Ranking-Dominance Relation for (Evolutionary) Multi-Objective Optimization
Kukkonen, Saku (2007)
Tiivistelmä
An alternative relation to Pareto-dominance relation is proposed. The new
relation is based on ranking a set of solutions according to each separate
objective and an aggregation function to calculate a scalar fitness value
for each solution. The relation is called as ranking-dominance and it
tries to tackle the curse of dimensionality commonly observedin
evolutionary multi-objective optimization. Ranking-dominance can beused
to sort a set of solutions even for a large number of objectives when
Pareto-dominance relation cannot distinguish solutions from one another
anymore. This permits search to advance even with a large number of
objectives. It is also shown that ranking-dominance does not violate
Pareto-dominance.
Results indicate that selection based on ranking-dominance is able to
advance search towards the Pareto-front in some cases, where selection
based on Pareto-dominance stagnates. However, in some cases it is also
possible that search does not proceed into direction of Pareto-front
because the ranking-dominance relation permits deterioration of individual
objectives.
Results also show that when the number of objectives increases, selection
based on just Pareto-dominance without diversity maintenance is able to
advance search better than with diversity maintenance. Therefore,
diversity maintenance is connive at the curse of dimensionality.
relation is based on ranking a set of solutions according to each separate
objective and an aggregation function to calculate a scalar fitness value
for each solution. The relation is called as ranking-dominance and it
tries to tackle the curse of dimensionality commonly observedin
evolutionary multi-objective optimization. Ranking-dominance can beused
to sort a set of solutions even for a large number of objectives when
Pareto-dominance relation cannot distinguish solutions from one another
anymore. This permits search to advance even with a large number of
objectives. It is also shown that ranking-dominance does not violate
Pareto-dominance.
Results indicate that selection based on ranking-dominance is able to
advance search towards the Pareto-front in some cases, where selection
based on Pareto-dominance stagnates. However, in some cases it is also
possible that search does not proceed into direction of Pareto-front
because the ranking-dominance relation permits deterioration of individual
objectives.
Results also show that when the number of objectives increases, selection
based on just Pareto-dominance without diversity maintenance is able to
advance search better than with diversity maintenance. Therefore,
diversity maintenance is connive at the curse of dimensionality.