Le but de cette thèse est de proposer des méthodes générales afin de contourner l’intractabilité de problèmes d’optimisation multi-objectifs.Dans un premier temps, nous essayons d’apprécier la portée de cette intractabilité en déterminant une borne supérieure, facilement calculable, sur le nombre de points non dominés, connaissant le nombre de valeurs prises par chaque critère.Nous nous attachons ensuite à produire des représentations discrètes et tractables de l’ensemble des points non dominés de toute instance de problèmes d’optimisation multi-objectifs. Ces représentations doivent satisfaire des conditions de couverture, i.e. fournir une bonne approximation, de cardinalité, i.e. ne pas contenir trop de points, et si possible de stabilité, i.e. ne pas contenir de redondances. En s’inspirant de travaux visant à produire des ensembles ε-Pareto de petite taille, nous proposons tout d’abord une extension directe de ces travaux, puis nous axons notre recherche sur des ensembles ε-Pareto satisfaisant une condition supplémentaire de stabilité. Formellement, nous considérons des ensembles ε-Pareto particuliers, appelés (ε, ε′)-noyaux, qui satisfont une propriété de stabilité liée à ε′. Nous établissons des résultats généraux sur les (ε, ε′)-noyaux puis nous proposons des algorithmes polynomiaux qui produisent des (ε, ε′)-noyaux de petite taille pour le cas bi-objectif et nous donnons des résultats négatifs pour plus de deux objectifs. / The goal of this thesis is to propose new general methods to get around the intractability of multi-objective optimization problems.First, we try to give some insight on this intractability by determining an, easily computable, upper bound on the number of nondominated points, knowing the number of values taken on each criterion. Then, we are interested in producingsome discrete and tractable representations of the set of nondominated points for each instance of multi-objective optimization problems. These representations must satisfy some conditions of coverage, i.e. providing a good approximation, cardinality, i.e. it does not contain too many points, and if possible spacing, i.e. it does not include any redundancies. Starting from works aiming to produce ε-Pareto sets of small size, we first propose a direct extension of these works then we focus our research on ε-Pareto sets satisfying an additional condition of stability. Formally, we consider special ε-Pareto sets, called (ε, ε′)-kernels, which satisfy a property of stability related to ε′. We give some general results on (ε, ε′)-kernels and propose some polynomial time algorithms that produce small (ε, ε′)-kernels for the bicriteria case and we give some negative results for the tricriteria case and beyond.

<ul> <li>Energy Optimization Stategies</li> <li>Hydraulic Models for Water Distribution Systems</li> <li>Heuristic Multi-objective Optimization Algorithms</li> <li>Multi-objective Optimization Problems</li> <li>System Constraints</li> <li>Encoding Techniques</li> <li>Optimal Pumping Operations</li> <li>Sovling Real-World Optimization Problems </li> </ul> / <p>The water supply industry is a very important element of a modern economy; it represents a key element of urban infrastructure and is an integral part of our modern civilization. Billions of dollars per annum are spent internationally in pumping operations in rural water distribution systems to treat and reliably transport water from source to consumers.</p> <p>In this dissertation, a new multi-objective optimization approach referred to as energy optimization strategy is proposed for minimizing electrical energy consumption for pumping, the cost, pumps maintenance cost, and the cost of maximum power peak, while optimizing water quality and operational reliability in rural water distribution systems. Minimizing the energy cost problem considers the electrical energy consumed for regular operation and the cost of maximum power peak. Optimizing operational reliability is based on the ability of the network to provide service in case of abnormal events (e.g., network failure or fire) by considering and managing reservoir levels. Minimizing pumping costs also involves consideration of network and pump maintenance cost that is imputed by the number of pump switches. Water quality optimization is achieved through the consideration of chlorine residual during water transportation.</p> <p>An Adaptive Parallel Clustering-based Multi-objective Particle Swarm Optimization (APC-MOPSO) algorithm that combines the existing and new concept of Pareto-front, operating-mode specification, selecting-best-efficiency-point technique, searching-for-gaps method, and modified K-Means clustering has been proposed. APC-MOPSO is employed to optimize the above-mentioned set of multiple objectives in operating rural water distribution systems.</p> <p>Saskatoon West is, a rural water distribution system, owned and operated by Sask-Water (i.e., is a statutory Crown Corporation providing water, wastewater and related services to municipal, industrial, government, and domestic customers in the province of Saskatchewan). It is used to provide water to the city of Saskatoon and surrounding communities. The system has six main components: (1) the pumping stations, namely Queen Elizabeth and Aurora; (2) The raw water pipeline from QE to Agrium area; (3) the treatment plant located within the Village of Vanscoy; (4) the raw water pipeline serving four major consumers, including PCS Cogen, PCS Cory, Corman Park, and Agrium; (5) the treated water pipeline serving a domestic community of Village of Vanscoy; and (6) the large Agrium community storage reservoir.</p> <p>In this dissertation, the Saskatoon West WDS is chosen to implement the proposed energy optimization strategy. Given the data supplied by Sask-Warer, the scope of this application has resulted in savings of approximately 7 to 14% in energy costs without adversely affecting the infrastructure of the system as well as maintaining the same level of service provided to the Sask-Water’s clients.</p> <p>The implementation of the energy optimization strategy on the Saskatoon West WDS over 168 hour (i.e., one-week optimization period of time) resulted in savings of approximately 10% in electrical energy cost and 4% in the cost of maximum power peak. Moreover, the results showed that the pumping reliability is improved by 3.5% (i.e., improving its efficiency, head pressure, and flow rate). A case study is used to demonstrate the effectiveness of the multi-objective formulations and the solution methodologies, including the formulation of the system-operational optimization problem as five objective functions. Beside the reduction in the energy costs, water quality, network reliability, and pumping characterization are all concurrently enhanced as shown in the collected results. The benefits of using the proposed energy optimization strategy as replacement for many existing optimization methods are also demonstrated.</p> / Doctor of Science (PhD)