In this paper we present some new, practical, geometric optimization techniques for computing polygon partitions, 1D and 2D point, interval, square and rectangle covers, as well as 1D and 2D interval and rectangle K-centers. All the techniques we present have immediate applications to several cost optimization and facility location problems which are quite common in … Read more
The number partitioning problem (NPP) is to divide n numbers a_1,…,a_n into two disjoint subsets such that the difference between the two subset sums – the discrepancy, D, is minimized. In the balanced version of NPP (BalNPP), the subsets must have the same cardinality. With $a_j$s chosen uniformly from $[1,R]$, R > 2^n gives the … Read more
Identifying critical nodes in a graph is important to understand the structural characteristics and the connectivity properties of the network. In this paper, we focus on detecting critical nodes, or nodes whose deletion results in the minimum pair-wise connectivity among the remaining nodes. This problem, known as the CRITICAL NODE PROBLEM has applications in several … Read more
This work addresses the computation of free-energy di fferences between protein conformations by using morphing (i.e., transformation) of a source conformation into a target conformation. To enhance the morph- ing procedure, we employ permutations of atoms; we transform atom n in the source conformation into atom \sigma(n) in the target conformation rather than directly transforming atom … Read more
We apply the level-3 Reformulation Linearization Technique (RLT3) to the Quadratic Assignment Problem (QAP). We then present our experience in calculating lower bounds using an essentially new algorithm, based on this RLT3 formulation. This algorithm is not guaranteed to calculate the RLT3 lower bound exactly, but approximates it very closely and reaches it in some … Read more
This paper presents seven test problems with all the optimal solutions known on the background of the layout optimization problem of a simplified international communication satellite module, aiming to evaluate the algorithm performance on solving three-dimensional packing problem with behavior constraints. The test problems are constructed in the following step. First, place N (=217) cylinders … Read more
Within the context of solving Mixed-Integer Linear Programs by a Branch-and-Cut algorithm, we propose a new strategy for branching. Computational experiments show that, on the majority of our test instances, this approach enumerates fewer nodes than traditional branching. On average, on instances that contain both integer and continuous variables the number of nodes in the … Read more
We consider the problem of minimizing the weighted sum of completion times on a single machine subject to bipartite precedence constraints where all minimal jobs have unit processing time and zero weight, and all maximal jobs have zero processing time and unit weight. For various probability distributions over these instances–including the uniform distribution–we show several … Read more
In this paper we consider two problems regarding the scheduling of available personnel in order to perform a given quantity of work, which can be arbitrarily decomposed into a sequence of activities. We are interested in schedules which minimize the overall dissatisfaction, where each employee’s dissatisfaction is modeled as a time-dependent linear function. For the … Read more
Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in … Read more