The Application of Evolutionary Computation and Artificial Neural Networks in the Multiobjective ProblemPeople often encounter multiobjective optimization problems in the practice. For example, when we invest in something, we usually want to invest less capital, have less risking and much returns. Because the objectives of the multiobjective problems restrict each other through the variables, and the optimization of one objective is at the cost of another objective, generally solving optimization problems with multiple objectives is a very difficult goal. Computational intelligence is a kind of theory and method that simulates mankind's intelligence by modern computing tools. Evolutionary computation and artificial neural networks are two important fields of computational intelligence. In this paper, we do some research on resolving the multiobjective optimization problem with the two kinds of methods.Because evolutionary computation has the ability to find multiple Paretooptimal solutions in one single run, it is good at resolving multiobjective optimizations. Although there are many multiobjective evolutionary algorithms at present, most work is about GA and ES, such as SPEA[8],MOGA[6],NSGA[42],NSGA[7] , PAES[9],MEES[53], little work is about EP.A 1999 review of 272 publications in multiobjective evolutionary algorithms found only one citation related to Evolutionary Programming [61]. Because EP is promising in single objective problem, there is need to research EP algorithm used to solve multiobjective problems.Since the first artificial neural network was proposed, it has developed rapidly. Particularly in 1980s, when the Hopfield network was used to solve combinatorial optimization problems, Hopfield neural network gets much attention. But most researchers put their emphasis on researching how to solve combinatorial optimization problems, and a typical problem is TSP. In order to solve optimization problems more efficiently, researches do much work to improve Hopfield model, such as E.Wacholder[65], Y.takefuji[66],Lillo[67]. But most of the work is about the single optimization and little work is about using Hopfield network to solve multiobjective optimization problems. Therefore we propose a method to solve multiobjective optimization problem based on Hopfield model.Based on the above backgrounds, we have done the following work: 1 Proposing a multiobjective evolutionary programming algorithm.The basic idea of this algorithm is to use a small population size and a reinitialization process. This algorithm takes advantage of Evolutionary Programming and introduce some strategies to overcome the disadvantages existed in conventional multiobjective evolutionary algorithms,such as the low effective Pareto ranking procedure, "population drifting" , etc. The experimentresult shows this algorithm can get a more uniform Pareto front than the conventionalevolutionary programming.2 Proposing a Hopfield model used to solve the multiobjective combinatorial problemsWe construct a new Hopfield neural networks model based on multiobjective optimization. Weconvert the multiobjective optimization problem into a single optimization problem using linearweighted sum, then solve this single optimization problem using Hopfield neural networks.3. Constructing a multiobjective model based on partner selection of virtual enterprisesVirtual Enterprises are dynamically constituted by individual entities that come together as ateam to achieve specific goals. This dynamic nature imposes strong demands on the formation ofthe Virtual Enterprise since the capability of effectively putting together the best team ofindividuals is the key to the success of the Virtual Enterprise itself. In this paper, we construct amultiobjective model based on partner selection of virtual enterprises, then we solve thisproblem using the abovementioned evolutionary programming, and finally we describe how tosolve this problem using the abovementioned Hopfield networks.Finally, we summarize our...
