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A survey of multi-objective sequential decision-making

- Roijers, Diederik, Vamplew, Peter, Whiteson, Shimon, Dazeley, Richard

  • Authors: Roijers, Diederik , Vamplew, Peter , Whiteson, Shimon , Dazeley, Richard
  • Date: 2013
  • Type: Text , Journal article
  • Relation: Journal of Artificial Intelligence Research Vol. 48, no. (2013), p. 67-113
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  • Description: Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work. © 2013 AI Access Foundation.
  • Description: C1

A new scalarization technique and new algorithms to generate pareto fronts

- Burachik, Renata, Kaya, Yalcin, Rizvi, Mustafa

  • Authors: Burachik, Renata , Kaya, Yalcin , Rizvi, Mustafa
  • Date: 2017
  • Type: Text , Journal article
  • Relation: SIAM journal on optimization Vol. 27, no. 2 (2017), p. 1010-1034
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  • Description: We propose a new scalarization technique for nonconvex multiobjective optimization problems and establish its theoretical properties. By combining our new scalarization approach with existing grid generation techniques, we design new algorithms for constructing reliable approximations of the Pareto fronts of three- and four-objective optimization problems. Our algorithms can be extended for problems with more objective functions to minimize. Four three-objective algorithms are formed by pairing up the new scalarization technique and three existing scalarization techniques with a grid of weights generated over the convex hull of individual minima (the CHIM grid) due to Das and Dennis. Four more algorithms are obtained by using, instead of the CHIM grid, the grid in the successive boundary generation algorithm (the SBG grid) by Mueller-Gritschneder, Graeb, and Schlichtmann. The new algorithms seem to perform better than existing algorithms, in terms of computational time and accuracy in constructing the boundary and the interior of the Pareto front. The advantages are tested, in particular, through a problem whose Pareto front has a hole in it. A rocket injector design problem with four objective functions illustrates the effectiveness of our new approach further. Keywords
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