Rešavanje problema CSP tehnikama svođenja na problem SAT
Solving of constraint satisfaction problems by reduction to SAT
Author
Stojadinović, Mirko S.Mentor
Marić, Filip
Committee members
Janičić, Predrag
Mitić, Nenad

Nikolić, Mladen

Vujošević, Mirko
Metadata
Show full item recordAbstract
Mnogi realni problemi se danas mogu predstaviti u obliku problema zadovoljenja
ogranicenja (CSP) i zatim rešiti nekom od mnogobrojnih tehnika za rešavanje
ovog problema. Jedna od tehnika podrazumeva svođenje na problem SAT, tj.
problem iskazne zadovoljivosti. Promenljive i ogranicenja problema CSP se prevode
(kodiraju) u SAT instancu, ona se potom rešava pomocu modernih SAT rešavaca
i rešenje se, ako postoji, prevodi u rešenje problema CSP. Glavni cilj ove teze je
unapređenje rešavanja problema CSP svođenjem na SAT.
Razvijena su dva nova hibridna kodiranja (prevođenja u SAT formulu) koja
kombinuju dobre strane postojecih kodiranja. Dat je dokaz korektnosti jednog od
kodiranja koji do sada nije postojao u literaturi. Razvijen je sistem meSAT koji
omogucava svođenje problema CSP na SAT pomocu cetiri osnovna i dva hibridna
kodiranja, kao i rešavanje problema CSP svođenjem na dva problema srodna problemu
SAT, SMT i PB.
Razvijen je portfolio za automatski odabir kodiranja/rešavaca za ulaznu... instancu
koju je potrebno rešiti i pokazano je da je razvijeni portfolio uporediv sa najefikasnijim
savremenim pristupima. Prikazan je novi pristup zasnovan na kratkim vremenskim
ogranicenjima sa ciljem da se znacajno smanji vreme pripreme portfolija.
Pokazano je da se ovim pristupom dobijaju rezultati konkurentni onima koji se dobijaju
korišcenjem standardnog vremena za pripremu. Izvršeno je poređenje nekoliko
tehnika mašinskog ucenja, sa ciljem da se ustanovi koja od njih je pogodnija za
pristup sa kratkim treniranjem.
Prikazan je jedan realan problem, problem raspoređivanja kontrolora leta, kao i
tri njegova modela. Veliki broj metoda rešavanja i raznovrsnih rešavaca je upotrebljeno
za rešavanje ovog problema. Razvijeno je više optimizacionih tehnika koje
imaju za cilj pronalaženje optimalnih rešenja problema. Pokazuje se da je najefikasnija
hibridna tehnika koja kombinuje svođenje na SAT i lokalnu pretragu.
Razmotren je i problem sudoku, kao i postojece tehnike rešavanja sudoku zagonetki
vecih dimenzija od 9 x 9. Pokazuje se da je u rešavanju ovih zagonetki
najefikasnije vec postojece svođenje na SAT. Unapređen je postojeci algoritam za
generisanje velikih sudoku zagonetki. Pokazano je da jednostavna pravila preprocesiranja
dodatno unapređuju brzinu generisanja sudokua.
Many real-world problems can be modeled as constraint satisfaction
problems (CSPs) and then solved by one of many available techniques for solving
these problems. One of the techniques is reduction to SAT, i.e. Boolean Satisfiability
Problem. Variables and constraints of CSP are translated (encoded) to SAT
instance, that is then solved by state-of-the-art SAT solvers and solution, if exists,
is translated to the solution of the original CSP. The main aim of this thesis is to
improve CSP solving techniques that are using reduction to SAT.
Two new hybrid encodings of CSPs to SAT are presented and they combine good
sides of the existing encodings. We give the proof of correctness of one encoding
that did not exist in literature. We developed system meSAT that enables reduction
of CSPs to SAT by using 4 basic and 2 hybrid encodings. The system also enables
solving of CSPs by reduction to two problems related to SAT, SMT and PB.
We developed a portfolio for automated selection of encoding/s...olver to be used
on some new instance that needs to be solved. The developed portfolio is comparable
with the state-of-the-art portfolios. We developed a hybrid approach based on short
solving timeouts with the aim of significantly reducing the preparation time of a
portfolio. By using this approach, we got results comparable to the ones obtained
by using preparation time of usual length. We made comparison between several
machine learning techniques with the aim to find out which one is the best suited
for the short training approach.
The problem of assigning air traffic controllers to shifts is described and three
models of this problem are presented. We used a large number of different solving
methods and a diverse set of solvers for solving this problem. We developed optimization
techniques that aim to find optimal solutions of the problem. A hybrid
technique combining reduction to SAT and local search is shown to be the most
efficient one.
We also considered sudoku puzzles and the existing techniques of solving the
puzzles of greater size than 9x9. Amongst the used techniques, the existing reduction
to SAT is the most efficient in solving these puzzles. We improved the existing
algorithm for generating large sudoku puzzles. It is shown that simple preprocessing
rules additionally improve speed of generating large sudokus.
Faculty:
Универзитет у Београду, Математички факултетDate:
13-10-2016Projects:
- Automated Reasoning and Data Mining (RS-174021)