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DOE OSTI2016

INFORMS Section on Location Analysis Dissertation Award Submission

This research effort can be summarized by two main thrusts, each of which has a chapter of the dissertation dedicated to it. First, I pose a novel polyhedral approach for identifying polynomially solvable in- stances of the QAP based on an application of the reformulation-linearization technique (RLT), a general procedure for constructing mixed 0-1 linear reformulations of 0-1 pro- grams. The feasible region to the continuous relaxation of the level-1 RLT form is a polytope having a highly specialized structure. Every binary solution to the QAP is associated with an extreme point of this polytope, and the objective function value is preserved at each such point. However, there exist extreme points that do not correspond to binary solutions. The key insight is a previously unnoticed and unexpected relationship between the polyhedral structure of the continuous relaxation of the level-1 RLT representation and various classes of readily solvable instances. Specifically, we show that a variety of apparently unrelated solvable cases of the QAP can all be categorized in the following sense: each such case has an objective function which ensures that an optimal solution to the continuous relaxation of the level-1 RLT form occurs at a binary extreme point. Interestingly, there exist instances that are solvable by the level-1 RLT form which do not satisfy the conditions of these cases, so that the level-1 form theoretically identifies a richer family of solvable instances. Second, I focus on instances of the QAP known in the literature as linearizable. An instance of the QAP is defined to be linearizable if and only if the problem can be equivalently written as a linear assignment problem that preserves the objective function value at all feasible solutions. I provide an entirely new polyheral-based perspective on the concept of linearizable by showing that an instance of the QAP is linearizable if and only if a relaxed version of the continuous relaxation of the level-1 RLT form is bounded. We also shows that the level-1 RLT form can identify a richer family of solvable instances than those deemed linearizable by demonstrating that the continuous relaxation of the level-1 RLT form can have an optimal binary solution for instances that are not linearizable. As a byproduct, I use this theoretical framework to explicity, in closed form, characterize the dimensions of the level-1 RLT form and various other problem relaxations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

University of Kansas Medical center Cancer Research Equipment Award Type: Construction Grant

A major mechanism to strengthen the overall cancer focus of KUCC and expand specific research programs is through targeted recruitment of additional cancer researchers to increase the national and international status of the Cancer Center, enhance the number of NCI/cancer-related grants, fill critical research needs, and enable new collaborative projects. Over the last five years KUCC has demonstrated the ability to recruit nationally recognized basic, translational and clinical scientists to fill key leadership positions and strengthen our research programs. These researchers require new and renovated research facilities require state-of-the-art laboratory equipment. This includes standard equipment for the renovated laboratories and more specialized equipment as part of new investigator start-up packages. This funding is used to support recruitment, facilities, equipment, shared resources, administration, and patient care services. KUCC is committed to recruiting additional cancer researchers to increase the national and international status of the Cancer Center, enhance the number of NCI/cancer-related grants, fill critical research positions and build the four cancer research programs. Each purposeful hire aims to further the scientific vision, mission, and goals of the Cancer Center research programs. The funds requested will be used to supplement the recruitment packages of future cancer center recruits primarily through purchase of key equipment items.

60 APPLIED LIFE SCIENCES↗