The grey wolf optimizer (GWO) is a novel type of swarm intelligence optimization algorithm. An improved grey wolf optimizer (IGWO) with evolution and elimination mechanism was proposed so as to achieve the proper compromise between exploration and exploitation, further accelerate the convergence and increase the optimization accuracy of GWO. The biological evolution and the “survival of the fittest” (SOF) principle of biological updating of nature are added to the basic wolf algorithm. The differential evolution (DE) is adopted as the evolutionary pattern of wolves. The wolf pack is updated according to the SOF principle so as to make the algorithm not fall into the local optimum. That is, after each iteration of the algorithm sort the fitness value that corresponds to each wolf by ascending order, and then eliminate R wolves with worst fitness value, meanwhile randomly generate wolves equal to the number of eliminated wolves. Finally, 12 typical benchmark functions are used to carry out simulation experiments with GWO with differential evolution (DGWO), GWO algorithm with SOF mechanism (SGWO), IGWO, DE algorithm, particle swarm algorithm (PSO), artificial bee colony (ABC) algorithm and cuckoo search (CS) algorithm. Experimental results show that IGWO obtains the better convergence velocity and optimization accuracy.

Whale optimization algorithm (WOA) is a swarm intelligence-based algorithm that simulates whale population predation in the sea. Aiming at the shortcomings of WOA such as low precision and slow convergence speed, an improved whale optimization algorithm based on nonlinear adaptive weight and golden sine operator (NGS-WOA) was proposed. NGS-WOA first introduced a non-linear adaptive weigh so that search agents can adaptively explore the search space, and balance the development and exploration stages. Secondly, the improved golden sine operator is incorporated into the WOA. Due to the special relationship between the sine function and the unit circle, traversing the sine function is equivalent to scanning the unit circle. The search agent performs an efficient search with a sine route so as to improve the convergence speed and global exploration capability of the algorithm. At the same time, the addition of the golden section coefficient allows search agents to exploit with a fixed shrink step. The search agent can develop to areas with excellent results, which improves the optimization accuracy and local exploitation ability of the algorithm. In the simulation experiments, the gold sine algorithm (GoldSA), whale optimization algorithm (WOA), particle swarm optimization (PSO) algorithm, firefly algorithm (FA), fireworks algorithm (FWA), sine cosine algorithm (SCA) and NGS-WOA were selected for comparison experiments. Then, the effectiveness of the proposed improved strategies is verified. Finally, the improved WOA is applied to high-dimensional optimization and engineering optimization problems. The experimental results show that the improved strategy can effectively improve the performance of the algorithm, so that NGS-WOA has the advantages of high global convergence and avoiding falling into local optimal values.

Long and short-term memory(LSTM) has been used in soft-sensor modeling of industrial processes in recent years. However, LSTM still has many defects for soft-sensor,this paper proposes a variational autoencoder bidirectional LSTM soft sensor modeling method based on batch training (Bt-VAEBiLSTM). Firstly, the training samples are divided into multiple batches according to the time series, in order to reduce the influence of abnormal points and random noise, the variational autoencoder(VAE) is then used to extract the data features of the training samples in each batch, in order to solve the problem of the global LSTM model discarding critical data information during training, this paper proposes a batch training method, that is to say the reconstructed samples are trained in batches according to the time series. After the training of a batch samples is completed, the structural parameters of the previous local BiLSTM model are shared with the next local BiLSTM model as the initial parameters to ensure that important industrial status information will not be lost. At the same time, in order to prevent the Bt-VAEBiLSTM model from overfitting, the L2 regularization term is introduced in the loss function. The effectiveness of the proposed method is verified by simulation experiments on the debutanizer column process and the grinding and classifying process.

The salp swarm algorithm (SSA) is a swarm intelligence optimization algorithm that simulates the chain movement behavior of salp populations in the sea. Aiming at the shortcomings of the SSA, such as low precision, low optimization dimension and slow convergence speed, an improved salp swarm algorithm based on Levy flight and sine cosine operator (LSC-SSA) was proposed. The Levy flight mechanism uses the route of short walks combined with long jumps to search the solution space, which can effectively improve the global exploration capability of the algorithm. Improved sine cosine operator use sine search for global exploration and cosine search for local exploitation. At the same time, an adaptively switching between the two function search methods can achieve a smooth transition between global exploration and local exploitation. In the simulation experiment, salp swarm algorithm (SSA), whale optimization algorithm (WOA), particle swarm algorithm (PSO), sine cosine algorithm (SCA), firefly algorithm (FA) and LSC-SSA were adopted for solving function optimization problems. Then, the feasibility of the improved algorithm for solving high-dimensional large-scale optimization problems and the effectiveness of the improvement strategy are evaluated. Finally, LSC-SSA was applied to train mutilayer perceptron neural network. Simulation results show that the introduction of Levy flight and improved sine cosine operator in LSC-SSA significantly improves optimization accuracy and convergence speed compared with other swarm optimization algorithms. In addition, the improved algorithm can effectively solve high-dimensional large-scale optimization problems. In the application of training muti-layer perceptron NN, the improved algorithm can avoid falling into the local optimal value and obtain the ideal classification accuracy.

Particle swarm optimization (PSO) algorithm is a swarm intelligent searching algorithm based on population that simulates the social behavior of birds, bees, or fish groups. The discrete binary particle swarm optimization (BPSO) algorithm maps the continuous search space to a binary space through a new transfer function, and the update process is designed to switch the position of the particles between 0 and 1 in the binary search space. Aiming at the existed BPSO algorithms which are easy to fall into the local optimum, a new Z-shaped probability transfer function is proposed to map the continuous search space to a binary space. By adopting nine typical benchmark functions, the proposed Z-probability transfer function and the V-shaped and S-shaped transfer functions are used to carry out the performance simulation experiments. The results show that the proposed Z-shaped probability transfer function improves the convergence speed and optimization accuracy of the BPSO algorithm.