What is the performance of the lexicographic optimization algorithm?

Despite the remarkable improvements in the performance of Minisat+ when integrated in a lexicographic optimization algorithm, MSUnCore integrated in a lexicographic optimization algorithm provides the best performance in terms of aborted problem instances.

What is the robust performance of the solvers?

The results indicate that, for the sets of problem instances considered, unsatisfiability-based solvers offer the most robust performance.

What is the correctness of the algorithm?

The correctness of the algorithm builds on the following: (i) unsatisfiability-based MaxSAT algorithms are correct [45,3]; and (ii) the transformations induced by unsatisfiability-based MaxSAT algorithms are parsimonious, i.e. the number of models remains unchanged in between iterations of the MaxSAT algorithm used.

What is the smallest fraction of weights where the BMO condition can be applied?

%MinR denotes the smallest fraction of weights where the BMO condition can be applied, over the total number of distinct weights for a given problem instance, over all the problem instances of the class.

What is the drawback of the unsatisfiability-based MaxSAT algorithm?

Another drawback is that, when compared to previous algorithms, a tighter integration with the underlying MaxSAT solver is necessary.

What is the optimum solution for the set of clauses?

This optimum solution is then used to filter the set of candidates for optimum assignments, by requiring this set of sets of clauses to satisfy its optimum solution.

Open AccessJournal Article10.1007/S10472-011-9233-2

Boolean lexicographic optimization: algorithms & applications

Joao Marques-Silva, +3 more

- 01 Jul 2011

- Annals of Mathematics and Artificial Int...

- Vol. 62, Iss: 3, pp 317-343

TL;DR: This paper develops and evaluates algorithms for solving MOCO problems, defined on Boolean domains, and where the optimality criterion is lexicographic, and shows that lexicography optimization conditions are observed in the majority of the problem instances from the MaxSAT evaluations.

Abstract: Multi-Objective Combinatorial Optimization (MOCO) problems find a wide range of practical application problems, some of which involving Boolean variables and constraints. This paper develops and evaluates algorithms for solving MOCO problems, defined on Boolean domains, and where the optimality criterion is lexicographic. The proposed algorithms build on existing algorithms for either Maximum Satisfiability (MaxSAT), Pseudo-Boolean Optimization (PBO), or Integer Linear Programming (ILP). Experimental results, obtained on problem instances from haplotyping with pedigrees and software package dependencies, show that the proposed algorithms can provide significant performance gains over state of the art MaxSAT, PBO and ILP algorithms. Finally, the paper also shows that lexicographic optimization conditions are observed in the majority of the problem instances from the MaxSAT evaluations, motivating the development of dedicated algorithms that can exploit lexicographic optimization conditions in general MaxSAT problem instances.

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Most frequently asked questions

1. What are the contributions mentioned in the paper "Boolean lexicographic optimization: algorithms & applications" ?

This paper develops and evaluates algorithms for solving MOCO problems, defined on Boolean domains, and where the optimality criterion is lexicographic.. Experimental results, obtained on problem instances from haplotyping with pedigrees and software package dependencies, show that the proposed algorithms can provide significant performance gains over state of the art MaxSAT, PBO and ILP algorithms.. Finally, the paper also shows that lexicographic optimization conditions are observed in the majority of the problem instances from the MaxSAT evaluations, motivating the development of dedicated algorithms that can exploit lexicographic optimization conditions in general MaxSAT problem instances.

2. What are the future works in "Boolean lexicographic optimization: algorithms & applications" ?

Future work will address tighter integration between default solvers and the algorithms for lexicographic optimization.. This can be done at different levels.

3. What is the p cost function for the optimization problem?

The p cost functions capturing the optimization problem represent a multi-dimensional function: f : {0, 1}n → Zp, with f(x) = (f1(x), . . . , fp(x)).

4. What is the optimum weight for the set of clauses?

In the first step, k = 1, the weights are rescaled such that w1 = 1 and w0 = 1×(1+1) = 2 = >, so that the set of weighted clauses isC = { (¬x1, 1)| {z } C1 , (x1,>)| {z } C0 }.

Table 6 Summary of MISC #3 – live results

Fig. 4 BLO improvements on MSUnCore vs. WPM1

Table 1 2008 MaxSAT Evaluation Statistics

Table 4 MaxSAT Evaluation Statistics using Upper Bounds

Table 3 Example Mancoosi [41,8] Benchmark Suites

Table 2 2009 MaxSAT Evaluation Statistics

Citations

•Journal Article

On solving the partial MAX-SAT problem

Zhaohui Fu, +1 more

- 01 Jan 2006

- Lecture Notes in Computer Science

TL;DR: Two solvers are implemented for the Partial MAX-SAT problem; the relative strengths and thus applicability of the two solvers for different solution scenarios are discussed and how both techniques benefit from the persistent learning techniques of incremental SAT.

