IdiS: Indicator-Based Multiobjective Search in High-Dimensional Spaces

Background

Dealing with high-dimensional search and objective spaces represents one of the major challenges in real-world optimization scenarios. For example, decision making is the more difficult the more solution alternatives, decision variables, and objective functions are involved; the visualization of such high-dimensional data is only one related problem. Furthermore, the search for good solutions in large search spaces is demanding and can cause immense computational costs.

Goals

This project addresses both decision making and optimization with respect to theoretical and practical investigations. On the one hand, we like to gain a basic understanding of problem structures and answer the question of what makes high-dimensional problems hard to tackle. Therefore, basic studies on the structures of multiobjective problems together with running time analyses of simple randomized search algorithms are necessary. On the other hand, we concentrate on dimensionality reduction methods and new indicator-based evolutionary algorithms to cope with high-dimensional problems in practice.

Collaborators

• B. Doerr, T. Friedrich, N. Hebbinghaus, C. Klein, and F. Neumann from Max-Planck-Institut für Informatik, Saarbrücken, Germany
• K. Deb and D. Kumar Saxena from Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology, Kanpur, India

Funding

• Swiss National Science Foundation (SNF), project number 112079

Publications

[1 — ubz2010a]

T. Ulrich, J. Bader, and E. Zitzler. Integrating Decision Space Diversity into Hypervolume-based Multiobjective Search. In Genetic and Evolutionary Computation Conference (GECCO 2010), New York, NY, USA, 2010. ACM. to appear. (bibtex)

[2 — abbz2009b]

A. Auger, J. Bader, D. Brockhoff, and E. Zitzler. Articulating User Preferences in Many-Objective Problems by Sampling the Weighted Hypervolume. In G. Raidl et al., editors, Genetic and Evolutionary Computation Conference (GECCO 2009), pages 555–562, New York, NY, USA, 2009. ACM. (PDF) (bibtex)

[3 — abbz2009c]

A. Auger, J. Bader, D. Brockhoff, and E. Zitzler. Investigating and Exploiting the Bias of the Weighted Hypervolume to Articulate User Preferences. In G. Raidl et al., editors, Genetic and Evolutionary Computation Conference (GECCO 2009), pages 563–570, New York, NY, USA, 2009. ACM. (PDF) (bibtex)

[4 — bfhk2009a]

D. Brockhoff, T. Friedrich, N. Hebbinghaus, C. Klein, F. Neumann, and E. Zitzler. On the Effects of Adding Objectives to Plateau Functions. IEEE Transactions on Evolutionary Computation, 13(3):591–603, 2009. (doi) (bibtex)

[5 — bz2009c]

D. Brockhoff and E. Zitzler. Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications. Evolutionary Computation, 17(2):135–166, 2009. (PDF) (bibtex) (suppl. material)

[6 — broc2009b]

D. Brockhoff. Many-Objective Optimization and Hypervolume-Based Search. PhD thesis, ETH Zurich, 2009. (bibtex)

[7 — sblz2009a]

T. Siegfried, S. Bleuler, M. Laumanns, E. Zitzler, and W. Kinzelbach. Multi-Objective Groundwater Management Using Evolutionary Algorithms. IEEE Transactions on Evolutionary Computation, 13(2):229–242, 2009. (PDF) (doi) (bibtex)

[8 — bz2009a]

D. Brockhoff and E. Zitzler. Automated Aggregation and Omission of Objectives to Handle Many-Objective Problems. In Conference on Multiple Objective and Goal Programming (MOPGP 2008), Lecture Notes in Economics and Mathematical Systems. Springer, 2009. to appear. (bibtex)

[9 — abbz2009a]

A. Auger, J. Bader, D. Brockhoff, and E. Zitzler. Theory of the Hypervolume Indicator: Optimal μ-Distributions and the Choice of the Reference Point. In Foundations of Genetic Algorithms (FOGA 2009), pages 87–102, New York, NY, USA, 2009. ACM. (PDF) (bibtex) (suppl. material)

[10 — zkt2008a]

E. Zitzler, J. Knowles, and L. Thiele. Quality Assessment of Pareto Set Approximations. In J. Branke, K. Deb, K. Miettinen, and R. Slowinski, editors, Multiobjective Optimization: Interactive and Evolutionary Approaches, pages 373–404. Springer, 2008. (bibtex) (online access)

