In this paper we study the t-branch split cuts introduced by Li and Richard (2008). They presented a family of mixed-integer programs with n integer variables and a single continuous variable and conjectured that the convex hull of integer solutions for any n has unbounded rank with respect to (n−1)-branch split cuts. It was shown earlier by Cook, Kannan and Schrijver (1990) that this conjectur...

The Casimir force on a D-dimensional sphere due to the confinement of a massless scalar field is computed as a function of D, where D is a continuous variable that ranges from −∞ to ∞. The dependence of the force on the dimension is obtained using a simple and straightforward Green’s function technique. We find that the Casimir force vanishes as D → +∞ (D non-even integer) and also vanishes whe...

Differential Evolution is a competive method for continuous number optimization problems. A novel Structure-Encoding Differential Evolution (SEDE) algorithm was proposed for optimization problems with integer-parameter representation. In the SEDE Algorithm, each decision variable of every individual consists of two domains. One domain is float-encoding which is confined in a narrow range [0, 1]...

Abstract In recent years there has been growing interest in generating valid inequalities for mixedinteger programs using sets with 2 or more constraints. In particular, Andersen et al. (2007) and Borozan and Cornuéjols (2007) study sets defined by equations that contain exactly one integer variable per row. The integer variables are not restricted in sign. Cutting planes based on this approach...

In the literature, few constructions of n-variable rotation symmetric bent functions have been presented, which either have restriction on n or have algebraic degree no more than 4. In this paper, for any even integer n = 2m ≥ 2, a first systemic construction of n-variable rotation symmetric bent functions, with any possible algebraic degrees ranging from 2 to m, is proposed.

A heuristic algorithm, GCDHEU, is described for polynomial GCD computation over the integers. The algorithm is based on evaluation at a single large integer value (for each variable), integer GCD computation, and a single-point interpolation scheme. Timing comparisons show that this algorithm is very efficient for most univariate problems and it is also the algorithm of choice for many problems...

This paper deals with a multi-period fixed charge production-distribution problem associated with backorder and inventories. The objective is to determine the size of the shipments from each supplier and backorder and inventories at each period, so that the total cost incurred during the entire period towards production, transportation, backorder and inventories is minimised. A 0-1 mixed intege...

This paper is concerned with behavior analysis and improvement of wind turbines with Doubly Fed Induction Generator (DFIG) when using a new fractional-order control strategy during wind variations. A doubly fed induction generator, two types of variable frequency power electronic converters and two input wind waveforms are considered. A fractional-order control strategy is proposed for the wind...

We show that an important broad class of integer programming problems in variable dimension with convex objective functions is solvable in polynomial time, and discuss various applications including to multiway transportation problems, packing problems and partitioning problems.

Many compiler techniques depend on the ability to count the number of integer points that satisfy a given set of linear inequalities. Typically, a subset of the variables are identified as the parameters ~ p and the number of possible values for the other, “counted” variables ~y needs to be counted as a function of those parameters. If each variable is either a parameter or counted, then the pr...