A multi-objective train scheduling model and solution

A green train scheduling model and fuzzy multi-objective optimization algorithm

With the rapid growth of electric vehicle (EV) ownership, the problem of increased peak loads on distribution networks due to large-scale EV integration needs to be addressed. This study proposes an active distribution network multi-objective optimization scheduling method. It takes into account the charging demands of large-scale EVs and aims to minimize distribution network operating costs, reduce net load variance, and maximize the photovoltaic (PV) consumption rate. First, the Monte Carlo sampling method is used to analyze the charging load demands of a large number of EVs. Next, we construct a multi-objective optimization scheduling model for the active distribution network. This model integrates the charging demands of EVs with the operating constraints of the distribution network. To tackle the multi-objective optimization problem, we propose the NSGAII-NDAX algorithm. Additionally, we employ a fuzzy theory-based method to select the Pareto optimal solution set, addressing the challenge of decision-making complexity posed by the large size and information-rich content of the optimal solution set. Finally, the effectiveness of the proposed method in the comparative analysis of multiple scenarios is verified by an improved IEEE 33-node example. The experimental results show that the proposed model and method can effectively utilize EV charging load optimization to reduce the peak-to-valley difference in the system load while ensuring the system’s economic operation and the maximum PV consumption rate. Compared with the other algorithm, the NSGAII-NDAX algorithm has stronger optimization ability and can better handle multi-objective optimization problems.

A multi-objective operational scheduling model with plug-in electric vehicles (PEVs) is proposed to minimize the operation cost and to improve the load characteristic of Micro- grid. In this model, the PEVs charging power and the distribute generations (DGs) output power of each time period are selected as decision variables, the driving behavior of PEVs is also taken into account. Multi-objective evolution algorithm NSGA-II is utilized to solve the multi-objective model and fuzzy clustering method is introduced to help obtaining the best Pareto front. The presented model is tested on the IEEE 34-node test feeder, the results obtained demonstrate the effectiveness of the proposed dispatching approach. Index Terms—multi-objective, Micro-grid, plug-in electric vehicles, NSGA-II, fuzzy clustering, optimal operation. NOMENCLATURE: T : Number of optimization hours t : Index for hour. DG N : Number of distributed generations(DGs). i : Index for distributed generations(DGs).

A multi-objective short term hydropower scheduling model for peak shaving

To integrate the combination of electric vehicles and wind power of the transmission system, a wind farm environment multi-objective transmission model considering plug-in electric vehicles was established. The fuzzy optimal scheduling model for the environment and economy target of wind farm power system considering grid interconnection of electric vehicles designed by the author has the following characteristics: A fuzzy multi-objective dynamic scheduling model for the design of wind farm power system considering grid connection of plug-in electric vehicle is established, and the original 10 systems are taken as an example for power system design. The results show that the better model shows that the electric vehicle grid connection can greatly reduce the disadvantage of wind power stochastic uncertainties of system scheduling. The model can be used under different conditions further analyzing the rationality of the model determined by the author. An improved particle swarm optimization algorithm is used to solve this problem. The model takes the environmental and economic benefits into account, which improves the efficiency of the model.

The Industrial Internet of Things (IIoT) enhances production efficiency through inter-factory resource sharing and intelligent human-machine interaction (HMI) in flexible manufacturing. This study addresses large-scale multiobjective resource scheduling optimization in the complex IIoT environments to improve production efficiency and resource scheduling under growing customization and order demands. We develop a multiobjective IIoT scheduling model under assumptions of task priority and resource constraints, optimizing makespan, logistics time, energy consumption, tardiness time, production cost, and carbon emission. To improve resource scheduling performance, a fuzzy decision-enhanced dual directed sampling-assisted large-scale multiobjective optimization algorithm (LMOEA-FDDS) is proposed. The algorithm employs a dual directed sampling method, uses two different types of search directions to guide the population evolution, and combines a complementary environmental selection strategy based on angle penalty distance (APD), effectively improving the algorithms search eiciency and performance. Experimental results show that LMOEA-FDDS achieves 30%-70% higher HV values than state-of-the-art algorithms, demonstrating its effectiveness in solving complex IIoT scheduling problems.

