstrated through experimental validation.

Multiobjective Economic/Environmental Dispatch Using Harris Hawks Optimization Algorithm

The eminence of Economic Dispatch (ED) in power systems is significantly high as it involves in scheduling the available power from various power plants with less cost by compensating equality and inequality constrictions. The emission of toxic gases from power plants leads to environmental imbalance and so it is highly mandatory to rectify this issues for obtaining optimal performance in the power systems. In this present study, the Economic and Emission Dispatch (EED) problems are resolved as multi objective Economic Dispatch problems by using Harris Hawk’s Optimization (HHO), which is capable enough to resolve the concerned issue in a wider range. In addition, the clustering approach is employed to maintain the size of the Pareto Optimal (PO) set during each iteration and fuzzy based approach is employed to extricate compromise solution from the Pareto front. To meet the equality constraint effectively, a new demand-based constraint handling mechanism is adopted. This paper also includes Wind energy conversion system (WECS) in EED problem. The conventional thermal generator cost is taken into account while considering the overall cost functions of wind energy like overestimated, underestimated and proportional costs. The quality of the non-dominated solution set is measured using quality metrics such as Set Spacing (SP) and Hyper-Volume (HV) and the solutions are compared with other conventional algorithms to prove its efficiency. The present study is validated with the outcomes of various literature papers.

The innovative path of diversified vocal music education reform in colleges and universities under the advanced educational concepts of China and the West

Abstract In order to conform to the development of the times and effectively promote the reform of vocal music education in colleges and universities, this paper proposes an innovative path of diversified vocal music education reform in colleges and universities under the modern advanced educational concepts that are steadily gaining utilisation and popular acceptance in China and the West. In this paper, the passive collective behaviour of biology is introduced in the teacher stage in the basic TLBO algorithm, and then the feedback stage is added after the student stage to increase the effectiveness of students’ learning methods, maintain the diversity of students and make available a system the deployment of which would swiftly bring students with poor grades to the attention of teachers; to this end, the algorithm is made to perform a local fine search, and the optimisation accuracy of the algorithm and its global search ability are improved. Finally, based on the numerical simulation of the standard test set and compared with the existing optimised TLOB algorithm, it is concluded that 92% of the solutions in the ETLBO are dominated or not dominated by the solutions in the non-dominated solution set of the optimised TLBO, while only 2% of the solutions in the non-dominated solution set of the optimised ETLBO are dominated by the non-dominated solutions of the TLBO. Centralised solutions dominate or do not dominate each other. It is concluded that the optimised TLBO algorithm has the best solution ability and also has practical application significance.

Optimal placement of manual and remote-controlled switches based on the Pareto front

Optimal switch placement is of paramount importance for improving the reliability of power distribution networks. In this context, this work proposes a model based on mixed-integer linear programming (MILP) for determining the optimal number of manual switches (MSs) and remote-controlled switches (RCSs) to be placed on the system nodes. The analysis relies on obtaining the Pareto front between cost and the expected energy not supplied (EENS) index. The method allows the simultaneous placement of both types of switches, thus being an important tool that can be incorporated into the decision-making process while taking into account two conflicting objectives, that is, cost and reliability. The proposed approach is applied to a benchmark test system, whereas the Pareto front is defined in terms of a set of non-dominated solutions. The results evidence that using MSs and RCSs simultaneously can significantly reduce the EENS by up to 80%.

Accuracy-diversity optimization in personalized recommender system via trajectory reinforcement based bacterial colony optimization

Personalized recommender systems have been extensively studied in human-centered intelligent systems. Existing recommendation techniques have achieved comparable performance in predictive accuracy; however, the trade-off between recommendation accuracy and diversity poses new challenges, as diversification may lead to accuracy loss, whereas it can solve the over-fitting problem and enhance the user experience. In this study, we propose a heuristic optimization-based recommendation model that jointly optimizes accuracy and diversity performance by obtaining a set of optimized solutions. To establish the best accuracy-diversity balance, a novel trajectory-reinforcement-based bacterial colony optimization algorithm was developed. The improved bacterial colony optimization algorithm was comprehensively evaluated by comparing it with eight popular and state-of-the-art algorithms on ten benchmark testing problems with different degrees of complexity. Furthermore, an optimization-based recommendation model was applied to a real-world recommendation dataset. The results demonstrate that the improved bacterial colony optimization algorithm achieves the best overall performance for benchmark problems in terms of convergence and diversity. In the real-world recommendation task, the proposed approach improved the diversity performance by 1.62% to 8.62% while maintaining superior (1.88% to 40.32%) accuracy performance. Additionally, the proposed personalized recommendation model can provide a set of nondominated solutions instead of a single solution to accommodate the ever-changing preferences of users and service providers. Therefore, this work demonstrates the excellence of an optimization-based recommendation approach for solving the accuracy-diversity trade-off.

