Section: New Results

Learning and Adaptation for Landscape-aware Algorithm Design

Participants: Bilel Derbel, Arnaud Liefooghe (external collaborators: Hernan Aguirre, Fabio Daolio, Miyako Sagawa and Kiyoshi Tanaka, Shinshu Univ., Japan; Cyril Fonlupt, Christopher Jankee and Sébastien Verel, Univ. Littoral, France)

In [13], 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 ($\rho$MNK-landscapes). Precisely, we investigate the expected 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 + $\epsilon$)−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.

Designing portfolio adaptive selection strategies is a promising approach to gain in generality when tackling a given optimization problem. However, we still lack much understanding of what makes a strategy effective, even if different benchmarks have been already designed for these issues. In [35], we propose a new model based on fitness cloud allowing us to provide theoretical and empirical insights on when an on-line adaptive strategy can be beneficial to the search. In particular, we investigate the relative performance and behavior of two representative and commonly used selection strategies with respect to static (off-line) and purely random approaches, in a simple, yet sound realistic, setting of the proposed model.

In evolutionary multi-objective optimization, variation operators are crucially important to produce improving solutions, hence leading the search towards the most promising regions of the solution space. In [39], we propose to use a machine learning modeling technique, namely random forest, in order to estimate, at each iteration in the course of the search process, the importance of decision variables with respect to convergence to the Pareto front. Accordingly, we are able to propose an adaptive mechanism guiding the recombination step with the aim of stressing the convergence of the so-obtained offspring. By conducting an experimental analysis using some of the WFG and DTLZ benchmark test problems, we are able to elicit the behavior of the proposed approach, and to demonstrate the benefits of incorporating machine learning techniques in order to design new efficient adaptive variation mechanisms.