Primal Cutting Plane Methods for the Traveling Salesman Problem
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Date
2017-04-26
Authors
Stratopoulos, Christos
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Most serious attempts at solving the traveling salesman problem (TSP)
are based on the dual fractional cutting plane approach, which
moves from one lower bound to the next.
This thesis describes methods for implementing a TSP
solver based on a primal cutting plane approach, which moves
from tour to tour with non-degenerate primal simplex pivots and
so-called primal cutting planes. Primal cutting
plane solution of the TSP has received scant attention in the
literature; this thesis seeks to redress this gap, and its findings
are threefold.
Firstly, we develop some theory around the computation of
non-degenerate primal simplex pivots, relevant to general primal
cutting plane computation. This theory guides highly efficient
implementation choices, a sticking point in prior studies.
Secondly, we engage in a practical study of several existing primal separation
algorithms for finding TSP cuts. These algorithms are
all conceptually simpler, easier to implement, or
asymptotically faster than their standard counterparts.
Finally, this thesis may constitute the first
computational study of the work of Fleischer, Letchford, and Lodi
on polynomial-time separation of simple domino parity
inequalities. We discuss exact and heuristic enhancements, including a
shrinking-style heuristic which makes the algorithm more suitable for
application on large-scale instances.
The theoretical developments of this thesis are integrated into a
branch-cut-price TSP solver which is used to obtain computational
results on a variety of test instances.
Description
Keywords
TSP, traveling salesman problem, cutting planes, primal algorithms, integer programming