Contribution to the evaluation and to the improvement of multi-objective optimization methods: application to the optimization of nuclear fuel reloading pattern

In this thesis, we study the general problem of the selection of a multi-objective optimization method, then we study the improvement so as to efficiently solve a problem. The pertinent selection of a method presume the existence of a methodology: we have built tools to perform evaluation of performances and we propose an original method dedicated to the classification of know optimization methods. Our step has been applied to the elaboration of new methods for solving a very difficult problem: the nuclear core reload pattern optimization. First, we looked for a non usual approach of performances measurement: we have 'measured' the behavior of a method. To reach this goal, we have introduced several metrics. We have proposed to evaluate the 'aesthetic' of a distribution of solutions by defining two new metrics: a 'spacing metric' and a metric that allow us to measure the size of the biggest hole in the distribution of solutions. Then, we studied the convergence of multi-objective optimization methods by using some metrics defined in scientific literature and by proposing some more metrics: the 'Pareto ratio' which computes a ratio of solution production. Lastly, we have defined new metrics intended to better apprehend the behavior of optimization methods: the 'speed metric', which allows to compute the speed profile and a 'distribution metric' which allows to compute statistical distribution of solutions along the Pareto frontier. Next, we have studied transformations of a multi-objective problem and defined news methods: the modified Tchebychev method, or the penalized weighted sum of objective functions. We have elaborated new techniques to choose the initial point. These techniques allow to produce new initial points closer and closer to the Pareto frontier and, thanks to the 'proximal optimality concept', allowing dramatic improvements in the convergence of a multi-objective optimization method. Lastly, we have defined new vectorial multi-objective optimization methods called MOCOSA and NSCOSA mainly based on the COSA method, which simulated a genetic algorithm by just using tools from the simulated annealing and, therefore, without crossover operator. The MOCOSA and NSCOSA methods uses tools from the MOGA and NSGA methods based on genetic algorithms. An other problem related to multi-objective optimization is the problem of data visualization. A redundant type of multi-objective problem is treated in scientific literature: the bi-objective problem, easy to illustrate. We propose, in this thesis, some methods allowing to visualize solutions set of arbitrary dimensions and, particularly, the MCDM method ('Multi-objective Concordance Discordance Mapping') which transforms a real multi-objective optimization problem (a problem which has more than two objective functions) in a simpler bi-objective problem. We have also defined new multidimensional transformation methods that are able to conserve a relation of order (such as dominance relation). The application of this transformation gives birth to the MCDM PC method ('Multi-objective Concordance Discordance Mapping Pareto Conservative'). Moreover, we have defined a new classification of multi-objective optimization methods with the goal to ease the choice of a multi-objective optimization method to solve a given problem. To focus this classification, we have extracted from multi-objective optimization methods the most important elements and we have organized these elements as a hierarchy. The 'navigation' through this hierarchy is done through some simple questions asked to the user, in direct relationship to the given problem. These results are applied to the multi-objective optimization of nuclear core reload pattern, which is composed of security constraints and economic criteria. This combinatorial optimization problem can be illustrated by using a check covered by pawns where a pawn corresponds to a nuclear assembly. The goal is to find a distribution of pawns so as to minimize some objective functions like the power peak, the fluency or the cycle natural length. This problem is hard to solve and has resisted to various attempt to solve 'automatically' this problem. Often, a human expert is needed to find the best solutions. We propose, in this thesis, an adaptation of evolutionary algorithms as well as and adaptation of various form of simulated annealing to the nuclear core reloading pattern optimization problem. (author)