A novel multi-objective evolutionary algorithm for hybrid renewable energy system design

As a result of the fossil fuel energy crisis and the focus on environmental protection, renewable energy is favoured throughout the world. Due to the unstable and unpredictable nature of renewable energy, a hybrid renewable energy system (HRES) that integrates traditional fossil fuel and renewable energy is a promising solution to overcome this challenge. In this paper, a novel multi-objective evolutionary algorithm with a diversity-maintained mechanism (MOEA-DM) is applied to the design of a multi-objective HRES. We propose a special environmental selection strategy to enhance the diversity of solutions, considering the discrete optimization of the HRES design. In the experiments, a stand-alone hybrid system including photovoltaic (PV) panels, wind power generators, batteries and diesel generators is applied to find the optimal combination of components with a set of nondominated solutions. The effectiveness, superiority and generalizability of the proposed algorithm are validated through a comparison with state-of-the-art algorithms.

Parallel Multiobjective Multiverse Optimizer for Path Planning of Unmanned Aerial Vehicles in a Dynamic Environment with Moving Obstacles

Path planning with collision avoidance for unmanned aerial vehicles (UAVs) in environments with moving obstacles is a complex process of navigation, often considered a hard optimization problem. Ordinary resolution algorithms may fail to provide flyable and collision-free paths under the time-consumption constraints required by the dynamic 3D environment. In this paper, a new parallel multiobjective multiverse optimizer (PMOMVO) is proposed and successfully applied to deal with the increased computation time of the UAV path planning problem in dynamic 3D environments. Collision constraints with moving obstacles and narrow pass zones were established based on a mathematical characterization of any intersection with lines connecting two consecutive drones’ positions. For the implementation, a multicore central processing unit (CPU) architecture was proposed according to the concept of master–slave processing parallelization. Each subswarm of the entire PMOMVO population was granted to a corresponding slave, and representative solutions were selected and shared with the master core. Slaves sent their local Pareto fronts to the CPU core representing the master that merged the received set of nondominated solutions and built a global Pareto front. Demonstrative results and nonparametric ANOVA statistical analyses were carried out to show the effectiveness and superiority of the proposed PMOMVO algorithm compared to other homologous, multiobjective metaheuristics.

A dynamic multi-objective evolutionary algorithm based on prediction

Abstract The dynamic multi-objective optimization problem (DMOP) is a common problem in optimization problems; the main reasons are the objective’s conflict and environment changes. In this paper, we provide a prediction approach based on diversity screening and special point prediction (DSSP) to tackle the dynamic optimization issue. First, we introduce a decision variable clustering and screening strategy that clusters the decision space of the non-dominated solution set to find the cluster centroids and then employs a decision variable screening strategy to filter out solutions that have an impact on the distribution of individuals. This approach can broaden the range of dynamic multi-objective optimization algorithms. Second, an approach for predicting special points is suggested. The algorithm’s convergence is improved following environmental changes by forecasting the special point tracking Pareto front in the object space. Finally, the forward-looking center points are used to predict the non-dominated solution set and eliminate the useless individuals in the population. The prediction strategy can help the solution set converge while maintaining its diversity, which is compared with the four other state-of-the-art strategies. Our experimental results demonstrate that the proposed algorithm, DSSP, can effectively tackle DMOPs.

A Multi-Objective Optimization of Physical Activity Spaces

Optimizing the location of physical activity spaces (PAS) to ensure health, equity and efficiency has long been an important issue in urban planning. Given the health benefits of urban green spaces (UGS), taking Gongshu District in Hangzhou as a case, we examine the issue of where such PAS should be located to optimize three objectives: (1) minimize the distance between PAS and UGS; (2) maximize the accessibility of PAS and (3) maximize the population that falls within the coverage range. This study develops a multi-objective optimization of physical activity spaces model (MOPAS) based upon multi-objective particle swarm optimization to yield a set of non-dominated Pareto optimum solutions that can be used to determine the most practical tradeoffs between the conflicting objectives. It compares the advantages and disadvantages of the Pareto solutions and evaluates the construction situation of locations and the implementation feasibility. Decision-makers can choose the best solution according to subjective preferences and objective conditions. The MOPSO holds great promise for improving the location optimization of PAS and the methods applied can be adapted to support multi-objective optimization of facilities in urban planning globally.

