Multi-objective partition planning for multi-infeed HVDC system

The close proximity and the necessity of coordination between multiple high-voltage direct currents(HVDCs)raise the issue of grid partitioning in multi-infeed HVDC systems.A multi-objective partition strategy is proposed in this paper.Several types of relationships to be coordinated and complemented are analyzed and formulated using quantitative indices.According to the graph theory,the HVDC partition is transformed into a graph-cut problem and solved via the spectral clustering algorithm.Finally,the proposed method is validated for a practical multi-HVDC grid,confirming its feasibility and effectiveness.

Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm

Robot manipulators perform a point-point task under kinematic and dynamic constraints.Due to multi-degreeof-freedom coupling characteristics,it is difficult to find a better desired trajectory.In this paper,a multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm(INSGA-II)is proposed.Trajectory function is planned with a new composite polynomial that by combining of quintic polynomials with cubic Bezier curves.Then,an INSGA-II,by introducing three genetic operators:ranking group selection(RGS),direction-based crossover(DBX)and adaptive precision-controllable mutation(APCM),is developed to optimize travelling time and torque fluctuation.Inverted generational distance,hypervolume and optimizer overhead are selected to evaluate the convergence,diversity and computational effort of algorithms.The optimal solution is determined via fuzzy comprehensive evaluation to obtain the optimal trajectory.Taking a serial-parallel hybrid manipulator as instance,the velocity and acceleration profiles obtained using this composite polynomial are compared with those obtained using a quintic B-spline method.The effectiveness and practicability of the proposed method are verified by simulation results.This research proposes a trajectory optimization method which can offer a better solution with efficiency and stability for a point-to-point task of robot manipulators.

Multi-objective evolutionary optimization for geostationary orbit satellite mission planning

In the past few decades, applications of geostationary orbit (GEO) satellites have attracted increasing attention, and with the development of optical technologies, GEO optical satellites have become popular worldwide. This paper proposes a general working pattern for a GEO optical satellite, as well as a target observation mission planning model. After analyzing the requirements of users and satellite control agencies, two objectives are simultaneously considered: maximization of total profit and minimization of satellite attitude maneuver angle. An NSGA-II based multi-objective optimization algorithm is proposed, which contains some heuristic principles in the initialization phase and mutation operator, and is embedded with a traveling salesman problem (TSP) optimization. The validity and performance of the proposed method are verified by extensive numerical simulations that include several types of point target distributions.

Multi-objective route planning approach for timely searching tasks of a supervised robot

To performance efficient searching for an operator-supervised mobile robot, a multiple objectives route planning approach is proposed considering timeliness and path cost. An improved fitness function for route planning is proposed based on the multi-objective genetic algorithm （MOGA） for multiple objectives traveling salesman problem （MOTSP）. Then, the path between two route nodes is generated based on the heuristic path planning method A ＊. A simplified timeliness function for route nodes is proposed to represent the timeliness of each node. Based on the proposed timeliness function, experiments are conducted using the proposed two-stage planning method. The experimental results show that the proposed MOGA with improved fitness function can perform the searching function well when the timeliness of the searching task needs to be taken into consideration.

Multi-Objective Production Planning Using Lexicographic Procedure

This paper presents a multi-objective production planning model for a factory operating under a multi-product, and multi-period environment using the lexicographic (pre-emptive) procedure. The model objectives are to maximize the profit, minimize the total cost, and maximize the Overall Service Level (OSL) of the customers. The system consists of three potential suppliers that serve the factory to serve three customers/distributors. The performance of the developed model is illustrated using a verification example. Discussion of the results proved the efficacy of the model. Also, the effect of the deviation percentages on the different objectives is discussed.

Improved Fuzzification Method for Multi-Objective Decision-Making and Its Application in Evaluation of Highway Planning

A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.

