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Articles 1 - 5 of 5
Full-Text Articles in Other Applied Mathematics
Characterizing Linearizable Qaps By The Level-1 Reformulation-Linearization Technique, Lucas Waddell, Warren Adams
Characterizing Linearizable Qaps By The Level-1 Reformulation-Linearization Technique, Lucas Waddell, Warren Adams
Faculty Journal Articles
The quadratic assignment problem (QAP) is an extremely challenging NP-hard combinatorial optimization program. Due to its difficulty, a research emphasis has been to identify special cases that are polynomially solvable. Included within this emphasis are instances which are linearizable; that is, which can be rewritten as a linear assignment problem having the property that the objective function value is preserved at all feasible solutions. Various known sufficient conditions for identifying linearizable instances have been explained in terms of the continuous relaxation of a weakened version of the level-1 reformulation-linearization-technique (RLT) form that does not enforce nonnegativity on a subset …
The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan
The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan
Honors Theses
This thesis investigates the previously unstudied Precedence-Constrained Quadratic Knapsack Problem (PC-QKP), an NP-hard nonlinear combinatorial optimization problem. The PC-QKP is a variation of the traditional Knapsack Problem (KP) that introduces several additional complexities. By developing custom exact and approximate solution methods, and testing these on a wide range of carefully structured PC-QKP problem instances, we seek to identify and understand patterns that make some cases easier or harder to solve than others. The findings aim to help develop better strategies for solving this and similar problems in the future.
An Lp-Based Characterization Of Solvable Qap Instances With Chess-Board And Graded Structures, Lucas Waddell, Jerry Phillips, Tianzhu Liu, Swarup Dhar
An Lp-Based Characterization Of Solvable Qap Instances With Chess-Board And Graded Structures, Lucas Waddell, Jerry Phillips, Tianzhu Liu, Swarup Dhar
Faculty Journal Articles
The quadratic assignment problem (QAP) is perhaps the most widely studied nonlinear combinatorial optimization problem. It has many applications in various fields, yet has proven to be extremely difficult to solve. This difficulty has motivated researchers to identify special objective function structures that permit an optimal solution to be found efficiently. Previous work has shown that certain such structures can be explained in terms of a mixed 0-1 linear reformulation of the QAP known as the level-1 reformulation-linearization-technique (RLT) form. Specifically, the objective function structures were shown to ensure that a binary optimal extreme point solution exists to the continuous …
Strengthening A Linear Reformulation Of The 0-1 Cubic Knapsack Problem Via Variable Reordering, Richard Forrester, Lucas Waddell
Strengthening A Linear Reformulation Of The 0-1 Cubic Knapsack Problem Via Variable Reordering, Richard Forrester, Lucas Waddell
Faculty Journal Articles
The 0-1 cubic knapsack problem (CKP), a generalization of the classical 0-1 quadratic knapsack problem, is an extremely challenging NP-hard combinatorial optimization problem. An effective exact solution strategy for the CKP is to reformulate the nonlinear problem into an equivalent linear form that can then be solved using a standard mixed-integer programming solver. We consider a classical linearization method and propose a variant of a more recent technique for linearizing 0-1 cubic programs applied to the CKP. Using a variable reordering strategy, we show how to improve the strength of the linear programming relaxation of our proposed reformulation, which ultimately …
Scaling Up Exact Neural Network Compression By Relu Stability, Thiago Serra, Xin Yu, Abhinav Kumar, Srikumar Ramalingam
Scaling Up Exact Neural Network Compression By Relu Stability, Thiago Serra, Xin Yu, Abhinav Kumar, Srikumar Ramalingam
Faculty Conference Papers and Presentations
We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. In this work, we introduce an algorithm based on solving a single optimization problem to identify all stable neurons. Our approach is on median 183 times faster than the state-of-art method on CIFAR-10, which allows us to explore exact compression on deeper (5 x 100) and wider …