Effect of multi-walled carbon nanotubes on the performance evaluation of nickel-based super-alloy–Udimet 720 machined using WEDM process

The diverse capabilities of nickel-based super-alloy (Udimet 720), like robust mechanical strength, ductility, resistance to excessive temperature deformation, and advanced corrosion and oxidation resistance, make it suitable for use in multiple applications. These super-alloys are identified as extremely difficult materials for machining to meet feature and manufacturing requirements. In the present work, we demonstrated the machining of Udimet 720 by employing the wire-electrical discharge machining (WEDM) technique. Pulse-on-time (Ton), pulse-off-time (Toff), current, and MWCNT amount were preferred as input variables. The effect of selected design variables was studied on material removal rate (MRR), surface roughness (SR), and recast layer thickness (RLT). Box-Behnken design was utilized to design an experimental matrix. For statistical analysis, analysis of variance (ANOVA) was employed. From ANOVA, the current had the highest contributor with 35.85% to affect MRR, while MWCNT amount was found to be the highest contributor for deciding the values of both SR and RLT with contributions of 42.66% and 40.07%, respectively. The addition of MWCNT at 1 g/L has substantially improved MRR from 0.8546 to 1.2199 g/min, SR reduced from 5.88 µm to 2.98 µm, and reduction in RLT from 17.8 to 11.61 µm. The passing vehicle search (PVS) algorithm was implemented, and the results of single-objective optimization presented the largest MRR of 1.8883 g/min, least SR of 1.89 µm, and least RLT of 9.70 µm. Additionally, a set of non-dominated solutions was obtained through Pareto optimal fronts. A small acceptable deviation was detected among the actual and forecasted results from PVS algorithm. It clearly reveals the acceptance of the PVS technique in the present study for Udimet 720. Lastly, the significance of MWCNT amount on surface textures was revealed by employing scanning electron microscopy (SEM).

A Slime Mould Algorithm Programming for Solving Single and Multi-Objective Optimal Power Flow Problems with Pareto Front Approach: A Case Study of the Iraqi Super Grid High Voltage

Optimal power flow (OPF) represents one of the most important issues in the electrical power system for energy management, planning, and operation via finding optimal control variables with satisfying the equality and inequality constraints. Several optimization methods have been proposed to solve OPF problems, but there is still a need to achieve optimum performance. A Slime Mould Algorithm (SMA) is one of the new stochastic optimization methods inspired by the behaviour of the oscillation mode of slime mould in nature. The proposed algorithm is characterized as easy, simple, efficient, avoiding stagnation in the local optima and moving toward the optimal solution. Different frameworks have been applied to achieve single and conflicting multi-objective functions simultaneously (Bi, Tri, Quad, and Quinta objective functions) for solving OPF problems. These objective functions are total fuel cost of generation units, real power loss on transmission lines, total emission issued by fossil-fuelled thermal units, voltage deviation at load bus, and voltage stability index of the whole system. The proposed algorithm SMA has been developed by incorporating it with Pareto concept optimization to generate a new approach, named the Multi-Objective Slime Mould Algorithm (MOSMS), to solve multi-objective optimal power flow (MOOPF) problems. Fuzzy set theory and crowding distance are the proposed strategies to obtain the best compromise solution and rank and reduce a set of non-dominated solutions, respectively. To investigate the performance of the proposed algorithm, two standard IEEE test systems (IEEE 30 bus IEEE 57 bus systems) and a practical system (Iraqi Super Grid High Voltage 400 kV) were tested with 29 case studies based on MATLAB software. The optimal results obtained by the proposed approach (SMA) were compared with other algorithms mentioned in the literature. These results confirm the ability of SMA to provide better solutions to achieve the optimal control variables.

Taekwondo Trajectory Tracking Based on Multitarget Detection Algorithm

In order to further improve the effect of fuzzy PID controller applied to joint robot trajectory tracking control, a Taekwondo trajectory tracking method based on multitarget detection algorithm is proposed in this study. Firstly, a fuzzy PID controller for trajectory tracking of joint robot is designed. Secondly, considering the two optimization objectives of controller output torque and trajectory tracking control deviation, an improved multiobjective PSO algorithm is designed to optimize the membership function and fuzzy rules of fuzzy PID controller. Finally, the multiobjective PSO algorithm and the improved multiobjective PSO algorithm are used to optimize the trajectory tracking fuzzy PID controller. The vector sets of the two optimization objectives are obtained, and the optimization results are compared and analyzed. The simulation results show that the simulation step length is t = 0.01 s, and the total simulation time is 10 s. Using the controller, the simulation values and output torque values of each joint angle at each time can be obtained, which are used to calculate the two objective function values in the optimization algorithm. According to the process, the optimization algorithm parameters are set, and the control simulation system designed above is run to complete the improved multiobjective PSO optimization of the trajectory tracking fuzzy PID controller of the joint robot. Conclusion. The improved multiobjective PSO algorithm has better nondominated solution set, which verifies the effectiveness and superiority of the algorithm to optimize the robot trajectory tracking fuzzy PID controller.

