A Theoretical and Algorithmic Characterization of Bulge Knees

This paper deals with the problem of finding convex bulges on the Pareto-front of a multi-objective optimization problem. The point of maximum bulge is of particular interest as this point shows good tradeoff properties and it is also close to the non-attainable utopia point. Our approach is to use a population based algorithm to simultaneously promote convex bulges and improve the current approximation of the individual minimum of the objectives. This is done by changing the ranking of the solutions, and by proposing a new domination scheme that is used to sort the solutions. Theoretical results characterize the interrelationships between the bulge knee, the weighted sum method, and the guided domination approach.