Minor glossary fixes
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\newacronym[see={[Glossary:]{gls-api}}]{api}{API\glsadd{gls-api}}{Application Programming Interface}
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\newacronym[see={[Glossary:]{gls-api}}]{api}{API\glsadd{gls-api}}{\emph{Application Programming Interface}}
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\newacronym[see={[Glossary:]{gls-ampl}}]{ampl}{AMPL\glsadd{gls-ampl}}{A Mathematical Programming Language}
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\newacronym[see={[Glossary:]{gls-ampl}}]{ampl}{AMPL\glsadd{gls-ampl}}{\emph{A Mathematical Programming Language}}
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\newacronym[see={[Glossary:]{gls-ast}}]{ast}{AST\glsadd{gls-ast}}{Abstract Syntax Tree}
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\newacronym[see={[Glossary:]{gls-ast}}]{ast}{AST\glsadd{gls-ast}}{\emph{Abstract Syntax Tree}}
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\newacronym[see={[Glossary:]{gls-cbc}}]{cbc}{CBC\glsadd{gls-cbc}}{COIN-OR Branch-and-Cut}
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\newacronym[see={[Glossary:]{gls-cbc}}]{cbc}{CBC\glsadd{gls-cbc}}{\emph{COIN-OR Branch-and-Cut}}
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\newacronym[see={[Glossary:]{gls-cbls}}]{cbls}{CBLS\glsadd{gls-cbls}}{Constraint-Based Local Search}
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\newacronym[see={[Glossary:]{gls-cbls}}]{cbls}{CBLS\glsadd{gls-cbls}}{\emph{Constraint-Based Local Search}}
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\newacronym[see={[Glossary:]{gls-chr}}]{chr}{CHR\glsadd{gls-chr}}{Constraint Handling Rules}
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\newacronym[see={[Glossary:]{gls-chr}}]{chr}{CHR\glsadd{gls-chr}}{\emph{Constraint Handling Rules}}
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\newacronym[see={[Glossary:]{gls-clp}}]{clp}{CLP\glsadd{gls-clp}}{Constraint Logic Programming}
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\newacronym[see={[Glossary:]{gls-clp}}]{clp}{CLP\glsadd{gls-clp}}{\emph{Constraint Logic Programming}}
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\newacronym[see={[Glossary:]{gls-cp}}]{cp}{CP\glsadd{gls-cp}}{Constraint Programming}
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\newacronym[see={[Glossary:]{gls-cp}}]{cp}{CP\glsadd{gls-cp}}{\emph{Constraint Programming}}
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\newacronym[see={[Glossary:]{gls-cse}}]{cse}{CSE\glsadd{gls-cse}}{Common Sub-expression Elimination}
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\newacronym{cnf}{CNF}{Conjunctive Normal Form}
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\newacronym{cnf}{CNF\glsadd{cnf}}{\emph{Conjunctive Normal Form}}
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\newacronym{cpu}{CPU}{Central Processing Unit}
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@ -24,23 +24,23 @@
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\newacronym{gbac}{GBAC}{Generalized Balanced Academic Curriculum}
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\newacronym[see={[Glossary:]{gls-lcg}}]{lcg}{LCG\glsadd{gls-lcg}}{Lazy Clause Generation}
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\newacronym[see={[Glossary:]{gls-lcg}}]{lcg}{LCG\glsadd{gls-lcg}}{\emph{Lazy Clause Generation}}
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\newacronym[see={[Glossary:]{gls-lns}}]{lns}{LNS\glsadd{gls-lns}}{Large Neighbourhood Search}
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\newacronym[see={[Glossary:]{gls-lns}}]{lns}{LNS\glsadd{gls-lns}}{\emph{Large Neighbourhood Search}}
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\newacronym{lp}{LP}{Linear Programming}
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\newacronym{maxsat}{MaxSAT}{Maximum Satisfiability}
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\newacronym{maxsat}{MaxSAT\glsadd{gls-maxsat}}{\emph{Maximum Satisfiability}}
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\newacronym{mix}{\textit{mix}}{mixed context}
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\newacronym[see={[Glossary:]{gls-mip}}]{mip}{MIP\glsadd{gls-mip}}{Mixed Integer Programming}
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\newacronym[see={[Glossary:]{gls-mip}}]{mip}{MIP\glsadd{gls-mip}}{\emph{Mixed Integer Programming}}
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\newacronym{neg}{\textit{neg}}{negative context}
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\newacronym{np}{NP}{Nondeterministic Polynomial-time}
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\newacronym{or}{OR}{Operational Research}
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\newacronym{or}{OR}{Operations Research}
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\newacronym[see={[Glossary:]{gls-opl}}]{opl}{OPL\glsadd{gls-opl}}{The Optimization Programming Language}
