## 1 Introduction  
In recent decades, a worldwide spread of distributed energy resources (DERs) has been evident, such as micro gas engines, wind turbines, photovoltaic panels, small hydropower units, storage devices, electric vehicle charging facilities, etc. However, not only do those emerging technological advances bring us great opportunities of renewable energy exploitation but also enormous challenges in optimal operation. The virtual power plant (VPP) is a promising solution to these issues. The concept of VPP was proposed in late 20 th century [1] and applications rapidly spread across Europe and America [2; 3; 4]. Based on advanced communication technology and software system, a VPP dispatches a number of DERs, coordinates the operations, and optimizes the overall performance [5]. In China, large-scale VPPs are built along with the dramatic growth of DERs [6]. The VPP standard initiated by the State Grid Corporation of China has been accepted by International Electrotechnical Commission (IEC) in 2018 [7]. A great deal of research concentrates on the optimization of VPP dispatch. Generally, economy is the primary objective, and other factors are also considered in some papers. For example, pollution emissions are taken into account in [8; 9] and power quality is set the secondary objective in [10]. On the other hand, various compositions of VPP are investigated. Reference [11] focuses on the performance of VPP integrating electric vehicles and analyzes the impact of access mode. The VPP-based wind-thermal cogeneration is studied in [12]. The coordination of wind power, solar power and pumped storage in a VPP is discussed in [13]. In recent years, the merging technology of combined cooling, heat and power (CCHP) has generated a new member of DER family. The integration of CCHPs results in new challenges due to the interconnection and coupling of multiple energies in forms of electrical, heat and cooling [14; 15]. As a sequel, VPPs integrating CCHPs are promoted to multi-energy virtual power plants (ME-VPPs). The dispatch of ME-VPP is highly challenging mainly due to two difficulties: uncertainties with DERs' and the model's complexity. The prediction of DERs' behavior is vital since it provides input data for the optimization model. Large numbers of efforts are devoted to improve the prediction accuracy and the methods can generally be classified into four categories: (1) Time-series method, which uses sliding mean average of the nearest historical data; (2) Kalman filtering method, which views the historical data as a state variable in a model to predict when the statistic character of noise is known; (3) Statistical method, which realizes parameter estimation and model checking through model identification; (4) Artificial neural networks method, which was made up of multiple neurons to imitate human brain's function and structure [16]. Traditional prediction methods mainly depend on function solving, such as the Grey model [17]. New and more popular prediction methods concentrated on artificial neural network and deep learning [18; 19; 20]. In comparison, new methods can fit and learn the historical data about uncertain variables, via which they can achieve more accurate and efficient predictions. There are plenty of general-purpose commercial optimizers, which are widely used in industry and academic research, such as CPLEX, LINPROG, GUROBI, MOSEK, etc. However, most of them are solely for classical optimization problems with a single objective. Therefore, it is necessary to develop specific algorithms for nontrivial optimization problems with multiple objectives. The chaotic differential evolution is proposed in [21]. An improved genetic algorithm is adopted to optimize VPPs' economic and environmental performances [22]. The multi-objective particle swarm optimization (MOPSO) is an enhanced version of PSO being devoted to multi-objective optimization problems.