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Decision making based on approximate and smoothed pareto curves
 In Proc. of 16th ISAAC
, 2005
"... We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the socalled decision maker’s approach in which both criteria are combined into a single (usually nonlinear) objective function. Pr ..."
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Cited by 11 (2 self)
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We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the socalled decision maker’s approach in which both criteria are combined into a single (usually nonlinear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curve for problems like Shortest Path, Spanning Tree, and Perfect Matching. We wish to determine for which classes of combined objective functions the approximate Pareto curve also yields an approximate solution to the decision maker’s problem. We show that an FPTAS for the Pareto curve also gives an FPTAS for the decision maker’s problem if the combined objective function is growth bounded like a quasipolynomial function. If the objective function, however, shows exponential growth then the decision maker’s problem is NPhard to approximate within any polynomial factor. In order to bypass these limitations of approximate decision making, we turn our attention to Pareto curves in the probabilistic framework of smoothed analysis. We show that in a smoothed model, we can efficiently generate the (complete and exact) Pareto curve with a small failure probability if there exists an algorithm for generating the Pareto curve whose worst case running time is pseudopolynomial. This way, we can solve the decision maker’s problem w.r.t. any nondecreasing objective function for randomly perturbed instances of, e. g.,
Timetable Information: Models and Algorithms
, 2006
"... We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transfor ..."
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Cited by 10 (7 self)
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We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transform the problems into shortest path problems are reviewed, including issues like the modeling of realistic details (e.g., train transfers) and further optimization criteria (e.g., the number of transfers). An important topic is also multicriteria optimization, where in general all attractive connections with respect to several criteria shall be determined. Finally, we discuss the performance of the described algorithms, which is crucial for their application in a real system.
Recent Advances in Multiobjective Optimization
 In Lecture Notes in Computer Science
, 2005
"... Multiobjective (or multicriteria) optimization is a research area with rich history and under heavy investigation within Operations Research and Economics in the last 60 years [1,2]. Its object of study is to investigate solutions to combinatorial optimization problems that are evaluated under sever ..."
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Cited by 2 (0 self)
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Multiobjective (or multicriteria) optimization is a research area with rich history and under heavy investigation within Operations Research and Economics in the last 60 years [1,2]. Its object of study is to investigate solutions to combinatorial optimization problems that are evaluated under several objective functions – typically defined on multidimensional attribute (cost) vectors. In multiobjective optimization, we are interested not in finding a single optimal solution, but in computing the tradeoff among the different objective functions, called the Pareto set (or curve) P, which is the set of all feasible solutions whose vector of the various objectives is not dominated by any other solution. Multiobjective optimization problems are usually NPhard due to the fact that the Pareto set is typically exponential in size (even in the case of two objectives). On the other hand, even if a decision maker is armed with the entire Pareto set, s/he is still left with the problem of which is the “best ” solution for the application at hand. Consequently, three natural approaches to deal with multiobjective optimization problems are to:
QoSaware multicommodity flows and transportation planning
 ATMOS 2006  6TH WORKSHOP ON ALGORITHMIC METHODS AND MODELS FOR OPTIMIZATION OF RAILWAYS, INTERNATIONALES BEGEGNUNGS UND FORSCHUNGSZENTRUM FUER INFORMATIK (IBFI), SCHLOSS DAGSTUHL
, 2006
"... We consider the QoSaware Multicommodity Flow problem, a natural generalization of the weighted multicommodity flow problem where the demands and commodity values are elastic to the QualityofService characteristics of the underlying network. The problem is fundamental in transportation planning ..."
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Cited by 2 (1 self)
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We consider the QoSaware Multicommodity Flow problem, a natural generalization of the weighted multicommodity flow problem where the demands and commodity values are elastic to the QualityofService characteristics of the underlying network. The problem is fundamental in transportation planning and also has important applications beyond the transportation domain. We provide a FPTAS for the QoSaware Multicommodity Flow problem by building upon a Lagrangian relaxation method and a recent FPTAS for the nonadditive shortest path problem.
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"... Whereas regular path finding is about finding an optimal path between two locations, given one criterion – such as travel time – multicriteria path finding takes multiple of such criteria into account. This thesis analyses this type of path finding using realistic example scenario’s. We prove that t ..."
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Whereas regular path finding is about finding an optimal path between two locations, given one criterion – such as travel time – multicriteria path finding takes multiple of such criteria into account. This thesis analyses this type of path finding using realistic example scenario’s. We prove that the theoretical complexity of any multicriteria path finding problem is N Pcomplete, and propose two methods to solve such a problem. The first method is able to solve an adapted version of the multicriteria path finding problem, by restricting the criteria aggregation function in such a way that we are able to treat the original problem as a regular path finding problem. To solve such a problem without any restrictions, we propose an
Efficient Algorithms for kDisjoint Paths Problems on DAGs
"... Given an acyclic directed graph and two distinct nodes s and t, we consider the problem of finding k disjoint paths from s to t satisfying some objective. We consider four objectives, MinMax, Balanced, MinSumMinMin, and MinSumMinMax. We use the algorithm by PerlShiloach and labelling and scaling ..."
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Given an acyclic directed graph and two distinct nodes s and t, we consider the problem of finding k disjoint paths from s to t satisfying some objective. We consider four objectives, MinMax, Balanced, MinSumMinMin, and MinSumMinMax. We use the algorithm by PerlShiloach and labelling and scaling techniques to devise an FPTAS for the first three objectives. For the fourth one, we propose a general and efficient polynomialtime algorithm.