Problem Features versus Algorithm Performance on Rugged Multiobjective Combinatorial Fitness Landscapes

Fabio Daolio, Arnaud Liefooghe, Sébastien Verel, Hernán Aguirre, Kiyoshi Tanaka
2017 Evolutionary Computation  
In this paper, we attempt to understand and to contrast the impact of problem features on the performance of randomized search heuristics for black-box multi-objective combinatorial optimization problems. At first, we measure the performance of two conventional dominance-based approaches with unbounded archive on a benchmark of enumerable binary optimization problems with tunable ruggedness, objective space dimension, and objective correlation (ρMNK-landscapes). Precisely, we investigate the
more » ... ected runtime required by a global evolutionary optimization algorithm with an ergodic variation operator (GSEMO) and by a neighborhood-based local search heuristic (PLS), to identify a (1 + ε)−approximation of the Pareto set. Then, we define a number of problem features characterizing the fitness landscape, and we study their intercorrelation and their association with algorithm runtime on the benchmark instances. At last, with a mixed-effects multi-linear regression we assess the individual and joint effect of problem features on the performance of both algorithms, within and across the instance classes defined by benchmark parameters. Our analysis reveals further insights into the importance of ruggedness and multi-modality to characterize instance hardness for this family of multi-objective optimization problems and algorithms. Keywords Evolutionary multi-objective optimization, black-box 0-1 multi-objective problems, feature-based analysis, fitness landscape and problem difficulty, empirical performance modeling, multi-level multi-variate analysis, random-effects mixed models.
doi:10.1162/evco_a_00193 pmid:27689467 fatcat:7lwr4sdq3fajtnni53vdkibd6a