|dc.contributor.author||Polash, Md. Masbaul Alam||
|dc.description.abstract||Combinatorial problems are believed to be hard in general, most of them are at least NPcomplete.
Constraint-based approaches employ some convenient and generic techniques
to solve these problems. These approaches use basic de nitons to model and wellde
ned constraints to represent a problem. Although these approaches produce good
results for smaller instances, for large-sized problems these do not perform so well.
In this case, problem speci c information can help to increase the scalability of these
approaches. Thus in this research, our focus is to nd out theoretically proven and
heuristically promising properties that goes beyond the basic de nition of a problem.
These properties help to model the problem e ciently and to reduce the e ective search
space of a problem. Also, during search these properties can be used as auxiliary or
streamlined constraint to boost the e ciency of a search algorithm. These properties
along with e cient data structures and modern constraint-based techniques can be used
to handle challenging combinatorial problems. The e ectiveness of these techniques is
shown throughout this thesis by solving several combinatorial problems, such as optimal
Golomb rulers, all-interval series and propositional satis ability.
Finding optimal Golomb rulers is an extremely challenging combinatorial problem. Different
approaches have been used so far to handle this problem. In this thesis, we provide
tight upper bounds for Golomb ruler marks and present symmetry-based domain reduction
technique. Using these along with tabu and con guration checking meta-heuristics, we
then develop a constraint-based multi-point local search algorithm to perform a satisfaction
search for optimal Golomb rulers of speci ed length. We then present an algorithm
to perform an optimisation search that minimises the length of a Golomb ruler using
the satisfaction search repeatedly. Experimental results demonstrate that our algorithms
perform signi cantly better than the existing state-of-the-art algorithms.
All-interval series is a standard benchmark problem for constraint satisfaction search.
Di erent approaches have been used to date to generate all the solutions of this problem
but the search space that must be explored still remains huge. In this thesis, we present
a constraint-directed backtracking-based tree search algorithm that performs e cient
lazy checking rather than immediate constraint propagation. Moreover, we prove several
key properties of all-interval series that help to reduce the search space signi cantly. The
reduced search space essentially results into fewer backtracking. We also present scalable parallel versions of our algorithm that can exploit the advantages of having multi-core
processors and even multiple computer systems. Experimental results show that our
new algorithm exhibits better performance than the satis ability-based state-of-the-art
approach for this problem.
The propositional satis ability (SAT) problem is one of the most studied combinatorial
problems in computer science. In recent years, local search approaches have become
one of the most e ective techniques in solving these SAT problems. In this research,
our focus is to exploit the hidden structures of SAT problems in local search. These
structures are generated in the form of logic gates. Due to the detection of gates, both
the number of independent variables and external gates decreases. Thus the search space
becomes narrower than before. But in some cases, the number of external gates or the
number of independent variables may become too few to guide the search e ciently. In
these cases, detecting only few but not all types of gates will actually perform better.
Thus in this research, we investigate the e ect of detecting only the basic gates and also
all types of gates. Then a dependency lattice is created to propagate the value of the
independent variables. However, detection of gates may led to the problem of cycling in
the dependency lattice. A new mechanism is proposed to remove those cycles as well.
Moreover, we propose a new stagnation recovery technique to handle the cycling problem
of local search. The experimental study on structured benchmarks shows that our new
approach signi cantly outperforms the corresponding CNF-based implementations.||
|dc.title||Exploiting Structures in Combinatorial Search||
|gro.faculty||Science, Environment, Engineering and Technology||
|gro.rights.copyright||The author owns the copyright in this thesis, unless stated otherwise.||
|gro.thesis.degreelevel||Thesis (PhD Doctorate)||
|gro.thesis.degreeprogram||Doctor of Philosophy (PhD)||
|gro.griffith.author||Polash, Md. Masbaul Alam MA.||