Convergence Criteria for Hierarchical Overlapping Coordination of Linearly Constrained Convex Design Problems

Decomposition of multidisciplinary engineering system design problems into smaller subproblems is desirable because it enhances robustness and understanding of the numerical results. Moreover, subproblems can be solved in parallel using the optimization technique most suitable for the underlying mathematical form of the subproblem. Hierarchical overlapping coordination (HOC) is an interesting strategy for solving decomposed problems. It simultaneously uses two or more design problem decompositions, each of them associated with different partitions of the design variables and constraints. Coordination is achieved by the exchange of information between decompositions. This article presents the HOC algorithm and several new sufficient conditions for convergence of the algorithm to the optimum in the case of convex problems with linear constraints. One of these equivalent conditions involves the rank of the constraint matrix that is computationally efficient to verify. Computational results obtained by applying the HOC algorithm to quadratic programming problems of various sizes are included for illustration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44766/1/10589_2004_Article_321085.pd

Preventing and resolving design conflicts for a collaborative convergence in distributed set-based design

En conception distribuée, dans la phase du dimensionnement du produit, des incohérences peuvent émerger entre les objectifs de conception et entre les procédures de travail des sous-systèmes hétérogènes. Dans cette phase, les acteurs de conception doivent collaborer d une manière concourante, car leurs tâches sont reliées les unes aux autres par les couplages de dimensionnement entre leurs sous-problèmes. Les incohérences peuvent provoquer des conflits de conception en raison de ces couplages. La question est de savoir comment obtenir une convergence collaborative pour satisfaire les objectifs globaux et individuels des acteurs de conception lorsque ces acteurs prennent des décisions de conception sous incertitude. L'objectif de cette thèse est de proposer un modèle pour empêcher et résoudre les conflits de conception, tout en surmontant le problème de l'incertitude de la conception avec l'approche de conception basée sur les ensembles (SBD). Pour cela, les attitudes de conception sont modélisées avec le paradigme Croyances-Désirs-Intentions afin d'explorer les incohérences et gérer les conflits dans les processus de conception. L'approche ascendante conventionnelle est ainsi étendue grâce à des techniques de modélisation multi-agents. Dans cette approche, les agents de conception peuvent fixer des exigences directement sur leurs indicateurs de bien-être . Ces indicateurs représentent la manière dont leurs objectifs de conception sont susceptibles d'être satisfaits à un moment donné du processus. Des simulations de Monte Carlo sont effectuées pour évaluer la performance de cette approche, offrant une variété d'attitudes de l'agent. Par rapport aux approches classiques de conception ascendante et descendante, les résultats révèlent moins de conflits de conception et une intensité des conflits réduite. Les techniques de problème de satisfaction de contraintes (CSP) et les attitudes de conception sont appliquées pour détecter et justifier des conflits de conception entre les agents hétérogènes. