In this paper, we present a multiobjective approach for solving the one-way car relocation problem.We fix three objectives that include the number of remaining rejected demands, the number of jockeys used for the relo...In this paper, we present a multiobjective approach for solving the one-way car relocation problem.We fix three objectives that include the number of remaining rejected demands, the number of jockeys used for the relocation operations, and the total time used by these jockeys. For this sake, we propose to apply two algorithms namely NSGA-Ⅱ and an adapted memetic algorithm(MA) that we call MARPOCS which stands for memetic algorithm for the one-way carsharing system. The NSGA-Ⅱ is used as a reference to compare the performance of MARPOCS. The comparison of the approximation sets obtained by both algorithms shows that the hybrid algorithm outperforms the classical NSGA-Ⅱ and so solutions generated by the MARPOCS are much better than the solutions generated by NSGA-Ⅱ. This observation is proved by the comparison of different quality indicators’ values that are used to compare the performance of each algorithm. Results show that the MARPOCS is promising to generate very good solutions for the multiobjective car relocation problem in one-way carsharing system. It shows a good performance in exploring the search space and in finding solution with very good fitness values.展开更多
The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
Let and A be the generator of an -times resolvent family on a Banach space X. It is shown that the fractional Cauchy problem has maximal regularity on if and only if is of bounded semivariation on .
In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded...In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.展开更多
The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous...The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.展开更多
文摘In this paper, we present a multiobjective approach for solving the one-way car relocation problem.We fix three objectives that include the number of remaining rejected demands, the number of jockeys used for the relocation operations, and the total time used by these jockeys. For this sake, we propose to apply two algorithms namely NSGA-Ⅱ and an adapted memetic algorithm(MA) that we call MARPOCS which stands for memetic algorithm for the one-way carsharing system. The NSGA-Ⅱ is used as a reference to compare the performance of MARPOCS. The comparison of the approximation sets obtained by both algorithms shows that the hybrid algorithm outperforms the classical NSGA-Ⅱ and so solutions generated by the MARPOCS are much better than the solutions generated by NSGA-Ⅱ. This observation is proved by the comparison of different quality indicators’ values that are used to compare the performance of each algorithm. Results show that the MARPOCS is promising to generate very good solutions for the multiobjective car relocation problem in one-way carsharing system. It shows a good performance in exploring the search space and in finding solution with very good fitness values.
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
文摘Let and A be the generator of an -times resolvent family on a Banach space X. It is shown that the fractional Cauchy problem has maximal regularity on if and only if is of bounded semivariation on .
文摘In this paper, based on the theories of α-times Integrated Cosine Function, we discuss the approximation theorem for α-times Integrated Cosine Function and conclude the approximation theorem of exponentially bounded α-times Integrated Cosine Function by the approximation theorem of n-times integrated semigroups. If the semigroups are equicontinuous at each point ? , we give different methods to prove the theorem.
文摘The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.
