Stochastic combinatorial optimization problems are combinatorial optimization problems where part of the problem data are probabilistic. The focus of this thesis is on stochastic routing problems, a class of stochastic combinatorial optimization problems that arise in distribution management. Stochastic routing problems involve finding the best solution to distribute goods across a logistic network. In the problems we tackle, we consider a setting in which the cost of a solution is described by a random variable; the goal is to find the solution that minimizes the expected cost. Solving such stochastic routing problems is a challenging task because of two main factors. First, the number of possible solutions grows exponentially with the instance size. Second, computing the expected cost of a solution is computationally very expensive. <br> To tackle stochastic routing problems, stochastic local search algorithms such as iterative improvement algorithms and metaheuristics are quite promising because they offer effective strategies to tackle the combinatorial nature of these problems. However, a crucial factor that determines the success of these algorithms in stochastic settings is the trade-off between the computation time needed to search for high quality solutions in a large search space and the computation time spent in computing the expected cost of solutions obtained during the search. <br> To compute the expected cost of solutions in stochastic routing problems, two classes of approaches have been proposed in the literature: analytical computation and empirical estimation. The former exactly computes the expected cost using closed-form expressions; the latter estimates the expected cost through Monte Carlo simulation. <br> Many previously proposed metaheuristics for stochastic routing problems use the analytical computation approach. However, in a large number of practical stochastic routing problems, due to the presence of complex constraints, the use of the analytical computation approach is difficult, time consuming or even impossible. Even for the prototypical stochastic routing problems that we consider in this thesis, the adoption of the analytical computation approach is computationally expensive. Notwithstanding the fact that the empirical estimation approach can address the issues posed by the analytical computation approach, its adoption in metaheuristics to tackle stochastic routing problems has never been thoroughly investigated. <br> In this thesis, we study two classical stochastic routing problems: the probabilistic traveling salesman problem (PTSP) and the vehicle routing problem with stochastic demands and customers (VRPSDC). The goal of the thesis is to design, implement, and analyze effective metaheuristics that use the empirical estimation approach to tackle these two problems. The main results of this thesis are: 1) The empirical estimation approach is a viable alternative to the widely-adopted analytical computation approach for the PTSP and the VRPSDC; 2) A principled adoption of the empirical estimation approach in metaheuristics results in high performing algorithms for tackling the PTSP and the VRPSDC. The estimation-based metaheuristics developed in this thesis for these two problems define the new state-of-the-art.

Eine sehr häufig benutzte Gruppe von Partitionierungsverfahren im VLSI-Design sind die Iterative Improvement Algorithms. Diese Verfahren lösen das Min-Cut Problem für Graphen bzw. Hypergraphen. Dabei soll der Graph bzw. Hypergraph in möglichtst unabhängige Teile aufgeteilt werden. Der Ausgangspunkt bei den Iterative Improvement Algorithms ist eine Anfangspartition, die sukzessiv durch geringfügige Änderungen verbessert wird. Mit diesen Verfahren können sehr gute Partitionen in einer sehr geringen Zeit erzeugt werden. In dieser Diplomarbeit wird die Anpassung der Iterative Improvement Algorithms auf die Partitionierung für die parallele Logiksimulation vorgestellt. Dabei wurden verschiedene Strategien für eine Anpassung der Iterative Improvement Algorithms untersucht.

Games on graphs have become an indispensable tool in modern computer science. They provide powerful and expressive models for numerous phenomena and are extensively used in computer- aided verification, automata theory, logic, complexity theory, computational biology, etc. The infinite games on finite graphs we study in this thesis have their primary applications in verification, but are also of fundamental importance from the complexity-theoretic point of view. They include parity, mean payoff, and simple stochastic games. We focus on solving graph games by using iterative strategy improvement and methods from linear programming and combinatorial optimization. To this end we consider old strategy evaluation functions, construct new ones, and show how all of them, due to their structural similarities, fit into a unifying combinatorial framework. This allows us to employ randomized optimization methods from combinatorial linear programming to solve the games in expected subexponential time. We introduce and study the concept of a controlled optimization problem, capturing the essential features of many graph games, and provide sufficent conditions for solvability of such problems in expected subexponential time. The discrete strategy evaluation function for mean payoff games we derive from the new controlled longest-shortest path problem, leads to improvement algorithms that are considerably more efficient than the previously known ones, and also improves the efficiency of algorithms for parity games. We also define the controlled linear programming problem, and show how the games are translated into this setting. Subclasses of the problem, more general than the games considered, are shown to belong to NP intersection coNP, or even to be solvable by subexponential algorithms. Finally, we take the first steps in investigating the fixed-parameter complexity of parity, Rabin, Streett, and Muller games.

