# Improved Particle Swarm Optimization for Sea Surface Temperature Prediction
## 2 Related Work  
SST data is typically long-time-sequence data, hence many researchers have regarded SSTP as a time-series regression problem, thus applying time-series prediction methods to SSTP. The traditional time-series prediction methods such as Autoregressive (AR) [13], Moving Average (MA) [14] and Autoregressive Moving Average (ARMA) [15] are linear. Yet, SST has non-stationary and nonlinear characteristics, thus these linear methods are not well-suited to the practical application of SSTP. Therefore, researchers have proposed some nonlinear methods to predict SST. [PERSON] et al. [16] have used SVM to predict SST and achieved good results. AC is often used for hydrological forecasting, and can also be used for time-series prediction. It can better mine the hidden information in the sequence, yet the method is sensitive to factors such as Pattern Length (PL), Interval Step (IS), and similarity measure. In the process of time-series data mining, the similarity measure is the basis of clustering, association rules and prediction. Euclidean distance [17] is a commonly used time-series similarity measure. It is simple to calculate, but can only process time series of equal length. It cannot handle the sequence stretching and bending on the time axis. DTW is based on the idea of Dynamic Programming (DP) [18], which was originally applied in isolate word speech recognition [19]. It was then introduced into the study of similarity measures of time series by [PERSON] et al. [20], achieving good results. DTW overcomes the shortcomings of Euclidean distance. It will not only measure the similarity of time series of different lengths, but also supports the stretching and bending of sequences on the time axis. It has a good measurement accuracy and robustness, which is why it is widely used. Cosine similarity [21] uses the cosine of the angles of two vectors in the vector space to measure the similarity between them. The closer the cosine value is to 1, the closer the angle is to 0, the more similar they are. Therefore, the method can better distinguish the difference in the direction of differentiation, and is not sensitive to the cosine value. By comparing the evaluation index of the different similarity measures, one that is suitable for measuring the similarity of SST sequences can be selected, and the multi-objective optimization method can be used as a solution to select the appropriate values for PL and IS. Many scholars have studied the theory and application of multi-optimization algorithms. Differential Evolution (DE) [22] is a simple but efficient parallel search algorithm proposed by [PERSON] in 1997, whose principle is similar to genetic algorithms. [PERSON] et al. [23] compared the Non-dominated Sorting Genetic Algorithm (NSGA) [24] with the Niche Pareto Genetic Algorithm (NPGA) [25], and the Vector-Evaluated Genetic Algorithm (VEGA) [26], finding that NSGA has the best performance. Yet, the computational complexity of NSGA is higher. Aiming at the shortcomings of NSGA, [PERSON] et al. [27] proposed the Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II), which reduces the time complexity of Pareto dominating sorting [28]. It is suitable for dealing with low-dimensional, multi-objective optimization problems. However, when dealing with high-dimensional, multi-objective problems, the crowding distance [29] is not applicable in high-dimensional space, and the computational complexity is also high. Inspired by the predatory behavior of natural bird populations, [PERSON] [30] proposed Particle Swarm Optimization (PSO). PSO is an evolutionary computation method based on individual improvement, population cooperation and competition mechanisms. It has the important characteristics of being simple and easy to implement, which makes it suited to single-objective optimization. When optimizing multiple targets (as in MOPSO [31]), [PERSON] et al. proposed OMOPSO (Optimal Multi-Objective Particle Swarm Optimization) [32], which uses the crowding factor to select the leaders,based on Pareto dominance.