Research On Two Types Of Stochastic Optimization Algorithm And Their Applications In Chemical Engineering

In the last thirty years, the energy price has been increasing, the control of environment has been more rigorous, and the product competition has become worldwide. Facing these pressures, optimization technique is an effective approach that can reduce the cost and increase the revenue of enterprise. From product design to supply chain management, optimization can be applied on any scale of chemical process. But the intrinsic nonlinearity in substance and energy conversion, addition to the discreteness of process operation, results in many difficulties for optimization of chemical process. In front of many practical problems, the classical mathematic programming methods are helpless. So the demand for stochastic and intelligent optimization methods is more urgent.Stochastic optimization algorithms, such as genetic algorithm, simulated annealing, tabu search, ant colony optimization and particle swarm optimization, have powerful searching ability, and they can approach the true solution of practical problem in reasonable time. These algorithms are usually related to artificial intelligence, statistical thermodynamics, biology evolutionism, and bionics, so they are also called intelligent optimization methods. The stochastic optimization algorithms are not limited to the structure of problem, and have not rigorous restriction on mathematic properties of problem. They needn't the first derivative, and even explicit objective function. They can not only deal with continuous problems, but also discrete problems. Stochastic algorithms can find the global optimum with great probability, and are easy to fuse the heuristic rules. Such advantages have made stochastic optimization algorithms applied to many chemical engineering problems successfully. This dissertation researched on two stochastic algorithms, one of which is genetic algorithm and the other is particle swarm optimization algorithm. Aiming at the specific engineering problems, some modifications have been proposed on the two algorithms, which can improve their efficiency in specific problems. Because particle swarm optimization algorithm is more concise, and it has rapid convergence, which bring it to be a research hotspot in the field of evolutionary computation, so it is an emphasis in this dissertation.Firstly, according to the difficulties in the optimization of chemical engineering and the intrinsic disadvantage of deterministic optimization algorithms, this work analyzed the importance and advantage of stochastic algorithms, and proposed some important aspects in research on them. Secondly, genetic algorithm was applied to two problems of data driven modeling, one of which was combination problem, the other was mixed integer nonlinear programming. Thirdly, systemic investigations were made on the basic structure, dynamic behavior and modifications of particle swarm optimization. Lastly, two kinds of proposed PSO algorithms were applied on calculation of phase equilibrium, which is nonconvex optimization. The major contributions of this work are summarized as follows.1. Spectral wavelength selection is an important spectrum preprocessing step, which can get the best combination of modeling variables for the best predictive performance. The near infrared spectrum has wide spectral range, and there are nearly 2¹⁰⁰⁰ combinations for wavelength selection. The optimization variables in this problem are binary and the problem hasn'texplicit optimization objective function. So moving window - iterative genetic algorithm (MW-IGA) was proposed to select wavelength, in which moving window scanning finds the information regions. Genetic algorithm selects the best combination of wavelength intervals. This approach considers the correlation of continuous wavelength points, and the resulted wavelengths contain some redundancy that make the model more robust. MW-IGA could be applied to wavelength selection for other spectrum. If the number of wavelength points is less than 200, the step of moving window could be neglected. This method has been applied to UV-Vis spectrum of cough syrup and NIR spectrum of corn.2. Artificial neural network is used to establish the nonlinear data-driven model, which is very common in operative optimization and process control for chemical process. A modified radical basis function - cyclic subspace regression (RBF-CSR) neural network was proposed, and it has standard network structure. The model contains real and integer variables simultaneously, so eugenic hybrid coding genetic algorithm (EHCGA) was devised to train the neural network. EHCGA adopted different coding methods for different types of variable, which means integer variables adopted binary codes, while real variables adopted float codes. It used different crossing and mutation operator separately for different codes and Powell eugenic operator was introduced to accelerate evolution. RBF-CSR model trained by EHCGA has applied on pulsed extraction process for recover caprolactam successfully. EHCGA can be applied to other MINLP problem.3. Particle swarm optimization usually converges prematurely for high dimensional problem, so a collaborative PSO (CLPSO) was proposed. The particle population is divided into two parts, one part is responsible for global exploration and the other part is responsible for local exploitation. The two parts work together and maintain the diversity of population, which improves the global searching ability.4. PSO converges very slowly in the late evolutionary period. Based on CLPSO, a locally accelerated PSO (LAPSO) algorithm was proposed. LAPSO introduced the concept of relative evolutionary extent, which could detect the evolutionary rate of algorithm. Some acceleration rules were introduced into LAPSO and Nelder-Mead simplex algorithm was adopted for local search. PSO finds the area that may include global solution, while simplex searches the solution in the area precisely in time. LAPSO also accelerates the convergence of PSO.5. In chemical engineering, there exist many linear constraints, such as material balance, mass balance and atom balance. A linear constraint PSO (LCPSO) was devised for this kind of problems. LCPSO modified the velocity and position updating operation, and the random number in every dimension for velocity updating adopted same value. So the new velocity for every particle became the linear combination of old velocity and position. LCPSO can be applied to nonconvex optimization constrained by linear equalities. It generates the initial population in feasible space, and utilizes its intrinsic linear operations to maintain the particle satisfying the constraints. LCPSO is an effective constrained optimization algorithm that deals with linear equalities.6. Phase stability analysis can determine whether the given phase is stable and whether the result of phase equilibrium calculation is right. Tangentplane distance function (TPDF) approach is the popular method for phase stability analysis. TPDF is nonconvex and the problem is constrained by the mole fraction summation. LCPSO was utilized to minimize the TPDF, and this method can applied to any thermodynamic model and can detect any type of instability. This work applied LCPSO to three types of thermodynamic model. According to thermodynamic theories, the objective functions were simplified, which greatly decreased the amount of calculation.7. For complex phase equilibrium system, the Gibbs energy function has several local minima, so it's difficult to get the global minimum by the local optimization algorithms. If chemical reactions don't occur, there are only material balances for phase equilibrium. Component phase fraction was introduced, which converts the original problem to an unconstrained one. LAPSO was utilized to solve the phase equilibrium without reactions, and it need not considering the actual number and type of phases and needn't the derivative. For phase equilibrium problem with chemical reaction, the constraints are atom balances, which are general linear equalities. LCPSO was utilized to compute this kind of equilibrium. LCPSO maintains the particle within feasible space and the computing efficiency is high. When atom balances are converted to element balances, the efficiency of generating initial feasible population is greatly improved.The facts that stochastic optimization algorithms were applied to chemical engineering successfully and the deterministic algorithms have the intrinsic disadvantages, will promote the research on stochastic algorithm in chemical engineering, especially in combinational and global optimization.