Title: A parallel approach to bi-objective integer programming,
Abstract: To obtain a better understanding of the trade-offs between various
objectives, Bi-Objective Integer Programming (BOIP) algorithms calculate the
set of all non-dominated vectors and present these as the solution to a BOIP
problem. Historically, these algorithms have been compared in terms of the
number of single-objective IPs solved and total CPU time taken to produce the
solution to a problem. This is equitable, as researchers can often have access
to widely differing amounts of computing power. However, the real world has
recently seen a large uptake of multi-core processors in computers, laptops,
tablets and even mobile phones. With this in mind, we look at how to best
utilise parallel processing to improve the elapsed time of optimisation
algorithms. We present two methods of parallelising the recursive algorithm
presented by Ozlen, Burton and MacRae. Both new methods utilise two threads and
improve running times. One of the new methods, the Meeting algorithm, halves
running time to achieve near-perfect parallelisation. The results are compared
with the efficiency of parallelisation within the commercial IP solver IBM ILOG
CPLEX, and the new methods are both shown to perform better.