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13
Decision making with multiple objectives using GAI networks
 Artif. Intell
, 2011
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Resolution for MaxSAT
, 2007
"... MaxSAT is the problem of finding an assignment minimizing the number of unsatisfied clauses in a CNF formula. We propose a resolutionlike calculus for MaxSAT and prove its soundness and completeness. We also prove the completeness of some refinements of this calculus. From the completeness proof ..."
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Cited by 5 (2 self)
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MaxSAT is the problem of finding an assignment minimizing the number of unsatisfied clauses in a CNF formula. We propose a resolutionlike calculus for MaxSAT and prove its soundness and completeness. We also prove the completeness of some refinements of this calculus. From the completeness proof we derive an exact algorithm for MaxSAT and a time upper bound. We also define a weighted MaxSAT resolutionlike rule, and show how to adapt the soundness and completeness proofs of the MaxSAT rule to the weighted MaxSAT rule. Finally, we give several particular MaxSAT problems that require an exponential number of steps of our MaxSAT rule to obtain the minimal number of unsatisfied clauses of the combinatorial principle. These results are based on the corresponding resolution lower bounds for those particular problems.
Multiobjective Russian Doll Search
 In Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI
, 2007
"... Russian Doll Search (RDS) is a wellknown algorithm for combinatorial optimization. In this paper we extend it from monoobjective to multiobjective optimization. We demonstrate its practical applicability in the challenging multipleorbit SPOT5 instances. Besides being much more efficient than an ..."
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Russian Doll Search (RDS) is a wellknown algorithm for combinatorial optimization. In this paper we extend it from monoobjective to multiobjective optimization. We demonstrate its practical applicability in the challenging multipleorbit SPOT5 instances. Besides being much more efficient than any other alternatives, multiobjective RDS can solve an instance which could not have been solved previously.
Enabling Local Computation for Partially Ordered Preferences
"... Abstract. Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A m ..."
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Abstract. Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A major strength of this work is that it is based on an algebraic description: what is proved is the correctness of the local computation algorithm under a few axioms on the algebraic structure. The instantiations of the framework in practice make use of totally ordered scales. The present paper focuses on the use of partially ordered scales and examines how such scales can be cast in the ShaferShenoy framework and thus benefit from local computation algorithms. It also provides several examples of such scales, thus showing that each of the algebraic structures explored here is of interest.
Exploiting Problem Decomposition in Multiobjective Constraint Optimization
"... Abstract. Multiobjective optimization is concerned with problems involving multiple measures of performance which should be optimized simultaneously. In this paper, we extend AND/OR BranchandBound (AOBB), a well known search algorithm, from monoobjective to multiobjective optimization. The new ..."
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Abstract. Multiobjective optimization is concerned with problems involving multiple measures of performance which should be optimized simultaneously. In this paper, we extend AND/OR BranchandBound (AOBB), a well known search algorithm, from monoobjective to multiobjective optimization. The new algorithm MOAOBB exploits efficiently the problem structure by traversing an AND/OR search tree and uses static and dynamic minibucket heuristics to guide the search. We show that MOAOBB improves dramatically over the traditional OR search approach, on various benchmarks for multiobjective optimization. 1
Computing convex coverage sets for multiobjective coordination graphs
 In ADT 2013: Proceedings of the Third International Conference on Algorithmic Decision Theory
, 2013
"... Abstract. Many realworld decision problems require making tradeoffs between multiple objectives. However, in some cases, the relative importance of the objectives is not known when the problem is solved, precluding the use of singleobjective methods. Instead, multiobjective methods, which compute ..."
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Abstract. Many realworld decision problems require making tradeoffs between multiple objectives. However, in some cases, the relative importance of the objectives is not known when the problem is solved, precluding the use of singleobjective methods. Instead, multiobjective methods, which compute the set of all potentially useful solutions, are required. This paper proposes new multiobjective algorithms for cooperative multiagent settings. Following previous approaches, we exploit loose couplings, as expressed in graphical models, to coordinate efficiently. Existing methods, however, calculate only the Pareto coverage set (PCS), which we argue is inappropriate for stochastic strategies and unnecessarily large when the objectives are weighted in a linear fashion. In these cases, the typically much smaller convex coverage set (CCS) should be computed instead. A key insight of this paper is that, while computing the CCS is more expensive in unstructured problems, in many loosely coupled settings it is in fact cheaper to compute because the local solutions are more compact. We propose convex multiobjective variable elimination, which exploits this insight. We analyze its correctness and complexity and demonstrate empirically that it scales much better in the number of agents and objectives than alternatives that compute the PCS.