Distribution Network Expansion Planning Based on Multi-objective PSO Algorithm

This paper presents a novel approach for electrical distribution network expansion planning using multi-objective particle swarm optimization (PSO). The optimization objectives are: investment and operation cost, energy losses cost, and power congestion cost. A two-phase multi-objective PSO algorithm is employed to solve this optimization problem, which can accelerate the convergence and guarantee the diversity of Pareto-optimal front set as well. The feasibility and effectiveness of both the proposed multi-objective planning approach and the improved multi-objective PSO have been verified by the 18-node typical system.

Gradient-based algorithms for multi-objective bi-level optimization

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of applications.However,its multi-objective and hierarchical bi-level nature makes it notably complex.Gradient-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement learning.Unfortunately,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical efficiency.To address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and efficient.Additionally,we demonstrate the theoretical validity by accomplishing the desirable Pareto stationarity.Numerical experiments confirm the practical efficiency of the proposed method and verify the theoretical results.To accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA algorithm.Comparative results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

Evolutionary Trajectory Planning for an Industrial Robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator （AdeptOne XL robot） in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm （NSGA-II） and multi-objective differential evolution （MODE）, have been used for the optimization. Two methods （normalized weighting objective functions and average fitness factor） are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.

A Multi-Objective Hybrid Genetic Based Optimization for External Beam Radiation

A multi-objective hybrid genetic based optimization algorithm is proposed according to the multi-objective property of inverse planning. It is based on hybrid adaptive genetic algorithm which combines the simulated annealing, uses adaptive crossover and mutation, and adopts niched tournament selection. The result of the test calculation demonstrates that an excellent converging speed can be achieved using this approach.

Multi-Objective Weather Routing Algorithm for Ships Based on Hybrid Particle Swarm Optimization

Maritime transportation has become an important part of the international trade system.To promote its sustainable de-velopment,it is necessary to reduce the fuel consumption of ships,decrease navigation risks,and shorten the navigation time.Ac-cordingly,planning a multi-objective route for ships is an effective way to achieve these goals.In this paper,we propose a multi-ob-jective optimal ship weather routing system framework.Based on this framework,a ship route model,ship fuel consumption model,and navigation risk model are established,and a non-dominated sorting and multi-objective ship weather routing algorithm based on particle swarm optimization is proposed.To fasten the convergence of the algorithm and improve the diversity of route solutions,a mutation operation and an elite selection operation are introduced in the algorithm.Based on the Pareto optimal front and Pareto optimal solution set obtained by the algorithm,a recommended route selection criterion is designed.Finally,two sets of simulated navigation simulation experiments on a container ship are conducted.The experimental results show that the proposed multi-objective optimal weather routing system can be used to plan a ship route with low navigation risk,short navigation time,and low fuel consumption,fulfilling the safety,efficiency,and economic goals.

Path Planning of Quadrotors in a Dynamic Environment Using a Multicriteria Multi-Verse Optimizer

Paths planning of Unmanned Aerial Vehicles(UAVs)in a dynamic environment is considered a challenging task in autonomous flight control design.In this work,an efficient method based on a Multi-Objective MultiVerse Optimization(MOMVO)algorithm is proposed and successfully applied to solve the path planning problem of quadrotors with moving obstacles.Such a path planning task is formulated as a multicriteria optimization problem under operational constraints.The proposed MOMVO-based planning approach aims to lead the drone to traverse the shortest path from the starting point and the target without collision with moving obstacles.The vehicle moves to the next position from its current one such that the line joining minimizes the total path length and allows aligning its direction towards the goal.To choose the best compromise solution among all the non-dominated Pareto ones obtained for compromise objectives,the modified Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)is investigated.A set of homologous metaheuristics such as Multiobjective Salp Swarm Algorithm(MSSA),Multi-Objective Grey Wolf Optimizer(MOGWO),Multi-Objective Particle Swarm Optimization(MOPSO),and Non-Dominated Genetic Algorithm II(NSGAII)is used as a basis for the performance comparison.Demonstrative results and statistical analyses show the superiority and effectiveness of the proposed MOMVO-based planning method.The obtained results are satisfactory and encouraging for future practical implementation of the path planning strategy.

