Name
Abstract | ||
|---|---|---|
Many state-of-the-art evolutionary vector optimization algorithms compute the contributing hypervolume for ranking candidate solutions. However, with an increasing number of objectives, calculating the volumes becomes intractable. Therefore, although hypervolume-based algorithms are often the method of choice for bi-criteria optimization, they are regarded as not suitable for many-objective optimization. Recently, Monte Carlo methods have been derived and analyzed for approximating the contributing hypervolume. Turning theory into practice, we employ these results in the ranking procedure of the multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) as an example of a state-of-the-art method for vector optimization. It is empirically shown that the approximation does not impair the quality of the obtained solutions given a budget of objective function evaluations, while considerably reducing the computation time in the case of multiple objectives. These results are obtained on common benchmark functions as well as on two design optimization tasks. Thus, employing Monte Carlo approximations makes hypervolume-based algorithms applicable to many-objective optimization. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.artint.2013.08.001 | Artif. Intell. |
Keywords | Field | DocType |
vector optimization,ranking candidate solution,state-of-the-art evolutionary vector optimization,design optimization task,hypervolume-based algorithm,monte carlo method,contributing hypervolume,many-objective optimization,bi-criteria optimization,monte carlo approximation,multi objective optimization,evolutionary algorithm | Evolutionary algorithm,Multi-objective optimization,Evolution strategy,CMA-ES,Artificial intelligence,Mathematical optimization,Monte Carlo method,Ranking,Vector optimization,Test functions for optimization,Algorithm,Mathematics,Machine learning | Journal |
Volume | Issue | ISSN |
204, | 1 | 0004-3702 |
Citations | PageRank | References |
17 | 0.56 | 32 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Karl Bringmann | 1 | 427 | 30.13 |
| Tobias Friedrich | 2 | 457 | 23.56 |
| Christian Igel | 3 | 1841 | 123.54 |
| Thomas Voí | 4 | 17 | 0.56 |