An advanced multi-objective optimization method combined with NSGA-II and SQP using multiple agents
Multi-objective optimization problems in chemical industry are far more important than before, especially for the lack of energy resource and environment problems. For example, in an ethylene plant, it is expected that the ethylene yield can be mostly promoted and the energy cost can be mostly reduced. The best way to solve and represent the solution of a multi-objective optimization problem is through the generation of a Pareto optimal set, which provides a spectrum of tradeoffs of the conflicting objectives. However, multi-objective optimization problems of chemical engineering are usually very complicated and associated with both equality and inequality constraints, so the process of calculating objective functions and constraint functions is very time-consuming. There are two general approaches to generate the Pareto set. One is to minimize weighted sums of the different objectives for various different settings of the weights. For a certain set of the weights, the multi-objective problem is transferred to a single objective optimization one which could be solved by a general method, such as Successive Quadratic Programming (SQP). This method ensures that every point gained is usually an exact Pareto point, but it is only effective when the Pareto curve is convex and even. An evenly distributed set of weights fails to produce an even distribution of points from all parts of the Pareto set. The other approach is to use multi-objective evolutionary algorithms (MOEAS), for example, Pareto-archived evolution strategy (PAES) and non-dominated sorting genetic algorithm II(NSGA-II),which are very popular these years. NSGA-II is able to maintain a better spread of solutions and converged better than other MOEAS, but when confronted with complicated and constrained chemical optimization problems, the efficiency of NSGA-II is not so ideal. The advanced multi-objective optimization method proposed here combines the two approaches together with a multi-agent architecture so that the advantages of the two approaches can be integrated effectively. There are two main agents in the architecture: SQP agent and NSGA-II agent. The two agents are executed independently, and sometimes exchange information of each other to improve their results. First of all, the SQP agent calculates a number of Pareto set with a set of even weights. Of course, this set of results is not evenly distributed but more converged to the real Pareto curve. At the same time, the NSGA-II agent gains a number of results as usual, and this set of results is usually evenly distributed but not so converged to the real Pareto curve as SQP agent does. Next, the SQP agent will compare its results and the ones obtained from NSGA-II agent and then determine another set of weights to make the points more even. The NSGA-II agent will absorb the results from the SQP agent as elites to make the results more converged to the real Pareto curve. This process can be iterated many times. And the last results are obtained from NSGA-II agent. In this way, the advantages of the two agents are combined effectively. A number of problems chosen from past studies in this area are tested to approve the efficiency of the advanced method. The results show that the method proposed can be more converged to the real Pareto curve and more efficient than previous methods. Because of the efficiency of treating constraints, this method should be more fitted to solve the chemical optimization problems.
Multi-objective optimization Pareto NSGA-II SQP Agent
Xiaodan Gao Bingzhen Chen Xiaorong He
Department of Chemical Engineering,Tsinghua University,Beijing,100084,China
国际会议
西安
英文
2007-08-15（万方平台首次上网日期，不代表论文的发表时间）