...read moreread less

266

•Book Chapter•10.1007/978-3-319-09284-3_33

Open-WBO: A Modular MaxSAT Solver ,

Ruben Martins, +2 more

- 14 Jul 2014

TL;DR: This paper presents open-wbo, a new MaxSAT solver, an open-source solver that can be easily modified and extended that may use any MiniSAT-like solver as the underlying SAT solver.

...read moreread less

225

•Journal Article•10.1016/J.ARTINT.2013.01.002

SAT-based MaxSAT algorithms

Carlos Ansótegui, +2 more

- 01 Mar 2013

- Artificial Intelligence

TL;DR: This paper presents several algorithms specially designed to deal with industrial or real problems based on the idea of solving MaxSAT through successive calls to a SAT solver, and shows that this SAT-based technique is efficient in solving industrial problems.

...read moreread less

194

Exact ground states of Ising spin glasses: new experimental results with a branch and cut algorithm

Caterina De Simone, +4 more

- 01 Jan 1994

TL;DR: In this paper, the exact ground states of grids of sizes up to 100×100 can be determined in a moderate amount of computation time, and extensive computational tests are conducted on more than 20,000 experiments.

...read moreread less

135

•Book Chapter•10.1007/978-3-319-21690-4_27

OptiMathSAT: A Tool for Optimization Modulo Theories

Roberto Sebastiani, +1 more

- 18 Jul 2015

TL;DR: OptiMathSAT is presented, an OMT tool extending the MathSAT5 SMT solver that allows for solving a list of optimization problems on SMT formulas with linear objective functions – on the Boolean, the rational and the integer domains, and on their combination thereof– including MaxSMT.

...read moreread less

134

...

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References

•Book

Theory of Linear and Integer Programming

Alexander Schrijver

- 01 Dec 1986

TL;DR: Introduction and Preliminaries.

...read moreread less

7.5K

•Book

Integer and Combinatorial Optimization

George L. Nemhauser, +1 more

- 01 Jan 1988

TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.

...read moreread less

6.3K

Book•10.1002/9781118627372

Integer and Combinatorial Optimization: Nemhauser/Integer and Combinatorial Optimization

George L. Nemhauser, +1 more

- 16 Jun 1988

Abstract: FOUNDATIONS. The Scope of Integer and Combinatorial Optimization. Linear Programming. Graphs and Networks. Polyhedral Theory. Computational Complexity. Polynomial-Time Algorithms for Linear Programming. Integer Lattices. GENERAL INTEGER PROGRAMMING. The Theory of Valid Inequalities. Strong Valid Inequalities and Facets for Structured Integer Programs. Duality and Relaxation. General Algorithms. Special-Purpose Algorithms. Applications of Special- Purpose Algorithms. COMBINATORIAL OPTIMIZATION. Integral Polyhedra. Matching. Matroid and Submodular Function Optimization. References. Indexes.

...read moreread less

4.4K

•Book

Multicriteria Optimization

Matthias Ehrgott

- 18 May 2005

TL;DR: This paper presents a meta-modelling framework for estimating the modeled solutions for various types of optimization problems in the multicriteria setting.

...read moreread less

2.4K

Integer and Combinatorial Optimization

Karla Hoffman, +1 more

- 01 Jan 2013

TL;DR: In today’s changing and competitive industrial environment, the difference between ad hoc planning methods and those that use sophisticated mathematical models to determine an optimal course of action can determine whether or not a company survives.

...read moreread less

2.3K

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Boolean lexicographic optimization: algorithms & applications

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AI Agents for this Paper

Most frequently asked questions

1. What are the contributions mentioned in the paper "Boolean lexicographic optimization: algorithms & applications" ?

2. What are the future works in "Boolean lexicographic optimization: algorithms & applications" ?

3. What is the p cost function for the optimization problem?

4. What is the optimum weight for the set of clauses?

5. What is the performance of the lexicographic optimization algorithm?

6. What is the robust performance of the solvers?

7. What is the correctness of the algorithm?

8. What is the smallest fraction of weights where the BMO condition can be applied?

9. What is the drawback of the unsatisfiability-based MaxSAT algorithm?

10. What is the optimum solution for the set of clauses?

Figures

Citations

On solving the partial MAX-SAT problem

Open-WBO: A Modular MaxSAT Solver ,

SAT-based MaxSAT algorithms

Exact ground states of Ising spin glasses: new experimental results with a branch and cut algorithm

OptiMathSAT: A Tool for Optimization Modulo Theories

References

Theory of Linear and Integer Programming

Integer and Combinatorial Optimization

Integer and Combinatorial Optimization: Nemhauser/Integer and Combinatorial Optimization

Multicriteria Optimization

Integer and Combinatorial Optimization

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