Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Relations and graphs: discrete mathematics for computer scientists
Relations and graphs: discrete mathematics for computer scientists
Many birds with one stone: multi-objective approximation algorithms
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Implementation of Relational Algebra Using Binary Decision Diagrams
ReIMICS '01 Revised Papers from the 6th International Conference and 1st Workshop of COST Action 274 TARSKI on Relational Methods in Computer Science
Random knapsack in expected polynomial time
Journal of Computer and System Sciences - Special issue: STOC 2003
Efficient Relational Calculation for Software Analysis
IEEE Transactions on Software Engineering
Primal-Dual Meets Local Search: Approximating MSTs With Nonuniform Degree Bounds
SIAM Journal on Computing
Multicriteria Optimization
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Relational approach to boolean logic problems
RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
RelView: an OBDD-based computer algebra system for relations
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Solving algorithmic problems on orders and lattices by relation algebra and RELVIEW
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Evaluating sets of search points using relational algebra
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
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Relational algebra has been shown to be a powerful tool for solving a wide range of combinatorial optimization problems with small computational and programming effort. The problems considered in recent years are single- objective ones where one single objective function has to be optimized. With this paper we start considerations on the use of relational algebra for multi-objective problems. In contrast to single-objective optimization multiple objective functions have to be optimized at the same time usually resulting in a set of different trade-offs with respect to the different functions. On the one hand, we examine how to solve the mentioned problem exactly by using relational algebraic programs. On the other hand, we address the problem of objective reduction that has recently been shown to be NP-hard. We propose an exact algorithm for this problem based on relational algebra. Our experimental results show that this algorithm drastically outperforms the currently best one.