Solving Multi-Objective Distributed Constraint Optimization Problems

For many decades, the field of optimization has progressed both in the way it represents real-life problem and how it solves these problems. However, most of the focus have been towards problems with a single objective to optimize whereas almost all real-life problems involve multiple objectives. In this thesis, we study the solving of multi-objective problems that we propose to view as two successive steps. The first step consists in finding the Pareto front of the given problem, i.e., the set of solutions offering optimal trade-offs of the objectives. As the size of this Pareto front can increase exponentially with the size of the problem, efficient algorithms are required to find the Pareto front or at least a good approximation. This first step is thus mostly about algorithms and searching for solutions. The second step then consists in using the previously found Pareto front to extract a single solution that can be implemented. It can be assumed that this second step is performed by a decision maker. However, selecting a solution from the Pareto front is rarely trivial for a human as the set of alternatives can be very large. Additionally, many problems require quick decisions, in which case interacting with a decision maker can be impossible. This second step is more about decision making and defining additional criteria to extract solutions from the Pareto front. In the first chapter of this thesis, we present the background of the main fields of research to which our thesis contributes. These fields are Optimization, Constraint Programming and Distributed Problem Solving. In the second chapter, we introduce the preliminary notions required for the understanding of our contribution. We present the framework used to represent multi-objective problems both for centralized and distributed systems, as well as for dynamic environments where the problem changes over time. In addition, we present some of the representative applications considered during this thesis. In the third chapter, we study the first step of multi-objective problem solving and propose two new algorithms for finding the Pareto front of multi-objective optimization problems in distributed systems. The first algorithm is the Multi-Objective Distributed Pseudo-tree Optimization, an exact algorithm based on dynamic programming techniques to find the complete Pareto front. The second algorithm is the Distributed Pareto Local Search, an algorithm based on local search techniques that provides an approximation of the Pareto front. In the fourth chapter, we study the second step of multi-objective problem solving and propose three multi-objective decision making methods to isolate subsets of Pareto fronts that can be deemed more interesting. The first selection method uses a preference-based criterion while the second and third selection methods use criteria specific to dynamic problems. In the fifth chapter, we discuss the related works and compare them with our proposed algorithms and decision methods. In the final chapter, we conclude this thesis by summing up our contribution and discussing the potential future works related to this thesis.