A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computatio...A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm pro-posed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.展开更多
The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type ...The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.展开更多
In this paper we study the Goursat problem for semilinear hyperbolicequations with zero boundary condition where the boundary is the characteristic conefor hyperbolic operator. Our result shows that the solution is Li...In this paper we study the Goursat problem for semilinear hyperbolicequations with zero boundary condition where the boundary is the characteristic conefor hyperbolic operator. Our result shows that the solution is Lipschitz and is smoothaway from the characteristic cone.展开更多
The paper studies a relaxation of the basic multidimensional variational problem, when the class of admissible functions is endowed with the Lipschitz convergence introduced by Morrey. It is shown that in this setup, ...The paper studies a relaxation of the basic multidimensional variational problem, when the class of admissible functions is endowed with the Lipschitz convergence introduced by Morrey. It is shown that in this setup, the integral of a variational problem must satisfy a classical growth condition, unlike the case of uniform convergence. The relaxations constructed here imply the existence of a Lipschitz convergent minimizing sequence. Based on this observation, the paper also shows that the Lavrentiev phenomenon does not occur for a class of nonconvex problems.展开更多
It is well known that hierarchies of mathematical programming formulatlons with different numbers of variables and constraints have a considerable impact regarding the quality of solutions obtained once these formulat...It is well known that hierarchies of mathematical programming formulatlons with different numbers of variables and constraints have a considerable impact regarding the quality of solutions obtained once these formulations are fed to a commercial solver. In addition, even if dimensions are kept the same, changes in formulations may largely influence solvability and quality of results. This becomes evident especially if redundant constraints are used. We propose a related framework for information collection based on these constraints. We exemplify by means of a well-known combinatorial optimization problem from the knapsack problem family, i.e., the multidimensional multiple-choice knapsack problem （MMKP）. This incorporates a relationship of the MMKP to some generalized set partitioning problems. Moreover, we investigate an application in maritime shipping and logistics by means of the dynamic berth allocation problem （DBAP）, where optimal solutions are reached from the root node within the solver.展开更多
A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that ...A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman’s coalescent is replaced byΞ-coalescent.We prove the existence of such a process by specifying its moments using the dual function-valuedΞ-coalescent process with geographical labels and migration,and then verifying a multidimensional Hausdorff moment problem.We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type.展开更多
文摘A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm pro-posed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.
文摘The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.
基金This work is partially supported by National Natural Science Foundation of China.
文摘In this paper we study the Goursat problem for semilinear hyperbolicequations with zero boundary condition where the boundary is the characteristic conefor hyperbolic operator. Our result shows that the solution is Lipschitz and is smoothaway from the characteristic cone.
文摘The paper studies a relaxation of the basic multidimensional variational problem, when the class of admissible functions is endowed with the Lipschitz convergence introduced by Morrey. It is shown that in this setup, the integral of a variational problem must satisfy a classical growth condition, unlike the case of uniform convergence. The relaxations constructed here imply the existence of a Lipschitz convergent minimizing sequence. Based on this observation, the paper also shows that the Lavrentiev phenomenon does not occur for a class of nonconvex problems.
文摘It is well known that hierarchies of mathematical programming formulatlons with different numbers of variables and constraints have a considerable impact regarding the quality of solutions obtained once these formulations are fed to a commercial solver. In addition, even if dimensions are kept the same, changes in formulations may largely influence solvability and quality of results. This becomes evident especially if redundant constraints are used. We propose a related framework for information collection based on these constraints. We exemplify by means of a well-known combinatorial optimization problem from the knapsack problem family, i.e., the multidimensional multiple-choice knapsack problem （MMKP）. This incorporates a relationship of the MMKP to some generalized set partitioning problems. Moreover, we investigate an application in maritime shipping and logistics by means of the dynamic berth allocation problem （DBAP）, where optimal solutions are reached from the root node within the solver.
基金NSF of Hebei Province(Grant No.A2019205299)Hebei Education Department(Grant No.QN2019073)+2 种基金NSFC(Grant No.11501164)and HNU(Grant No.L2019Z01)X.Zhou’s research is supported by Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2016-06704)National Science Foundation of China(Grant No.11771018)。
文摘A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman’s coalescent is replaced byΞ-coalescent.We prove the existence of such a process by specifying its moments using the dual function-valuedΞ-coalescent process with geographical labels and migration,and then verifying a multidimensional Hausdorff moment problem.We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type.
