TY - GEN

T1 - Improved step size adaptation for the MO-CMA-ES

AU - Voß, T.

AU - Hansen, N.

AU - Igel, Christian

PY - 2010

Y1 - 2010

N2 - The multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) is an evolutionary algorithm for continuous vector-valued optimization. It combines indicator-based selection based on the contributing hypervolume with the efficient strategy parameter adaptation of the elitist covariance matrix adaptation evolution strategy (CMA-ES). Step sizes (i.e., mutation strengths) are adapted on individual-level using an improved implementation of the 1/5-th success rule. In the original MO-CMA-ES, a mutation is regarded as successful if the offspring ranks better than its parent in the elitist, rank-based selection procedure. In contrast, we propose to regard a mutation as successful if the offspring is selected into the next parental population. This criterion is easier to implement and reduces the computational complexity of the MO-CMA-ES, in particular of its steady-state variant. The new step size adaptation improves the performance of the MO-CMA-ES as shown empirically using a large set of benchmark functions. The new update scheme in general leads to larger step sizes and thereby counteracts premature convergence. The experiments comprise the first evaluation of the MO-CMA-ES for problems with more than two objectives.

AB - The multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) is an evolutionary algorithm for continuous vector-valued optimization. It combines indicator-based selection based on the contributing hypervolume with the efficient strategy parameter adaptation of the elitist covariance matrix adaptation evolution strategy (CMA-ES). Step sizes (i.e., mutation strengths) are adapted on individual-level using an improved implementation of the 1/5-th success rule. In the original MO-CMA-ES, a mutation is regarded as successful if the offspring ranks better than its parent in the elitist, rank-based selection procedure. In contrast, we propose to regard a mutation as successful if the offspring is selected into the next parental population. This criterion is easier to implement and reduces the computational complexity of the MO-CMA-ES, in particular of its steady-state variant. The new step size adaptation improves the performance of the MO-CMA-ES as shown empirically using a large set of benchmark functions. The new update scheme in general leads to larger step sizes and thereby counteracts premature convergence. The experiments comprise the first evaluation of the MO-CMA-ES for problems with more than two objectives.

U2 - 10.1145/1830483.1830573

DO - 10.1145/1830483.1830573

M3 - Article in proceedings

SP - 487

EP - 494

BT - Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2010)

PB - Association for Computing Machinery

Y2 - 7 July 2010 through 11 July 2010

ER -