<p>Games on graphs have become an indispensable tool in modern computer science. They provide powerful and expressive models for numerous phenomena and are extensively used in computer- aided verification, automata theory, logic, complexity theory, computational biology, etc.</p><p>The infinite games on finite graphs we study in this thesis have their primary applications in verification, but are also of fundamental importance from the complexity-theoretic point of view. They include parity, mean payoff, and simple stochastic games.</p><p>We focus on solving graph games by using iterative strategy improvement and methods from linear programming and combinatorial optimization. To this end we consider old strategy evaluation functions, construct new ones, and show how all of them, due to their structural similarities, fit into a unifying combinatorial framework. This allows us to employ randomized optimization methods from combinatorial linear programming to solve the games in expected subexponential time.</p><p>We introduce and study the concept of a controlled optimization problem, capturing the essential features of many graph games, and provide sufficent conditions for solvability of such problems in expected subexponential time.</p><p>The discrete strategy evaluation function for mean payoff games we derive from the new controlled longest-shortest path problem, leads to improvement algorithms that are considerably more efficient than the previously known ones, and also improves the efficiency of algorithms for parity games.</p><p>We also define the controlled linear programming problem, and show how the games are translated into this setting. Subclasses of the problem, more general than the games considered, are shown to belong to NP intersection coNP, or even to be solvable by subexponential algorithms.</p><p>Finally, we take the first steps in investigating the fixed-parameter complexity of parity, Rabin, Streett, and Muller games.</p>

Stochastic combinatorial optimization problems are combinatorial optimization problems where part of the problem data are probabilistic. The focus of this thesis is on stochastic routing problems, a class of stochastic combinatorial optimization problems that arise in distribution management. Stochastic routing problems involve finding the best solution to distribute goods across a logistic network. In the problems we tackle, we consider a setting in which the cost of a solution is described by a random variable; the goal is to find the solution that minimizes the expected cost. Solving such stochastic routing problems is a challenging task because of two main factors. First, the number of possible solutions grows exponentially with the instance size. Second, computing the expected cost of a solution is computationally very expensive. <p><br><p>To tackle stochastic routing problems, stochastic local search algorithms such as iterative improvement algorithms and metaheuristics are quite promising because they offer effective strategies to tackle the combinatorial nature of these problems. However, a crucial factor that determines the success of these algorithms in stochastic settings is the trade-off between the computation time needed to search for high quality solutions in a large search space and the computation time spent in computing the expected cost of solutions obtained during the search. <p><br><p>To compute the expected cost of solutions in stochastic routing problems, two classes of approaches have been proposed in the literature: analytical computation and empirical estimation. The former exactly computes the expected cost using closed-form expressions; the latter estimates the expected cost through Monte Carlo simulation.<p><br><p>Many previously proposed metaheuristics for stochastic routing problems use the analytical computation approach. However, in a large number of practical stochastic routing problems, due to the presence of complex constraints, the use of the analytical computation approach is difficult, time consuming or even impossible. Even for the prototypical stochastic routing problems that we consider in this thesis, the adoption of the analytical computation approach is computationally expensive. Notwithstanding the fact that the empirical estimation approach can address the issues posed by the analytical computation approach, its adoption in metaheuristics to tackle stochastic routing problems has never been thoroughly investigated. <p><br><p>In this thesis, we study two classical stochastic routing problems: the probabilistic traveling salesman problem (PTSP) and the vehicle routing problem with stochastic demands and customers (VRPSDC). The goal of the thesis is to design, implement, and analyze effective metaheuristics that use the empirical estimation approach to tackle these two problems. The main results of this thesis are: <p>1) The empirical estimation approach is a viable alternative to the widely-adopted analytical computation approach for the PTSP and the VRPSDC; <p>2) A principled adoption of the empirical estimation approach in metaheuristics results in high performing algorithms for tackling the PTSP and the VRPSDC. The estimation-based metaheuristics developed in this thesis for these two problems define the new state-of-the-art. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

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