A New Genetic Algorithm Applied to Multi-Objectives Optimal of Upgrading Infrastructure in NGWN

A problem of upgrading to the Next Generation Wireless Network (NGWN) is backward compatibility with pre-existing networks, the cost and operational benefit of gradually enhancing networks, by replacing, upgrading and installing new wireless network infrastructure elements that can accommodate both voice and data demand. In this paper, we propose a new genetic algorithm has double population to solve Multi-Objectives Optimal of Upgrading Infrastructure (MOOUI) problem in NGWN. We modeling network topology for MOOUI problem has two levels in which mobile users are sources and both base stations and base station controllers are concentrators. Our objective function is the sources to concentrators connectivity cost as well as the cost of the installation, connection, replacement, and capacity upgrade of infrastructure equipment. We generate two populations satisfy constraints and combine them to build solutions and evaluate the performance of my algorithm with data randomly generated. Numerical results show that our algorithm is a promising approach to solve this problem.

Analysis of Energy Storage Operation Configuration of Power System Based on Multi-Objective Optimization

Driven by the goal of“carbon neutrality,”the increase in use of renewable energy power systems will be inevitable in the future.Uncontrolled output power and random volatility make it difficult to balance power in real time during system operation.Therefore,energy storage is considered to be an effective way to ensure the real-time balance of system power.However,cost of energy storage is relatively expensive.As a solution,energy storage can be used to balance the system power in order to reduce system operating costs.Taking the high proportion of wind power systems as an example,the impact of the“supply side”low-carbon transformation on the economics and reliability of power system operation is explored.In order to solve the problem of power system operation configuration optimization under the background of“carbon neutrality,”this paper establishes a multi-objective programming model.

Optimal planning of energy storage system in active distribution system based on fuzzy multi-objective bi-level optimization

A fuzzy multi-objective bi-level optimization problem is proposed to model the planning of energy storage system(ESS) in active distribution systems(ADS). The proposed model enables us to take into account how optimal operation strategy of ESS in the lower level can affect and be affected by the optimal allocation of ESS in the upper level. The power characteristic model of micro-grid(MG)and typical daily scenarios are established to take full consideration of time-variable nature of renewable energy generations(REGs) and load demand while easing the burden of computation. To solve the bi-level mixed integer problem, a multi-subgroup hierarchical chaos hybrid algorithm is introduced based on differential evolution(DE) and particle swarm optimization(PSO). The modified IEEE-33 bus benchmark distribution system is utilized to investigate the availability and effectiveness of the proposed model and the hybrid algorithm. Results indicate that the planningmodel gives an adequate consideration to the optimal operation and different roles of ESS, and has the advantages of objectiveness and reasonableness.

Bi-level Multi-objective Joint Planning of Distribution Networks Considering Uncertainties

With the increasing penetration of photovoltaics in distribution networks,the adaptability of distribution network under uncertainties needs to be considered in the planning of distribution systems.In this paper,the interval arithmetic and affine arithmetic are applied to deal with uncertainties,and an affine arithmetic based bi-level multi-objective joint planning model is built,which can obtain the planning schemes with low constraint-violation risk,high reliability and strong adaptability.On this basis,a bi-level multi-objective solution methodology using affine arithmetic based non-dominated sorting genetic algorithm II is proposed,and the planning schemes that simultaneously meet economy and adaptability goals under uncertainties can be obtained.To further eliminate bad solutions and improve the solution qualities,an affine arithmetic based dominance relation weakening criterion and a deviation distance based modification method are proposed.A 24-bus test system and a 10 kV distribution system of China are used for case studies.Different uncertainty levels are compared,and a sensitivity analysis of key parameters is conducted to explore their impacts on the final planning schemes.The simulation results verify the advantages of the proposed affine arithmetic based planning method.

