# A Metaheuristic Framework with Experience Reuse for Dynamic Multi-Objective Big Data Optimization
## 3 The Proposed Framework
### Experience Reuse and Parallel Computing  
Solving big data optimization problems is a very time-consuming task that requires high performance of the algorithm and computing power. Moreover, solving DMBODPs becomes even more challenging when the problem changes rapidly. It is not realistic in terms of time to obtain the optimal PS for each problem, so some strategies should be adopted to obtain the best possible approximate optimal PS efficiently. In the process of solving a dynamic problem, some solutions in the PS of the previous problem are randomly replaced, and then that PS is used as the initial population of the new problem. This approach is very effective because periodic functions incur changes in most dynamic multi-objective optimization test problems, and the difference between the new PS and the old PS is minimal. Therefore, the use of this strategy ensures fast convergence of the algorithm. However, in many situations, the change in the problem may be random, and therefore the distribution of the solutions to the problem may vary significantly, in which case the above strategy may not help to speed up the computation. Therefore, this work proposes an experience reuse method based on experience accumulation to accelerate optimization. A fixed-size external archive supports the experience reuse method by storing historical information in the form of quadruples \((\mathbf{f},\mathbf{p},iteration,trial)\), where \(\mathbf{f}\) represents the features of time series data for different problems, \(\mathbf{p}\) is the current best approximate optimal PS for this problem, _iteration_ is used to record the number of times the algorithm has been run since the quadruple was added to the archive, and \(trial\) indicates how many times this information item has been used by the experience reuse method. Before introducing the experience reuse method, the update mechanism of the archive is first explained. No history information exists when the algorithm is run for the first time, so its initial population is randomly generated according to the requirements of different problems. The archive update occurs every time the algorithm restarts and invokes the experience reuse method. As shown in Algorithm 1, the inputs of the update algorithm are the features \(\mathbf{f}_{last}\) of the previous problem and the approximate optimal PS of that problem \(\mathbf{p}\). If the archive is empty, the information on the previous problem is directly added to the archive, and _iteration_ and _trial_ would be initialized. Otherwise, the similarity between the input problem features and the problem features stored in the archive would be computed using the dynamic time warping (DTW) algorithm. Here, a threshold named \(MinimumSimilarity\) needs to be set, and if all the similarities computed are greater than or equal to this threshold, the problem is considered a new problem. If the archive is not yet full, the information about the new problem is stored directly in the archive. If the archive size has reached the fixed size,the least-used record will be deleted, and new problem information will be added to the archive. If the least-used record cannot be found, the archive will not be updated. The specific judgment method is shown in lines 12-18 of Algorithm 1, which means that if a record has existed for a long time but is the one used least frequently, it will be deleted. If the similarity is below the threshold, then there exists a problem in the archive that is highly similar or identical to the input problem, and the two problems need to be compared. If the hypervolume of new solutions is greater than the hypervolume of old solutions, the old PS is replaced with the new PS. It is important to note that the stored problem features are not updated, and in this simple way, it is ensured that all the information stored in the archive is for different problems. Since the experience reuse method only properly references the historical experience, it is not necessary to store all the exact information.