The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxe...The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxes into a single container. Both algorithms adopt the concept of building layers on one face of the container, but the first heuristic determines the layer face once for all, while the second treats the remaining container space as a reduced-sized container after one layer is loaded and, hence, selects the layer face dynamically. To handle the layout design problem at a layer's level, a block-based 2D packing procedure is also developed. Numerical studies demonstrate the efficiency of the heuristics.展开更多
By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local ...By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means.展开更多
为解决集装箱船舶贝内配载优化问题,以最小化倒箱次数为目标建立数学模型。提出基于力矩平衡和逐列装载的装船规则(ship loading rule based on moment balance and stowing column by column,SLR-MBSCC),根据装船方向的不同,将SLR-MBSC...为解决集装箱船舶贝内配载优化问题,以最小化倒箱次数为目标建立数学模型。提出基于力矩平衡和逐列装载的装船规则(ship loading rule based on moment balance and stowing column by column,SLR-MBSCC),根据装船方向的不同,将SLR-MBSCC规则分为由内向外(Inside-Out)装船和由外向内(Out-Inside)装船的两种规则。采用演化策略算法(ES),设计二维实数编码和基于SLR-MBSCC规则的解码方法,采用基于三点交叉互换的重组算子和基于两点互换的变异算子。在两种不同方向装船规则中,算例计算表明,由内向外方向下的规则对于减小横倾力矩更有效。通过不同规模算例分析验证了演化策略算法求解贝内配载问题的有效性。展开更多
基金the Natural Sciences and Engineering Research Council of Canada (NSERC) under the Discovery Grant Program
文摘The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxes into a single container. Both algorithms adopt the concept of building layers on one face of the container, but the first heuristic determines the layer face once for all, while the second treats the remaining container space as a reduced-sized container after one layer is loaded and, hence, selects the layer face dynamically. To handle the layout design problem at a layer's level, a block-based 2D packing procedure is also developed. Numerical studies demonstrate the efficiency of the heuristics.
基金supported by Joint Fund of Advanced Aerospace Manufacturing Technology Research(No. U1937601)the partial financial support of this research by the budget program of Ukraine“Support for the Development of Priority Research Areas”(No.CPCEC 6451230)。
文摘By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means.
文摘为解决集装箱船舶贝内配载优化问题,以最小化倒箱次数为目标建立数学模型。提出基于力矩平衡和逐列装载的装船规则(ship loading rule based on moment balance and stowing column by column,SLR-MBSCC),根据装船方向的不同,将SLR-MBSCC规则分为由内向外(Inside-Out)装船和由外向内(Out-Inside)装船的两种规则。采用演化策略算法(ES),设计二维实数编码和基于SLR-MBSCC规则的解码方法,采用基于三点交叉互换的重组算子和基于两点互换的变异算子。在两种不同方向装船规则中,算例计算表明,由内向外方向下的规则对于减小横倾力矩更有效。通过不同规模算例分析验证了演化策略算法求解贝内配载问题的有效性。