Multi-Objective Optimization (MOO) has always been an important issue in the field of wireless communications. With the development of 5G networks, more objectives have been concerned to improve the user experience. The relationship between these multiple objectives is complex or even conflicting, which increases the difficulty of solving the MOO problems. Traditional multi-objective optimization algorithms (e.g., genetic algorithm) have higher computation complexity and require to store multiple models for the preference of different objectives. Therefore, in this paper, a multi-objective scheduling model based on the Actor-Critic framework is proposed, which can effectively solve the multi-user scheduling problem under Massive Multiple-Input Multiple-Output (MIMO), and utilize a single model to approximate the Pareto frontier. In the single-cell downlink scheduling scenario, the proposed model is applied to the two objective optimization, i.e., channel capacity and fairness. The simulation results show that the performance of our model is close to the theoretical optimal value in the single-objective case. The Pareto frontier can be uniformly approximated in the multi-objective case, and it has strong robustness to never-seen preference combinations.

A multi-objective robust scheduling model and solution algorithm for a novel virtual power plant connected with power-to-gas and gas storage tank considering uncertainty and demand response

Steam supply scheduling (SSS) plays an important role in providing uninterrupted reliable energy to meet the heat and electricity demand in both the industrial and residential sectors. However, the system complexity makes it challenging to operate efficiently. Besides, the operational objectives in terms of economic cost and thermodynamic efficiency are usually contradictory, making the online scheduling even more intractable. To this end, the thermodynamic efficiency is evaluated based on exergetic analysis in this paper, and an economic-exergetic optimal scheduling model is formulated into a mixed-integer linear programming (MILP) problem. Moreover, the ε-constraint method is used to obtain the Pareto front of the multi-objective optimization model, and fuzzy satisfying approach is introduced to decide the unique operation strategy of the SSS. In the single-period case results, compared with the optimal scheduling which only takes the economic index as the objective function, the operation cost of the multi-objective optimization is increased by 4.59%, and the exergy efficiency is increased by 9.3%. Compared with the optimal scheduling which only takes the exergetic index as the objective function, the operation cost of the multi-objective optimization is decreased by 19.83%, and the exergy efficiency is decreased by 2.39%. Furthermore, results of single-period and multi-period multi-objective optimal scheduling verify the effectiveness of the model and the solution proposed in this study.

Optimal operation scheduling of household energy hub: A multi-objective optimization model considering integrated demand response

In order to cope with the increasingly complex challenges in power system scheduling, especially in the context of large-scale integration of renewable energy and frequent fluctuations in load demand, this study aims to solve multi-objective optimization problems in power system scheduling, including economy, reliability, and environmental friendliness. First, by introducing a state space model (SSM) to accurately model and predict the dynamic evolution process of the power system in order to grasp the real-time state of the system. On this basis, a multi-objective optimization scheduling model was constructed, which combines various constraints of the power system, adopts an adaptive weight particle swarm optimization (PSO) algorithm for search, and further optimizes the solution using the Cauchy–Lorentz (CL) distribution, aiming to achieve the best balance between economy, environmental protection, and efficiency in power system scheduling and obtain the Pareto optimal solution set. The experimental results indicate that the strategy proposed in this study has significant advantages in improving the operational efficiency of power systems, enhancing system adaptability, and promoting green and low-carbon development. Not only does it provide new theoretical guidance and technical means for the field of power system scheduling, but it also provides strong support for promoting the optimization and transformation of energy structure and achieving sustainable development goals.

