Bi-level hybrid local search approach for three-dimensional loading problem with balancing constraints

This paper presents a bi-level hybrid local search(BHLS)algorithm for the three-dimensional loading problem with balancing constraints(3DLP-B),where several rectangular boxes with even densities but different sizes are loaded into a single cubic bin to meet the requirements of the space or capacity utilization and the balance of the center of gravity.The proposed algorithm hybridizes a novel framed-layout procedure in which the concept of the core block and its generation strategy are introduced.Once the block-loading sequence has been determined,we can load one block at a time by the designed construction heuristic.Then,the double-search is introduced;its external search procedure generates a list of compact packing patterns while its internal search procedure is used to search the core-block frames and their best distribution locations.The approach is extensively tested on weakly to strongly heterogeneous benchmark data.The results show that it has better performance in improving space utilization rate and balanced condition of the placement than existed techniques:the overall averages from 79.85%to 86.45%were obtained for the balanced cases and relatively high space-usage rate of 89.44%was achieved for the unbalanced ones.

NUMERICAL EXPERIMENTS ON MULTI-LEVEL STATISTICAL ESTIMATION OF DYNAMIC BALANCE CONSTRAINTS IN GRAPES-3DVAR

This paper further explores the estimating and expressing of dynamic balance constraints using statistical methods in GRAPES-3DVAR(Version GM). Unlike the single-level scheme which only considers the coupling between mass and wind at one level, the multi-level scheme considers the coupling between their vertical profiles and calculates the balanced mass field at each layer using the rotational wind at all model levels. A reformed ridge regression method is used in the new scheme to avoid the multicollinearity problem and reduce the noises caused by unbalanced mesoscale disturbances. The results of numerical experiments show that the new scheme can get more reasonable vertical mass field, reduce the magnitude of the adjustment by the initialization, and improve the potential temperature analysis performance. Furthermore, the results of forecast verification in January(winter) and July(summer) both confirm that the new scheme can significantly improve the temperature forecast accuracy and bring slight positive effects to the pressure and wind forecast.

Optimization of Line Configuration and Balancing for Flexible Machining Lines

Line configuration and balancing is to select the type of line and allot a given set of operations as well as machines to a sequence of workstations to realize high-efficiency production. Most of the current researches for machining line configuration and balancing problems are related to dedicated transfer lines with dedicated machine workstations. With growing trends towards great product variety and fluctuations in market demand, dedicated transfer lines are being replaced with flexible machining line composed of identical CNC machines. This paper deals with the line configuration and balancing problem for flexible machining lines. The objective is to assign operations to workstations and find the sequence of execution, specify the number of machines in each workstation while minimizing the line cycle time and total number of machines. This problem is subject to precedence, clustering, accessibility and capacity constraints among the features, operations, setups and workstations. The mathematical model and heuristic algorithm based on feature group strategy and polychromatic sets theory are presented to find an optimal solution. The feature group strategy and polychromatic sets theory are used to establish constraint model. A heuristic operations sequencing and assignment algorithm is given. An industrial case study is carried out, and multiple optimal solutions in different line configurations are obtained. The case studying results show that the solutions with shorter cycle time and higher line balancing rate demonstrate the feasibility and effectiveness of the proposed algorithm. This research proposes a heuristic line configuration and balancing algorithm based on feature group strategy and polychromatic sets theory which is able to provide better solutions while achieving an improvement in computing time.

Freights loading optimization with balanced and unconcentrated loading constraints

The optimization of high density and concentrated-weight freights loading requires an even distribution of the freight's weight and unconcentrated loading on the floor of the car.Based on the characteristics of concentrated-weight category freights,an improvement method is put forward to build freight towers and a greedy-construction algorithm is utilized based on heuristic information for the initial layout.Then a feasibility analysis is performed to judge if the balanced and unconcentrated loading constrains are reached.Through introducing optimization or adjustment methods,an overall optimal solution can be obtained.Experiments are conducted using data generated from real cases showing the effectiveness of our approach: volume utility ratio of 90.4% and load capacity utility ratio of 86.7% which is comparably even to the packing of the general freights.