Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to generate bounds for mixed-integer linear programming problems. Traditionally, these methods have been viewed as distinct from polyhedral methods, in which bounds are obtained by dynamically generating valid inequalities to strengthen a linear programming relaxation. ...

Given an undirected graph with edge weights, the MAX-CUT problem consists in finding a partition of the nodes into two subsets, such that the sum of the weights of the edges having endpoints in different subsets is maximized. It is a well-known NP-hard problem with applications in several fields, including VLSI design and statistical physics. In this paper, a greedy randomized adaptive search p...

Self-aligned multiple patterning (SAMP), due to its low overlay error, has emerged as the leading option for 1D gridded back-end-of-line (BEOL) in sub-14nm nodes. To form actual routing patterns from a uniform “sea of wires”, a cut mask is needed for line-end cutting or realization of space between routing segments. Constraints on cut shapes and minimum cut spacing result in end-of-line (EOL) e...

alstroemeria flower is one of the most important cut flowers in the world. some materials can increase longevity of cut flowers. the aim of this research was evaluating the effect of some chemical solutions on postharvest alstroemeria (cv. stratus) cut flowers. this experiment was conducted with two factors of sucrose at four concentrations, 0, 5, 10 and 15 g/l and salicylic acid (sa) at four c...

The MAXIMUM CUT problem (MAX-CUT) is one of the simplest graph partitioning problems to conceptualize, and yet it is one of the most difficult combinatorial optimization problems to solve. The objective of MAX-CUT is to partition the set of vertices of a graph into two subsets, such that the sum of the weights of the edges having one endpoint in each of the subsets is maximum. This problem is k...

1 In this paper we present a branch-and-cut algorithm for a structured 0/1 integer programming problem referred to as the \truck dispatching scheduling (TDS) problem." The TDS problem is a vehicle routing and scheduling problem that arose from an oil company's desire to better utilize regional truck eets and drivers. Many studies on diierent variations of vehicle routing and scheduling have app...

We describe a general N -solitonic solution of the focusing nonlinear Schrödinger equation in the presence of a condensate by using the dressing method. We give the explicit form of oneand two-solitonic solutions and study them in detail as well as solitonic atoms and degenerate solutions. We distinguish a special class of solutions that we call regular solitonic solutions. Regular solitonic so...

A maximum principle is proved for the weak solutions u ∈ L∞(R× T3) of the telegraph equation utt − xu + cut + λu = f (t, x), in space dimension three, when c > 0, λ ∈ (0, c2/4] and f ∈ L∞(R × T3) (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semili...