The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory. We prove some new surjectivity theorems under some conditions a...The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory. We prove some new surjectivity theorems under some conditions and give its application in differential equation.展开更多
In this paper, an objective-based gradient multi-objective optimization （MOO） technique, the Objective-Based Gradient Algorithm （OBGA）, is proposed with the goal of defining the Pareto domain more precisely and ef...In this paper, an objective-based gradient multi-objective optimization （MOO） technique, the Objective-Based Gradient Algorithm （OBGA）, is proposed with the goal of defining the Pareto domain more precisely and efficiently than current MOO techniques. The performance of the OBGA in locating the Pareto domain was evaluated in terms of precision, computation time and number of objective function calls, and compared to two current MOO algorithms： Dual Population Evolutionary Algorithm （DPEA） and Non-Dominated Sorting Genetic Algorithm I1 （NSGA-II）, using four test problems. For all test problems, the OBGA systematically produced a more precise Pareto domain than DPEA and NSGA-II. With the adequate selection of the OBGA parameters, computation time required for the OBGA can be lower than that required for DPEA and NSGA-II. Results clearly show that the OBGA is a very effective and efficient algorithm for locating the Pareto domain.展开更多
基金Foundation item： Supported by the Shanxi Gaoxiao Keji Kaifa Yanjiu（2007129） Supported by Boshi Ke yan Qidong Jijin of Shanxi University of Finance and Economics（2006） Supported by the Natural Science Foundation of Shanxi Province（2008011002-3）.Acknowledgment The authors wish to express thanks to referees for valuable suggestions.
文摘The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory. We prove some new surjectivity theorems under some conditions and give its application in differential equation.
文摘In this paper, an objective-based gradient multi-objective optimization （MOO） technique, the Objective-Based Gradient Algorithm （OBGA）, is proposed with the goal of defining the Pareto domain more precisely and efficiently than current MOO techniques. The performance of the OBGA in locating the Pareto domain was evaluated in terms of precision, computation time and number of objective function calls, and compared to two current MOO algorithms： Dual Population Evolutionary Algorithm （DPEA） and Non-Dominated Sorting Genetic Algorithm I1 （NSGA-II）, using four test problems. For all test problems, the OBGA systematically produced a more precise Pareto domain than DPEA and NSGA-II. With the adequate selection of the OBGA parameters, computation time required for the OBGA can be lower than that required for DPEA and NSGA-II. Results clearly show that the OBGA is a very effective and efficient algorithm for locating the Pareto domain.
