Comparative Run-Time Performance of Evolutionary Algorithms on Multi-objective Interpolated Continuous Optimisation Problems

Abstract

We propose a new class of multi-objective benchmark problems on which we analyse the performance of four well established multiobjective evolutionary algorithms (MOEAs) -each implementing a different search paradigm -by comparing run-time convergence behaviour over a set of 1200 problem instances. The new benchmarks are created by fusing previously proposed single-objective interpolated continuous optimisation problems (ICOPs) via a common set of Pareto non-dominated seeds. They thus inherit the ICOP property of having tunable fitness landscape features. The benchmarks are of intrinsic interest as they derive from interpolation methods and so can approximate general problem instances. This property is revealed to be of particular importance as our extensive set of numerical experiments indicates that choices pertaining to (i) the weighting of the inverse distance interpolation function and (ii) the problem dimension can be used to construct problems that are challenging to all tested multi-objective search paradigms. This in turn means that the new multi-objective ICOPs problems (MO-ICOPs) can be used to construct well-balanced benchmark sets that discriminate well between the run-time convergence behaviour of different solvers.

Landscape features and automated algorithm selection for multi-objective interpolated continuous optimisation problems

“…Multi-objective interpolated continuous optimisation problems (MO-ICOPs) have been recently introduced in [34] as a new class of benchmark problems with tunable landscapes. MO-ICOPs are defined by an objective function vector that combines singleobjective ICOPs generated using a common set of seeds.…”

“…We consider the set of bi-objective problems proposed in [34]. For each MO-ICOP, the set of seeds is randomly generated in the variable space = [−5, 5] .…”

“…By analysing the outputs of the experiments reported in [34] 1 , the present work focusses on the comparative performance of four different MOEAs parameterised using recommended settings from the literature. In [34], the authors state that these MOEAs were chosen because they exemplify different well-proven multi-objective optimisation strategies.…”

“…This allows cost efficient application (in terms of evaluations) to automated algorithm selection and performance prediction. The second work this paper builds upon outlines a method for generating a diversified benchmark set of continuous MOOPs [34]. The generator uses interpolated continuous optimisation problems to produce MOOPs with various characteristics and structures.…”

“…We then use the features as predictors for performance prediction and algorithm selection on random forest regression and classification models, respectively. We also analyse the predictive power of the proposed landscape features against the parameters used by the random multi-objective interpolated continuous optimisation problem generator from [34].…”