The thesis concentrates on a methodological research on categorical structural optimization by means of manifold learning. The main difficulty of handling the categorical optimization problems lies in the description of the design variables: they are presented in a discrete manner and do not have any orders. Thus the treatment of the design space is a key issue. In this thesis, the non-ordinal categorical variables are treated as multi-dimensional discrete variables, thus the dimensionality of corresponding design space becomes high. In order to reduce the dimensionality, the manifold learning techniques are introduced to find the intrinsic dimensionality and map the original design space to a reduced-order space. The mechanisms of both linear and non-linear manifold learning techniques are firstly studied. Then numerical examples are tested to compare the performance of manifold learning techniques. It is found that Principal Component Analysis (PCA) and Multi-dimensional Scaling (MDS) can only deal with linear or globally approximately linear cases. Isomap preserves the geodesic distances for non-linear manifold, however, its time consuming is the most. Locally Linear Embedding (LLE) preserves the neighbour weights and can yield good results in a short time. Kernel Principal Component Analysis (KPCA) works as a non-linear classifier and we proves the reason why it cannot preserve distances or angles in some cases.Based on the reduced-order representation obtained by Isomap, the graph-based evolutionary crossover and mutation operators are proposed to deal with categorical structural optimization problems, including the design of dome, six-story rigid frame and dame-like structures. The results show that the proposed graph-based evolutionary approach constructed on the reduced-order space performs more efficiently than traditional methods including simplex approach or evolutionary approach without reduced-order space.The Locally Linear Embedding is applied to reduce the data dimensionality and a polynomial interpolation helps to construct the responding surface from lower dimensional representation to original data. Then the continuous search method of moving asymptotes is executed and yields a competitively good but inadmissible solution within only a few of iteration numbers. Then in the second stage, a discrete search strategy is proposed to find out better solutions based on a neighbour search. The ten-bar truss and dome structural design problems are tested to show the validity of the method. In the end, this method is compared to the Simulated Annealing algorithm and Covariance Matrix Adaptation Evolutionary Strategy, showing its better optimization efficiency.In order to deal with the case in which the categorical design instances are distributed on several manifolds, we propose a k-manifolds learning method based on the Weighted Principal Component Analysis. The obtained manifolds are integrated in the lower dimensional design space. Then the two-stage search method is applied to solve the ten-bar truss, the dome and the dam-like structural design problems. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Due to the high cost of manual content creation within the game development industry, methods for procedural generation of content such as game maps and levels have emerged. However, methods for generating game maps have remained relatively unexplored in competitive multiplayer contexts. Presumably, this is due to the opposing goals of generating game maps that are both interesting and fair. This study aims to explore the possibility of satisfying both these goals simultaneously by separating the generative phase from the phase that enforces fairness. In this endeavor, simple game maps for a generic multiplayer grand strategy game are generated using noise-based methods. The task of partitioning the game map fairly between the players is then modeled as a constrained categorical multiobjective minimization problem that is subsequently solved by two genetic algorithms, the reference-point-based algorithm NSGA-III and the decomposition-based algorithm MOEA/D-IEpsilon. In a primary study, the proposed partitioning method is evaluated based on the quality of the solutions produced, its scalability, and its ability to find symmetrical partitions of symmetrical game maps. The results show that the proposed method makes significant improvement from the initial guess but fails to produce completely fair partitions in general. Explanations and possible solutions to this are presented. The timing results indicate that the proposed method is not applicable in real-time contexts. However, the proposed method might still be applicable in online contexts if smaller game maps are considered and in offline contexts if larger game maps are considered. Finally, the partitioning results show that the proposed method successfully finds fair partitions of symmetrical game maps but fails to find the obvious symmetrical partitions. In a secondary study, the two genetic algorithms are compared to determine which algorithm produces dominating solutions and which algorithm produces most diverse solution. The results indicate that, for the partitioning problems considered in this study, the reference-point-based algorithm is both dominant and produces the most diverse solutions.

La thèse se concentre sur une recherche méthodologique sur l'optimisation structurelle catégorielle au moyen d'un apprentissage multiple. Dans cette thèse, les variables catégorielles non ordinales sont traitées comme des variables discrètes multidimensionnelles. Afin de réduire la dimensionnalité, les nombreuses techniques d'apprentissage sont introduites pour trouver la dimensionnalité intrinsèque et mapper l'espace de conception d'origine sur un espace d'ordre réduit. Les mécanismes des techniques d'apprentissage à la fois linéaires et non linéaires sont d'abord étudiés. Ensuite, des exemples numériques sont testés pour comparer les performances de nombreuses techniques d’apprentissage. Sur la base de la représentation d'ordre réduit obtenue par Isomap, les opérateurs de mutation et de croisement évolutifs basés sur les graphes sont proposés pour traiter des problèmes d'optimisation structurelle catégoriels, notamment la conception du dôme, du cadre rigide de six étages et des structures en forme de dame. Ensuite, la méthode de recherche continue consistant à déplacer des asymptotes est exécutée et fournit une solution compétitive, mais inadmissible, en quelques rares itérations. Ensuite, lors de la deuxième étape, une stratégie de recherche discrète est proposée pour rechercher de meilleures solutions basées sur la recherche de voisins. Afin de traiter le cas dans lequel les instances de conception catégorielles sont réparties sur plusieurs variétés, nous proposons une méthode d'apprentissage des variétés k-variétés basée sur l'analyse en composantes principales pondérées. / The thesis concentrates on a methodological research on categorical structural optimizationby means of manifold learning. The main difficulty of handling the categorical optimization problems lies in the description of the categorical variables: they are presented in a category and do not have any orders. Thus the treatment of the design space is a key issue. In this thesis, the non-ordinal categorical variables are treated as multi-dimensional discrete variables, thus the dimensionality of corresponding design space becomes high. In order to reduce the dimensionality, the manifold learning techniques are introduced to find the intrinsic dimensionality and map the original design space to a reduced-order space. The mechanisms of both linear and non-linear manifold learning techniques are firstly studied. Then numerical examples are tested to compare the performance of manifold learning techniques mentioned above. It is found that the PCA and MDS can only deal with linear or globally approximately linear cases. Isomap preserves the geodesic distances for non-linear manifold however, its time consuming is the most. LLE preserves the neighbour weights and can yield good results in a short time. KPCA works like a non-linear classifier and we proves why it cannot preserve distances or angles in some cases. Based on the reduced-order representation obtained by Isomap, the graph-based evolutionary crossover and mutation operators are proposed to deal with categorical structural optimization problems, including the design of dome, six-story rigid frame and dame-like structures. The results show that the proposed graph-based evolutionary approach constructed on the reduced-order space performs more efficiently than traditional methods including simplex approach or evolutionary approach without reduced-order space. In chapter 5, the LLE is applied to reduce the data dimensionality and a polynomial interpolation helps to construct the responding surface from lower dimensional representation to original data. Then the continuous search method of moving asymptotes is executed and yields a competitively good but inadmissible solution within only a few of iteration numbers. Then in the second stage, a discrete search strategy is proposed to find out better solutions based on a neighbour search. The ten-bar truss and dome structural design problems are tested to show the validity of the method. In the end, this method is compared to the Simulated Annealing algorithm and Covariance Matrix Adaptation Evolutionary Strategy, showing its better optimization efficiency. In chapter 6, in order to deal with the case in which the categorical design instances are distributed on several manifolds, we propose a k-manifolds learning method based on the Weighted Principal Component Analysis. And the obtained manifolds are integrated in the lower dimensional design space. Then the method introduced in chapter 4 is applied to solve the ten-bar truss, the dome and the dame-like structural design problems.