Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorith...Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorithm and Lipschitz constant to limit the search area effectively;this is essential for solving constrained nonlinear optimization problems. We obtain a more appropriate Lipschitz constant by applying the formula manipulation system of each divided area. Therefore, we obtain a better approximate solution without using a lot of searching points. The efficiency of our proposed algorithm has been shown by the results of some numerical experiments.展开更多
This paper presents a new algorithm for clustering a large amount of data.We improved the ant colony clustering algorithm that uses an ant’s swarm intelligence,and tried to overcome the weakness of the classical clus...This paper presents a new algorithm for clustering a large amount of data.We improved the ant colony clustering algorithm that uses an ant’s swarm intelligence,and tried to overcome the weakness of the classical cluster analysis methods.In our proposed algorithm,improvements in the efficiency of an agent operation were achieved,and a new function "cluster condensation" was added.Our proposed algorithm is a processing method by which a cluster size is reduced by uniting similar objects and incorporating them into the cluster condensation.Compared with classical cluster analysis methods,the number of steps required to complete the clustering can be suppressed to 1% or less by performing this procedure,and the dispersion of the result can also be reduced.Moreover,our clustering algorithm has the advantage of being possible even in a small-field cluster condensation.In addition,the number of objects that exist in the field decreases because the cluster condenses;therefore,it becomes possible to add an object to a space that has become empty.In other words,first,the majority of data is put on standby.They are then clustered,gradually adding parts of the standby data to the clustering data.The method can be adopted for a large amount of data.Numerical experiments confirmed that our proposed algorithm can theoretically applied to an unrestricted volume of data.展开更多
文摘Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorithm and Lipschitz constant to limit the search area effectively;this is essential for solving constrained nonlinear optimization problems. We obtain a more appropriate Lipschitz constant by applying the formula manipulation system of each divided area. Therefore, we obtain a better approximate solution without using a lot of searching points. The efficiency of our proposed algorithm has been shown by the results of some numerical experiments.
基金Project (No.18510132) supported by the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research
文摘This paper presents a new algorithm for clustering a large amount of data.We improved the ant colony clustering algorithm that uses an ant’s swarm intelligence,and tried to overcome the weakness of the classical cluster analysis methods.In our proposed algorithm,improvements in the efficiency of an agent operation were achieved,and a new function "cluster condensation" was added.Our proposed algorithm is a processing method by which a cluster size is reduced by uniting similar objects and incorporating them into the cluster condensation.Compared with classical cluster analysis methods,the number of steps required to complete the clustering can be suppressed to 1% or less by performing this procedure,and the dispersion of the result can also be reduced.Moreover,our clustering algorithm has the advantage of being possible even in a small-field cluster condensation.In addition,the number of objects that exist in the field decreases because the cluster condenses;therefore,it becomes possible to add an object to a space that has become empty.In other words,first,the majority of data is put on standby.They are then clustered,gradually adding parts of the standby data to the clustering data.The method can be adopted for a large amount of data.Numerical experiments confirmed that our proposed algorithm can theoretically applied to an unrestricted volume of data.
