Towards a Link between Knee Solutions and Preferred Solution Methodologies

In a bi-criteria optimization problem, often the user is interested in a subset of solutions lying in the knee region. On the other hand in many problem-solving tasks, often one or a few methodologies are commonly used. In this paper, we argue that there is a link between the knee solutions in bi-criteria problems and the preferred methodologies when viewed from a conflicting bi-criterion standpoint. We illustrate our argument with the help of a number of popularly used problem-solving tasks. Each task, when perceived as a bicriteria problem, seems to exhibit a knee or a knee-region and the commonly-used methodology seems to lie within the knee-region. This linking is certainly an interesting finding and may have a long-term implication in the development of efficient solution methodologies for different scientific and other problem-solving tasks.

[1]  Lily Rachmawati,et al.  A multi-objective evolutionary algorithm with weighted-sum niching for convergence on knee regions , 2006, GECCO '06.

[2]  Francois Dion,et al.  COMPARISON OF DELAY ESTIMATES AT UNDER-SATURATED AND OVER-SATURATED PRE-TIMED SIGNALIZED INTERSECTIONS , 2004 .

[3]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[4]  Lily Rachmawati,et al.  Multiobjective Evolutionary Algorithm With Controllable Focus on the Knees of the Pareto Front , 2009, IEEE Transactions on Evolutionary Computation.

[5]  Liping Fu,et al.  Delay Variability at Signalized Intersections , 2000 .

[6]  Simon M. Lucas,et al.  Parallel Problem Solving from Nature - PPSN X, 10th International Conference Dortmund, Germany, September 13-17, 2008, Proceedings , 2008, PPSN.

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

[8]  Kalyanmoy Deb,et al.  Multi-objective optimization of a leg mechanism using genetic algorithms , 2005 .

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

[10]  Sascha Ossowski,et al.  Proceedings of the 2010 ACM Symposium on Applied Computing (SAC), Sierre, Switzerland, March 22-26, 2010 , 2010, SAC.

[11]  Indraneel Das.  On characterizing the “knee” of the Pareto curve based on Normal-Boundary Intersection , 1999 .

[12]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[13]  Marco Laumanns,et al.  Approximating the Knee of an MOP with Stochastic Search Algorithms , 2008, PPSN.

[14]  Khaled Ghédira,et al.  Searching for knee regions in multi-objective optimization using mobile reference points , 2010, SAC '10.