# A parallel approach to bi-objective integer programming

## TL;DR

This paper introduces two parallel algorithms for bi-objective integer programming that significantly reduce computation time by effectively utilizing multi-core processors, outperforming existing methods and commercial solvers.

## Contribution

It proposes two novel parallelization techniques for a recursive BOIP algorithm, achieving near-perfect speedup with two threads and surpassing CPLEX's parallel efficiency.

## Key findings

- Meeting algorithm halves running time
- Both methods outperform CPLEX's parallelization
- Near-perfect parallelization achieved with two threads

## 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.