Local Computation Schemes with Partially Ordered Preferences
"... Abstract. Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A m ..."
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Abstract. Many computational problems linked to uncertainty and preference management can be expressed in terms of computing the marginal(s) of a combination of a collection of valuation functions. Shenoy and Shafer showed how such a computation can be performed using a local computation scheme. A major strength of this work is that it is based on an algebraic description: what is proved is the correctness of the local computation algorithm under a few axioms on the algebraic structure. The instantiations of the framework in practice make use of totally ordered scales. The present paper focuses on the use of partially ordered scales and examines how such scales can be cast in the ShaferShenoy framework and thus benefit from local computation algorithms. It also provides many examples of such scales, thus showing that each of the algebraic structures explored here is of interest.
Linear Support for MultiObjective Coordination Graphs
"... Many realworld decision problems require making tradeoffs among multiple objectives. However, in some cases, the relative importance of these objectives is not known when the problem is solved, precluding the use of singleobjective methods. Instead, multiobjective methods, which compute the set ..."
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Many realworld decision problems require making tradeoffs among multiple objectives. However, in some cases, the relative importance of these objectives is not known when the problem is solved, precluding the use of singleobjective methods. Instead, multiobjective methods, which compute the set of all potentially useful solutions, are required. This paper proposes variable elimination linear support (VELS), a new multiobjective algorithm for multiagent coordination that exploits loose couplings to compute the convex coverage set (CCS): the set of optimal solutions for all possible weights for linearly weighted objectives. Unlike existing methods, VELS exploits insights from POMDP solution methods to build the CCS incrementally. We prove the correctness of VELS and show that for moderate numbers of objectives its complexity is better than that of previous methods. Furthermore, we present empirical results showing that VELS can tackle both random and realistic problems with many more agents than was previously feasible. The incremental nature of VELS also makes it an anytime algorithm, i.e., its intermediate results constitute εoptimal approximations of the CCS, with ε decreasing the longer it runs. Our empirical results show that, by allowing even very small ε, VELS can enable large additional speedups.
BranchandBound for Soft Constraints Based on Partially Ordered Degrees of Preference
"... Abstract. The handling of partially ordered degrees of preference can be important for constraintbased languages, especially when there is more than one criterion that we are interested in optimising. This paper describes branch and bound algorithms for a very general class of soft constraint optim ..."
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Abstract. The handling of partially ordered degrees of preference can be important for constraintbased languages, especially when there is more than one criterion that we are interested in optimising. This paper describes branch and bound algorithms for a very general class of soft constraint optimisation problems. At each node of the search tree, a propagation mechanism is applied which generates an upper bound (since we are maximising) of the preference degrees of all complete assignments below the node. We show how this propagation can be achieved using an extended minibuckets algorithm. However, since the degrees of preference ordering are only partially ordered, such an upper bound can be very uninformative, and so it can be desirable to instead generate an upper bound set, which contains an upper bound for the degree of preference for each complete assignment below the node. It is shown how such propagation can also be achieved using this extended minibuckets approach. 1
MultiObjective Variable Elimination for Collaborative Graphical Games
"... maastrichtuniversity.nl In this paper we propose multiobjective variable elimination (MOVE), an efficient solution method for multiobjective collaborative graphical games (MOCoGGs), that exploits loose couplings. MOVE computes the convex coverage set, which can be much smaller than the Pareto fro ..."
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maastrichtuniversity.nl In this paper we propose multiobjective variable elimination (MOVE), an efficient solution method for multiobjective collaborative graphical games (MOCoGGs), that exploits loose couplings. MOVE computes the convex coverage set, which can be much smaller than the Pareto front. In an empirical study, we show that MOVE can tackle multiobjective problems much faster than methods that do not exploit loose couplings.