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@ -52,7 +52,7 @@
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\newacronym{root}{\textit{root}}{root context}
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\newacronym[see={[Glossary:]{gls-sat}}]{sat}{SAT\glsadd{gls-sat}}{Boolean Satisfiability}
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\newacronym[see={[Glossary:]{gls-sat}}]{sat}{SAT\glsadd{gls-sat}}{\emph{Boolean Satisfiability}}
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\newacronym{tsp}{TSP}{Travelling Salesperson Problem}
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@ -126,6 +126,11 @@
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description={A type of expression that makes a choice between two or more expressions. In \minizinc{} these expressions take the form \mzninline{if @\(B\)@ then @\(X\)@ else @\(Y\)@endif}.},
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}
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\newglossaryentry{gls-cnf}{
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name={conjunctive normal form},
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description={The formulation of a Boolean formula as a conjunction of disjunctions of Boolean literals. This a standardized format for \gls{gls-sat} problems.},
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}
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\newglossaryentry{constraint}{
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name={constraint},
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description={A formalized rule of a problem. Constraints are generally expressed in terms of Boolean logic.},
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@ -396,6 +401,11 @@
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description={A \gls{trs} has reached its normal form when none of the rewriting rules can be applied.},
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}
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\newglossaryentry{gls-maxsat}{
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name={Maximum Satisfiability},
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description={An extension of the \gls{gls-sat} problem class into an \gls{opt-prb}. A \gls{gls-sat} problem in \gls{gls-cnf} is extended with weights for each clause. An \gls{opt-sol} of a problem \instance{} maximizes the weights of the \gls{satisfied} clauses.},
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}
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\newglossaryentry{gls-mip}{
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name={mixed integer programming},
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description={
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@ -483,7 +493,7 @@
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}
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\newglossaryentry{gls-sat}{
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name={boolean satisfiability},
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name={Boolean satisfiability},
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description={
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A problem class that tries to find a valid \gls{assignment} for a set of Boolean \glspl{variable} subject to a logical formula.
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Boolean satisfiability is extensively studied and there are many \glspl{solver} dedicated to solving this problem class.
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@ -676,10 +676,10 @@ Instead, it is sometimes better to use a \gls{propagator} with a lower level of
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Although it does not eliminate all possible values of the domain, searching the values that are not eliminated may take less time than achieving domain consistency.
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This is, for example, the case for integer linear \constraints{} \[ \sum_{i} c_{i} x_{i} = d\] where \(c_{i}\) and \(d\) are integer \parameters{} and \(x_{i}\) are integer \variable{}.
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For these \constraints{}, a realistic \gls{domain-con} \gls{propagator} cannot exist because the problem is \gls{np}-hard \autocite{choi-2006-fin-cons}.
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For these \constraints{}, a realistic \gls{domain-con} \gls{propagator} cannot exist because the problem is \glsxtrshort{np}-hard \autocite{choi-2006-fin-cons}.
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A more feasible problem is to find the minimal and maximal values, or \gls{bounds}, for the \variables{} had they been rational numbers.
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A \gls{boundsr-con} \gls{propagator} then ensures that the values in the \domain{} of the integer \variables{} are between their rational \gls{bounds}.