Optimization of a Spark Ignition Engine Knock and Performance Using the Epsilon-Constrained Differential Evolution Algorithm and Multi-Objective Differential Evolution Algorithm.

Since the advent of the internal combustion engine, knock has been a vital issue limiting the thermal efficiency of spark ignition engines under heavy load conditions. The occurrence of knock is also directly influenced by several operating parameters simultaneously. In order to investigate the effects of multiple variables on economic performance and power performance under knock limits, this study adopts single-objective optimization and multi-objective optimization methods to optimize the engine operating parameters, including exhaust gas recirculation rate, exhaust valve timing, spark timing, and intake valve timing. The optimization aims to obtain maximum volumetric efficiency, brake mean effective pressure, and minimum brake specific fuel consumption on the knock limit. First, based on the bench test data at the operation point 2800 rpm and 11.42 bar, a one-dimensional simulation engine model is established in GT-power software and verified. Second, four engine operating parameters are input into the GT-power model as controlled parameters. The epsilon-constrained differential evolution algorithm and the multi-objective differential evolution algorithm are employed to optimize the above four parameters to minimize the knock index and the damage to engine performance due to knock suppression, respectively. Finally, the results show that the two optimization algorithms optimize four parameters. The results of the epsilon-constrained differential evolution algorithm indicate that the decreasing extent of the knock index is 73.3%. In addition, the decreasing extent of brake mean effective pressure is 10.2%. What is more, the increased brake specific fuel consumption is only 0.07%. The multi-objective differential evolution algorithm gives a set of nondominated Pareto optimal solution sets. The optimal solution has a 64.4% decrease in the knock index, a 5.78% decrease in brake mean effective pressure, and a 1.45% decrease in brake specific fuel consumption.

Transit network design considering link capacities

Appropriate public transport systems are crucial in modern cities. Given the high costs that they represent and the impact they have on people's lives, effective tools are required to support their design. The Transit Network Design and Frequency Setting problem (TNDFSP) has been extensively studied in operations research. This problem consists of designing a set of public transport lines and a service frequency to each line. The main contribution of this work is to consider, for some links of the underlying network, a maximum ‘combined’ frequency among all the lines using that link and addressing the crowding issues that can result from that. These additional constraints intend to limit, for instance, the number of buses circulating in certain areas, in line with current urban design policies. A bi-objective memetic algorithm is proposed to solve the problem. The algorithm generates a set of non-dominated solutions that comply with the link-capacity constraints in 1 h of computing time. Additionally, alternative solutions are generated by designing the line plan without considering the link-capacity constraints and adapting the frequencies afterwards, to compare the two approaches. The algorithm is tested on an instance representing the bus network in the city of Utrecht, The Netherlands. The algorithm that takes into account the link-capacity constraints during the optimization process, generates better results. Moreover, the algorithm generates transit networks with less lines traversing the city centre, allowing higher individual frequencies for those lines. The algorithm could become an important tool for policy makers and transit operators, allowing the design of efficient transit systems that adjust better to contemporary urban requirements.

A pareto optimal front of fluidic diode for a wave energy harnessing device

A twin-turbine or turbine duo (TUD) is constructed from a pair of unidirectional turbines. Flow reversal hampers the performance of these units. A Fluidic diode (FD) that offers a variable resistance to the flow can be used with TUD to prevent flow reversal, and its performance is governed by diodicity. With the increase in diodicity, flow blockage improves, but the resistance across the turbines increases too. As these turbines operate under a smaller pressure drop, the FD used with them should have higher diodicity with lesser fluid resistance across them. This study presents a multi-objective shape optimization of an FD to maximize diodicity and minimize pressure drop. The shape optimization is performed by simultaneously varying six design parameters. The performance of FD was evaluated by solving the 3D Reynolds Averaged Navier-Stokes equations. The popular evolutionary search algorithm (NSGA-II) with an artificial neural network produced a set of non-dominated optimal solutions (Pareto optimal set). Compared to the base model, the optimal design set shows improved diodicity from 17.2 to 21.57% and pressure drop from −2.535% to 78.67%, respectively. Further, the flow analyses of optimal designs show that the nozzle angle and the toroidal cup radius affect more than the other variables.