Bi-level Optimal Planning of Voltage Regulator in Distribution Systems Considering Maximization of Incentive-based Photovoltaic Energy Integration

This paper focuses on optimal voltage regulator(VR)planning to maximize the photovoltaic(PV)energy integration in distribution grids.To describe the amount of dynamic PV energy that can be integrated into the power system,the concept of PV accommodation capability(PVAC)is introduced and modeled with optimization.Our proposed planning model is formulated as a Benders decomposition based bi-level stochastic optimization problem.In the upper-level problem,VR planning decisions and PVAC are determined via mixed integer linear programming(MILP)before considering uncertainty.Then in the lower-level problem,the feasibility of first-level results is checked by critical network constraints(e.g.voltage magnitude constraints and line capacity constraints)under uncertainties considered by time-varying loads and PV generations.In this paper,these uncertainties are represented in the form of operational scenarios,which are generated by the Gaussian copula theory and reduced by a well-studied backward-reduction algorithm.The modified IEEE 33-node distribution grid is utilized to verify the effectiveness of the proposed model.The results demonstrate that a PV energy integration can be significantly enhanced after optimal voltage regulator planning.

Multi-objective optimization of inverse planning for accurate radiotherapy

The multi-objective optimization of inverse planning based on the Pareto solution set, according to the multi-objective character of inverse planning in accurate radiotherapy, was studied in this paper. Firstly, the clinical requirements of a treatment plan were transformed into a multi-objective optimization problem with multiple constraints. Then, the fast and elitist multi-objective Non-dominated Sorting Genetic Algorithm （NSGA-） was introduced to optimize the problem. A clinical example was tested using this method. The results show that an obtained set of non-dominated solutions were uniformly distributed and the corresponding dose distribution of each solution not only approached the expected dose distribution, but also met the dosevolume constraints. It was indicated that the clinical requirements were better satisfied using the method and the planner could select the optimal treatment plan from the non-dominated solution set.

Study of Multi-objective Fuzzy Optimization for Path Planning

During path planning, it is necessary to satisfy the requirements of multiple objectives. Multi-objective synthesis is based on the need of flight mission and subjectivity inclination of decision-maker. The decision-maker, however, has illegibility for under- standing the requirements of multiple objectives and the subjectivity inclination. It is important to develop a reasonable cost performance index for describing the illegibility of the decision-maker in multi-objective path planning. Based on Voronoi dia- gram method for the path planning, this paper studies the synthesis method of the multi-objective cost performance index. Ac- cording to the application of the cost performance index to the path planning based on Voronoi diagram method, this paper ana- lyzes the cost performance index which has been referred to at present. The analysis shows the insufficiency of the cost per- formance index at present, i.e., it is difficult to synthesize sub-objective flmctions because of the great disparity of the sub-objective fimctions. Thus, a new approach is developed to optimize the cost performance index with the multi-objective fuzzy optimization strategy, and an improved performance index is established, which could coordinate the weight conflict of the sub-objective functions. Finally, the experimental result shows the effectiveness of the proposed approach.

Optimization of train plan for urban rail transit in the multi-routing mode

The train plan of urban rail transit under multi-routing mode can be divided into three parts： train formation, train operation periods and corresponding train counts of each routing in each period. Based on the analysis of passen- ger＇s general travel expenses and operator＇s benefits, the constraints and objective functions are defined and the multiobjective optimization model for the train plan of urban rail transit is presented. Factors considered in the multi- objective optimization model include transport capacity, the requirements of traffic organization, corporation benefits, passenger demands, and passenger choice behavior under multi-train-routing mode. According to the characteristics of this model and practical planning experience, a three-phase solution was designed to gradually optimize the train formarion, train counts as well as operation periods. The instance of Changsha Metro Line 2 validates the feasibility and efficiency of this approach.