# A Metaheuristic Framework with Experience Reuse for Dynamic Multi-Objective Big Data Optimization
## 1 Introduction  
According to the research of the International Data Corporation (IDC) [1], by 2025, approximately six billion consumers, or 75% of the world's population, will interact with data every day. Furthermore, the global datasphere will grow from 45 zettabytes in 2019 to 175 by 2025. Nearly 30% of the world's data will need real-time processing. Optimization problems have also faced big data challenges, which means that matching solutions are urgently needed. In many real-world situations, objective functions, decision space, or constraints of multi-objective optimization problems (MOPs) may change over time, making MOPs have dynamic features. These problems are dynamic multi-objective optimization problems (DMOPs). The DMOP was first systematically described and presented by [PERSON] et al. [2] in 2004, and the DMOP can be formally defined in a minimization way as\[ \begin{array}{rl}\min&\mathbf{f}(\mathbf{x},t)=(f_{1}(\mathbf{x},t),\ldots,f_{M}( \mathbf{x},t))\\ \text{s.t.}&\mathbf{x}\in\Omega\\ &g_{i}(\mathbf{x},t)\leq 0,\quad i=1,\ldots,m\\ &h_{j}(\mathbf{x},t)=0,\quad j=1,\ldots,n\end{array}  \tag{1}\]  
where \(\mathbf{x}=(\mathbf{x_{1}},\ldots,\mathbf{x_{D}})\in\Omega\) is a solution vector with \(D\) decision variables, and \(\Omega\subseteq\mathbb{R}^{D}\) is the decision space; \(f\rightarrow\mathbb{R}^{M}\) consists of \(M\) conflicting objectives; \(g_{i}(\mathbf{x},t)\) and \(h_{j}(\mathbf{x},t)\) represent, respectively, \(m\) inequality constraints and \(n\) equality constraints. Variable \(t\) represents time and the dynamic nature of the problem. [PERSON] et al. [3] illustrated the challenges of big data optimization and the application of metaheuristic algorithms to solve such problems, which lays a good foundation for the emergence of DMBDOPs. In some real-world big data applications, the volume of data and streaming features introduce new challenges for optimization tasks. We could roughly classify these new challenges in optimization problems into two aspects:  
* The tremendous volume of data may cause the optimization problem to have a high-dimensional decision space, which is hard to formulate and tackle using traditional methods. It also has a higher requirement for computing power. Furthermore, on account of the veracity feature, the convergence and fitness evaluations of optimization algorithms could be rather time-consuming when tackling noisy data. Thus, designing efficient algorithms to address high-dimensional and noisy data problems is challenging. * In many real-world big data optimization tasks, apart from the mentioned features, data could be transmitted quickly as a streaming form from different sources, and streaming data are inherently dynamic. For example, the ever-changing traffic signal data in transportation planning and the constantly updated investment data in quantitative investing. Considering transmission speed and the dynamic nature of streaming, relevant algorithms must process the streaming data quickly and react efficiently to the resulting change in the problem. Consequently, managing streaming data, detecting rapid changes in the problem, and then restarting the algorithm to solve the new problem effectively is a significant challenge. From the perspective of all of the above, when DMOPs are combined with the characteristics of big data, DMBDOPs appear. The DMBDOP is a particular case of the DMOP, so a DMBDOP can also be expressed using Equation (1) in a mathematical way. The difference is that, in a DMBDOP, the dynamic feature of the problem is brought about by streaming data. In addition, the decision space \(\Omega\) may contain hundreds, thousands, or even millions of variables. Therefore, a DMBDOP can be defined as a DMOP with the characteristics of streaming data and possibly with a high-dimensional decision space simultaneously.