Design of Experiments for the Tuning of Optimisation Algorithms

This thesis presents a set of rigorous methodologies for tuning the performance of algorithms that solve optimisation problems. Many optimisation problems are difficult and time-consuming to solve exactly. An alternative is to use an approximate algorithm that solves the problem to an acceptable level of quality and provides such a solution in a reasonable time. Using optimisation algorithms typically requires choosing the settings of tuning parameters that adjust algorithm performance subject to this compromise between solution quality and running time. This is the parameter tuning problem. This thesis demonstrates that the Design Of Experiments (DOE) approach can be adapted to successfully address the parameter tuning problem for algorithms that find approximate solutions to optimisation problems. The thesis introduces experiment designs and analyses for (1) determining the problem characteristics affecting algorithm performance (2) screening and ranking the most important tuning parameters and problem characteristics and (3) tuning algorithm parameters to maximise algorithm performance for a given problem instance. Desirability functions are introduced for tackling the compromise of achieving satisfactory solution quality in reasonable running time. Five case studies apply the thesis methodologies to the Ant Colony System and the Max-Min Ant System algorithms for the Travelling Salesperson Problem. New results are reported and open questions are answered regarding the importance of both existing tuning parameters and proposed new tuning parameters. A new problem characteristic is identified and shown to have a very strong effect on the quality of the algorithms’ solutions. The tuning methodologies presented here yield solution quality that is as good as or better than than the general parameter settings from the literature. Furthermore, the associated running times are orders of magnitude faster than the results obtained with the general parameter settings. All experiments are performed with publicly available algorithm code, publicly available problem generators and benchmarked experimental machines.