An exploratory computational analysis of dual degeneracy in mixed-integer programming

Dual degeneracy, i.e., the presence of multiple optimal bases to a linear programming (LP) problem, heavily affects the solution process of mixed integer programming (MIP) solvers. Different optimal bases lead to different cuts being generated, different branching decisions being taken and different solutions being found by primal heuristics. Nevertheless, only a few methods have been published that either avoid or exploit dual degeneracy. The aim of the present paper is to conduct a thorough computational study on the presence of dual degeneracy for the instances of well-known public MIP instance collections. How many instances are affected by dual degeneracy? How degenerate are the affected models? How does branching affect degeneracy: Does it increase or decrease by fixing variables? Can we identify different types of degenerate MIPs? As a tool to answer these questions, we introduce a new measure for dual degeneracy: the variable–constraint ratio of the optimal face. It provides an estimate for the likelihood that a basic variable can be pivoted out of the basis. Furthermore, we study how the so-called cloud intervals—the projections of the optimal face of the LP relaxations onto the individual variables—evolve during tree search and the implications for reducing the set of branching candidates.

On the Role of Grains in Plastic Deformation and Low Cycle Fatigue of Polycrystalline Metal

In the previous papers, the author discussed the role of r-value (anisotropic parameter in plasticity) on the surface roughening after plastic deformation. In the present paper, discussion is made on the effects of mutual constraint of deformation between neighboring grains at the grain boundary on the surface roughening. A characteristic parameter called constraint ratio is introduced to express the degree of the mutual restriction between grains. The well-known Coffin-Manson relation in low cycle fatigue is deduced considering to the surface roughening after cyclic deformation.

Uniqueness of the macromolecular crystallographic phase problem

Uniqueness of the phase problem in macromolecular crystallography, and its relationship to the case of single particle imaging, is considered. The crystallographic problem is characterized by a constraint ratio that depends only on the size and symmetry of the molecule and the unit cell. The results are used to evaluate the effect of various real-space constraints. The case of an unknown molecular envelope is considered in detail. The results indicate the quite wide circumstances under whichab initiophasing should be possible.

Finite Element Analysis on Critical Constraint Ratio of All-Steel Buckling Restrained Brace

The bearing capacity of the all-steel BRB consists of a rectangular core plate and a square outer tube is analyzed by finite element method using ABAQUS. The influences of configuration parameters, including the initial eccentricity of the core, the ratio of the width to the thickness of the core, and the ratio of the gap to the width of the core, on the critical constraint ratio are investigated. The fitted equation obtained based on the analysis can be used to guide the design of the BRB.

The Experimental Research of Carbon Fiber Confined Concrete Considering Strain Rate under Uniaxial Compression

In the three kinds of constraint ratio (ξ = 0.065, ξ= 0.1025, ξ= 0.205), respectively, by the comparative analysis of 55 prism specimens using CFRP confined concrete(strain ratses are 10-5/s-1, 10-4/s-1, 10-3/s-1and 10-2/s-1), the stress-strain curves, strength, strain, elastic modulus and Poisson's ratio were studied at different constraints and different strain rate. The results show that: (1) with the strain rate increased,the inflexion strength and ultimate strength of concrete were improved; (2) with the strain rate increased, the static and dynamic elastic modulus increased slightly; (3) Poisson's ratio increased slightly with the growth strain rate.