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Note that this is a relaxation of calculating the integer \gls{bounds}, to create a \gls{boundsz-con} \gls{propagator}, which is still \gls{np}-hard.
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Note that this is a relaxation of calculating the integer \gls{bounds}, to create a \gls{boundsz-con} \gls{propagator}, which is still \glsxtrshort{np}-hard.
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We will see the same relaxation in mathematical programming, discussed in the next section.
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Thus far, we have only considered finding \glspl{sol} for \glspl{dec-prb}.
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@ -723,7 +723,7 @@ It was questioned whether the same problem could be solved in worst-case polynom
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Methods for solving linear programs provide the foundation for a harder problem.
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In \gls{lp} our \variables{} must be continuous.
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If we require that one or more take an integer value (\(x_{i} \in \mathbb{Z}\)), then the problem becomes \gls{np} hard.
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If we require that one or more take an integer value (\(x_{i} \in \mathbb{Z}\)), then the problem becomes \glsxtrshort{np}-hard.
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The problem is referred to as \gls{mip} (or Integer Programming if \textbf{all} \variables{} must take an integer value).
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Unlike \gls{lp}, there is not an algorithm that solves a mixed integer program in polynomial time.
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@ -784,7 +784,7 @@ An indicator variable \(y_{i}\) is a \gls{avar} that for a \variable{} \(x\) tak
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\glsreset{maxsat}
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The study of the \gls{sat} problem is one of the oldest in computer science.
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The DPLL algorithm that is still the basis for modern \gls{sat} solving stems from the 1960s \autocite{davis-1960-dpll, davis-1962-dpll}, and \gls{sat} was the first problem to be proven to be \gls{np}-complete \autocite{cook-1971-sat}.
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The DPLL algorithm that is still the basis for modern \gls{sat} solving stems from the 1960s \autocite{davis-1960-dpll, davis-1962-dpll}, and \gls{sat} was the first problem to be proven to be \glsxtrshort{np}-complete \autocite{cook-1971-sat}.
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The problem asks if there is an \gls{assignment} for the \variables{} of a given Boolean formula, such that the formula is \gls{satisfied}.
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This problem is a restriction of the general \gls{dec-prb} where all \variables{} have a Boolean type and all \constraints{} are simple Boolean formulas.
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@ -23,7 +23,7 @@ The following algorithms are examples of \gls{meta-optimization}.
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Instead, it can be achieved using a \gls{meta-optimization} approach: find a \gls{sol} to a (single-objective) problem, then add more \constraints{} to the original problem and repeat.
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\item[\gls{lns}] \autocite{shaw-1998-local-search}
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This is a very successful \gls{meta-optimization} algorithm to quickly improve \gls{sol} quality.
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This \gls{meta-optimization} algorithm was first introduced as a heuristic to vehicle routing problem, but has proven to be a very successful method to quickly improve \gls{sol} quality for many types of problem.
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After finding a (sub-optimal) \gls{sol} to a problem, \constraints{} are added to restrict the search in the \gls{neighbourhood} of that \gls{sol}.
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When a new \gls{sol} is found, the \constraints{} are removed, and \constraints{} for a new \gls{neighbourhood} are added.
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@ -4,8 +4,8 @@
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%************************************************
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\noindent{}All experiments included in this thesis were conducted on a dedicated node in a computational cluster.
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The machine operates using an \textbf{Intel Xeon 8260} \gls{cpu}, which has 24 non-hyperthreaded cores, and has access to \textbf{268.55 GB} of \gls{ram}.
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Each experimental test was given exclusive access to a single \gls{cpu} core and access to sufficient \gls{ram}.
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The machine operates using an \textbf{Intel Xeon 8260} \glsxtrshort{cpu}, which has 24 non-hyperthreaded cores, and has access to \textbf{268.55 GB} of \gls{ram}.
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Each experimental test was given exclusive access to a single \glsxtrshort{cpu} core and access to sufficient \glsxtrshort{ram}.
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\section{Experimental Design}%
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\label{sec:bench-env}
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