论文信息 - On the interrelationships between knees and aggregate objective functions

On the interrelationships between knees and aggregate objective functions

Optimizing several objectives that are often at odds with each other provides difficult challenges that are not encountered if having only one goal at hand. One intuitive way to solve a multi-objective problem is to aggregate the objectives and reformulate it as an optimization problem having just a single goal. This goal can be a designer specific aggregation of the objectives or a characterization of knees, trade-offs, utilities, stronger optimality concepts or preferences. This paper examines the theoretical relationships between two knee concepts and aggregate objective functions methods. The changes in the fitness landscape by utilizing different aggregations is also discussed.

[1] John von Neumann,et al. Theory of Games and Economic Behavior (60th-Anniversary Edition) , 2007 .

[2] Kalyanmoy Deb,et al. Finding Knees in Multi-objective Optimization , 2004, PPSN.

[3] A. M. Geoffrion. Proper efficiency and the theory of vector maximization , 1968 .

[4] Hartmut Schmeck,et al. A Framework for Incorporating Trade-Off Information Using Multi-Objective Evolutionary Algorithms , 2010, PPSN.

[5] Hartmut Schmeck,et al. Theory and Algorithms for Finding Knees , 2013, EMO.

[6] Pradyumn Kumar Shukla,et al. In Search of Proper Pareto-optimal Solutions Using Multi-objective Evolutionary Algorithms , 2007, International Conference on Computational Science.

[7] K. Deb,et al. Understanding knee points in bicriteria problems and their implications as preferred solution principles , 2011 .