A note on branch-and-cut-and-price

In this paper, we propose a methodology for branch-and-cut-and-price when cuts and columns are generated simultaneously. The methodology is illustrated with two application cases: the Split Delivery Vehicle Routing Problem (SDVRP) and the Bus Rapid Transit Route Design Problem (BRTRDP).     

Queues with impolite customers

An interesting behavior of customers arriving to a queue for service concerns the manner in which they join the queue. The arrival discipline of the customers may be impolite, in the sense that an arriving customer who finds all servers busy may pick a position which is not necessarily at the end of the line. We introduce and discuss in detail such an arrival discipline of sufficient generality which has interesting applications. In particular, we show that the more impolite an arrival discipline is, the bigger is the variance of the waiting time. We also study a special model in more depth to provide simple computational formulas for several performance measures.     

Depth-Optimized Convexity Cuts

This paper presents a general, self-contained treatment of convexity or intersection cuts. It describes two equivalent ways of generating a cut—via a convex set or a concave function—and a partial-order notion of cut strength. We then characterize the structure of the sets and functions that generate cuts that are strongest with respect to the partial order. Next, we specialize this analytical framework to the case of mixed-integer linear programming (MIP). For this case, we formulate two kinds of the deepest cut generation problem, via sets or via functions, and subsequently consider some special cases which are amenable to efficient computation. We conclude with computational tests of one of these procedures on a large set of MIPLIB problems.     

Multiple Cuts with a Homogeneous Analytic Center Cutting Plane Method

This paper analyzes the introduction of multiple central cuts in a conic formulation of the analytic center cutting plane method (in short ACCPM). This work extends earlier work on the homogeneous ACCPM, and parallels the analysis of the multiple cut process in the standard ACCPM. The main issue is the calculation of a direction that restores feasibility after introducing p new cutting planes at the query point. We prove that the new analytic center can be recovered in O(p log p) damped Newton iterations, where is a parameter depending of the data. We also present two special cases where the complexity can be decreased to O (p log p). Finally, we show that the number of calls to the oracle is the same as in the single cut case, up to a factor .     

Using two successive subgradients in the ellipsoid method for nonlinear programming

A variant of the ellipsoid method for nonlinear programming is introduced to enhance the speed of convergence. This variant is based on a new simple scheme to reduce the ellipsoid volume by using two center cuts generated in two consecutive iterations of the ellipsoid method. Computational tests show a significant improvement in computational efficiency. The tests show that the improvement is more significant for larger-size problems.     

A Rao-type characterization for a sequence to have a realization containing a split graph

For a given graph H, a non-increasing sequence π=(d₁,d₂,…,d_n) of nonnegative integers is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. The split graph on r+s vertices is denoted by S_r,s. In this paper, we give a Rao-type characterization for π to be potentially S_r,s-graphic. A simplification of this characterization is also presented.     

Thickness Effect of Pulse Shaper on Dynamic Stress Equilibrium and Dynamic Deformation Behavior in the Polycarbonate Using SHPB Technique

0Introduction Thehighstrainratestress strainresponsesofpolymersandpolymericcompositematerialshave receivedincreasedscientificandindustrialattentioninrecentyears.Polymericmaterialsaresubjected todynamicloadingandhighstrainratedeformationinavarietyofimporta…     

硬质聚氨酯泡沫塑料本构关系的研究

介绍用大尺寸分离式Ｈｏｐｋｉｎｓｏｎ压杆对四种密度的硬质聚氨酯泡沫塑料进行高应变率实验，完整地给出了这种材料在１０３／ｓ高应变率下的包括弹性区、屈服区和致密区变形全过程的动态应力应变曲线，并提出了包括应力、应变、应变率和密度等参量的本构关系．