Abstract
We propose a propositional logic based approach to solve MultiObjective Discrete Optimization Problems (MODOPs). In our approach, there exists a one-to-one correspondence between a Pareto front point of MODOP and a \(P\)-minimal model of the CNF formula obtained from MODOP. This correspondence is achieved by adopting the order encoding as CNF encoding for multiobjective functions. Finding the Pareto front is done by enumerating all P-minimal models. The beauty of the approach is that each Pareto front point is blocked by a single clause that contains at most one literal for each objective function. We evaluate the effectiveness of our approach by empirically contrasting it to a state-of-the-art MODOP solving technique.
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MODOP other than multiobjective functions can be encoded by existing CNF encodings: direct, multivalue, support, log, and hybrid encodings.
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Note that there is no essential differences between them.
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The terminology “block” is often used in SAT/MaxSAT communities to denote adding a constraint which prevents a solution to be found again (to “block” it) in an iterative process.
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#Sets = 20 is used only for #Items = 100. #Sets = 30 is used only for #Items = 150.
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We confirmed in our computational environment that the BDD solver was able to solve 55 instances out of the 60 MSCP instances, compared with 53 in [6].
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Soh, T., Banbara, M., Tamura, N., Le Berre, D. (2017). Solving Multiobjective Discrete Optimization Problems with Propositional Minimal Model Generation. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_38
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