In multi-objective Bayesian optimization, an infill criterion is an important part, as it is the indicator to evaluate how much good a new set of solutions is, compared to a Pareto-front approximation set. This paper presents a deterministic algorithm for computing the Expected R2 Indicator for bi-objective problems and studies its use as an infill criterion in Bayesian Global Optimization. The R2-Indicator was introduced in 1998 by M. Hansen and A. Jaszkiewicz for performance assessment in multi-objective optimization and is more recently also used in indicator-based multi-criterion evolutionary algorithms (IBEAs). In Bayesian Global Optimization, we propose the Expected R2-indicator Improvement (ER2I) as an infill criterion. It is defined as the expected decrease of the R2 indicator by a point that is sampled from a predictive Gaussian distribution. The ER2I can also be used as a pre-selection criterion in surrogate-assisted IBEAs. It provides an alternative to the Expected Hypervolume-Indicator Improvement (EHVI) that requires a reference point, bounding the Pareto front from above. In contrast, the ER2I works with a utopian reference point that bounds the Pareto front from below. In addition, the ER2I supports preference modelling with utility functions and its computation time grows only linearly with the number of considered weight combinations. It is straightforward to approximate the ER2I by Monte Carlo Integration, but so far a deterministic algorithm to solve the non-linear integral remained unknown. We outline a deterministic algorithm for the computation of the bi-objective ER2I with Chebychev utility functions. Moreover, we study monotonicity properties of the ER2I w.r.t. parameters of the predictive distribution and numerical simulations demonstrate fast convergence to Pareto fronts of different shapes and the ability of the ER2I Bayesian optimization to fill gaps in the Pareto front approximation.

Radiation therapy treatment planning is inherently a multiobjective problem, aiming to obtain the best tradeoffs between irradiating the tumor with the prescribed dose and sparing as much as possible the surrounding healthy organs. Many different multiobjective approaches have been proposed for the optimization of radiation intensities for fixed beam irradiation directions. However, multiobjective beam angle optimization is seldom considered. The purpose of this paper is to introduce a new multiobjective optimization framework that explicitly and simultaneously considers the optimization of intensities and also beam directions. Whilst multiobjective optimization of radiation intensities considering a fixed set of beam directions gives rise to a single Pareto front, beam angle optimization gives rise to the appearance of multiple Pareto fronts, each one associated with a given beam angle set. Our framework proposes a beam angle set choice based on the evaluation of non-dominated solutions belonging to different Pareto fronts, using a tree-based approach and a performance indicator to assess the quality of each Pareto front. The proposed approach, illustrated by head-and-neck cancer cases, allows for more flexibility in the calculation of solutions and a better understanding of the existing compromises between different objectives.

In this paper, a multi-objective optimization model tackling the optimal planning and scheduling of surgical operations is proposed. The model determines the assignment of time slots to the surgical teams and schedules the elective inpatient surgical operations on the basis of clinical priorities. The proposed multi-objective approach takes into account and suitable balances some strategic and conflicting goals, related to the improvement of resources utilization and considering patient's priority value. In order to find the Pareto frontier, a metaheuristic approach based on the efficient implementation of genetic algorithms has been proposed. This approach allows to obtain the set of efficient solutions within reasonable computational time. Some preliminary experiments based on real-life data are reported. The results demonstrate the effectiveness of the proposed approach, even though more extensive testing is necessary in order to finally assess and validate its impact to health care systems.

Petri nets and railway networks are considered in this paper with the aim of providing a comprehensive model to be used for analysis, optimisation, and control purposes. The overall model consists of two interconnected Petri nets that represent, respectively, the physical part of the network (stations, blocks, crossovers, tracks, and so on, as well as trains travelling on the network) and the logical part of it (train schedule over the available lines). The former Petri net has a fixed structure whereas the second one changes in accordance with the number of trains, lines, and timetable. In the paper, the main elements of the two Petri nets are described in detail, making use of an example of network which is representative of real-word railways. Moreover, some applications of the proposed model are discussed in order to highlight the effectiveness in employing Petri nets to analyse, optimise, and control railway networks and train schedules.