In this paper branching for attacking MILP is investigated. Under certain circumstances branches can be done concurrently. By introducing a new calculus it is shown there are restrictions for dual values. As a second result of this study a new class of cuts for MILP is found, which are defined by those values. This class … Read more
We study approaches for the exact solution of the \NP–hard minimum spanning tree problem under conflict constraints. Given a graph $G(V,E)$ and a set $C \subset E \times E$ of conflicting edge pairs, the problem consists of finding a conflict-free minimum spanning tree, i.e. feasible solutions are allowed to include at most one of the … Read more
We present a framework for obtaining Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely the Calculus of K-approximation Functions and the Calculus of K-approximation Sets. Using our framework, we provide … Read more
We consider the problem of scheduling on uniform processors with nonsimultaneous machine available times with the purpose of mini\-mi\-zing the maximum completion time. We give a variant of the Multifit algorithm which generates schedules which end within $1.382$ times the optimal maximum completion times. This results from properties of the Multifit algorithm when used for … Read more
The uniqueness of sparsest solutions of underdetermined linear systems plays a fundamental role in the newly developed compressed sensing theory. Several new algebraic concepts, including the sub-mutual coherence, scaled mutual coherence, coherence rank, and sub-coherence rank, are introduced in this paper in order to develop new and improved sufficient conditions for the uniqueness of sparsest … Read more
The maximum stable set problem is a well-known NP-hard problem in combinatorial optimization, which can be formulated as the maximization of a quadratic square-free polynomial over the (Boolean) hypercube. We investigate a hierarchy of linear programming relaxations for this problem, based on a result of Handelman showing that a positive polynomial over a polytope can … Read more
Assortment optimization is an important problem that arises in many practical applications such as retailing and online advertising. In an assortment optimization problem, the goal is to select a subset of items that maximizes the expected revenue in the presence of the substitution behavior of consumers specified by a choice model. In this paper, we … Read more
This research presents a very efficient method of solving a broad class of large-scale capacitated resource management problems by introducing a new formulation and decomposition. A heuristic called Likelihood of Assignment is utilized not only to find high quality initial integer feasible solutions, but also to guide the Branch-and-Price (B&P) Algorithm towards stabilization. Although Column … Read more
The $pq$-relaxation for the pooling problem can be constructed by applying McCormick envelopes for each of the bilinear terms appearing in the so-called $pq$-formulation of the pooling problem. This relaxation can be strengthened by using piecewise-linear functions that over- and under-estimate each bilinear term. The resulting relaxation can be written as a mixed integer linear … Read more
The high school timetabling is a classical problem and has many combinatorial variations. It is NP-Complete and since the use of exact methods for this problem is restricted, heuristics are usually employed. This paper applies three Iterated Local Search (ILS) algorithms which includes two newly proposed neighborhood operators to heuristically solve a benchmark of the … Read more