405 research outputs found
Fuzzy Maximum Satisfiability
In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to
{\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the
problem of finding an assignment to the variables in {\Phi} that satisfies the
maximum number of formulae. Three possible solutions (encodings) are proposed
to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer
Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem
(WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have
numerous applications in optimization problems that involve vagueness.Comment: 10 page
Balanced Combinations of Solutions in Multi-Objective Optimization
For every list of integers x_1, ..., x_m there is some j such that x_1 + ...
+ x_j - x_{j+1} - ... - x_m \approx 0. So the list can be nearly balanced and
for this we only need one alternation between addition and subtraction. But
what if the x_i are k-dimensional integer vectors? Using results from
topological degree theory we show that balancing is still possible, now with k
alternations.
This result is useful in multi-objective optimization, as it allows a
polynomial-time computable balance of two alternatives with conflicting costs.
The application to two multi-objective optimization problems yields the
following results:
- A randomized 1/2-approximation for multi-objective maximum asymmetric
traveling salesman, which improves and simplifies the best known approximation
for this problem.
- A deterministic 1/2-approximation for multi-objective maximum weighted
satisfiability
ASlib: A Benchmark Library for Algorithm Selection
The task of algorithm selection involves choosing an algorithm from a set of
algorithms on a per-instance basis in order to exploit the varying performance
of algorithms over a set of instances. The algorithm selection problem is
attracting increasing attention from researchers and practitioners in AI. Years
of fruitful applications in a number of domains have resulted in a large amount
of data, but the community lacks a standard format or repository for this data.
This situation makes it difficult to share and compare different approaches
effectively, as is done in other, more established fields. It also
unnecessarily hinders new researchers who want to work in this area. To address
this problem, we introduce a standardized format for representing algorithm
selection scenarios and a repository that contains a growing number of data
sets from the literature. Our format has been designed to be able to express a
wide variety of different scenarios. Demonstrating the breadth and power of our
platform, we describe a set of example experiments that build and evaluate
algorithm selection models through a common interface. The results display the
potential of algorithm selection to achieve significant performance
improvements across a broad range of problems and algorithms.Comment: Accepted to be published in Artificial Intelligence Journa
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Parameterized algorithms of fundamental NP-hard problems: a survey
Parameterized computation theory has developed rapidly over the last two decades. In theoretical computer science, it has attracted considerable attention for its theoretical value and significant guidance in many practical applications. We give an overview on parameterized algorithms for some fundamental NP-hard problems, including MaxSAT, Maximum Internal Spanning Trees, Maximum Internal Out-Branching, Planar (Connected) Dominating Set, Feedback Vertex Set, Hyperplane Cover, Vertex Cover, Packing and Matching problems. All of these problems have been widely applied in various areas, such as Internet of Things, Wireless Sensor Networks, Artificial Intelligence, Bioinformatics, Big Data, and so on. In this paper, we are focused on the algorithms’ main idea and algorithmic techniques, and omit the details of them
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