[11 — bfn2008a]

D. Brockhoff, T. Friedrich, and F. Neumann. Analyzing Hypervolume Indicator Based Algorithms. In G. Rudolph et al., editors, Conference on Parallel Problem Solving From Nature (PPSN X), volume 5199 of LNCS, pages 651–660. Springer, 2008. (PDF) (bibtex) (online access)

[12 — ubz2008a]

T. Ulrich, D. Brockhoff, and E. Zitzler. Pattern Identification in Pareto-Set Approximations. In M. Keijzer et al., editors, Genetic and Evolutionary Computation Conference (GECCO 2008), pages 737–744. ACM, 2008. (PDF) (bibtex)

[13 — bsdz2007a]

D. Brockhoff, D. K. Saxena, K. Deb, and E. Zitzler. On Handling a Large Number of Objectives A Posteriori and During Optimization. In J. Knowles, D. Corne, and K. Deb, editors, Multiobjective Problem Solving from Nature: From Concepts to Applications, pages 377–403. Springer, 2007. (doi) (bibtex) (online access) (suppl. material)

[14 — bz2007c]

D. Brockhoff and E. Zitzler. Improving Hypervolume-based Multiobjective Evolutionary Algorithms by Using Objective Reduction Methods. In Congress on Evolutionary Computation (CEC 2007), pages 2086–2093. IEEE Press, 2007. (PDF) (bibtex) (suppl. material)

[15 — bfhk2007a]

D. Brockhoff, T. Friedrich, N. Hebbinghaus, C. Klein, F. Neumann, and E. Zitzler. Do Additional Objectives Make a Problem Harder?. In D. Thierens et al., editors, Genetic and Evolutionary Computation Conference (GECCO 2007), pages 765–772, New York, NY, USA, 2007. ACM Press. (PDF) (bibtex) (online access)

[16 — bz2007d]

D. Brockhoff and E. Zitzler. Dimensionality Reduction in Multiobjective Optimization: The Minimum Objective Subset Problem. In K. H. Waldmann and U. M. Stocker, editors, Operations Research Proceedings 2006, pages 423–429. Springer, 2007. (PDF) (bibtex) (online access) (suppl. material)

[17 — bz2007a]

D. Brockhoff and E. Zitzler. Offline and Online Objective Reduction in Evolutionary Multiobjective Optimization Based on Objective Conflicts. TIK Report 269, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, April 2007. (PDF) (bibtex) (suppl. material)

[18 — zbt2007a]

E. Zitzler, D. Brockhoff, and L. Thiele. The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration. In S. Obayashi et al., editors, Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS, pages 862–876, Berlin, 2007. Springer. (PDF) (bibtex) (online access) (suppl. material)

[19 — bz2006d]

D. Brockhoff and E. Zitzler. Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization. In T. P. Runarsson et al., editors, Conference on Parallel Problem Solving from Nature (PPSN IX), volume 4193 of LNCS, pages 533–542, Berlin, Germany, 2006. Springer. (PDF) (bibtex) (online access) (suppl. material)

[20 — bz2006f]

M. Basseur and E. Zitzler. A Preliminary Study On Handling Uncertainty in Multiobjective Optimization. In F. Rothlauf, J. Branke, S. Cagnoni, et al., editors, European Workshop on Evolutionary Algorithms in Stochastic and Noisy Environments (EvoSTOC 2006), volume 3907 of LNCS, pages 727–739. Springer, 2006. (PDF) (bibtex)

[21 — bz2006c]

D. Brockhoff and E. Zitzler. Dimensionality Reduction in Multiobjective Optimization with (Partial) Dominance Structure Preservation: Generalized Minimum Objective Subset Problems. TIK Report 247, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, April 2006. (PDF) (bibtex) (suppl. material)

[22 — bz2006a]

D. Brockhoff and E. Zitzler. On Objective Conflicts and Objective Reduction in Multiple Criteria Optimization. TIK Report 243, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, February 2006. (PDF) (bibtex) (suppl. material)

[23 — bz2006e]

M. Basseur and E. Zitzler. Handling Uncertainty in Indicator-Based Multiobjective Optimization. International Journal of Computational Intelligence Research, 2(3):255–272, 2006. (PDF) (bibtex)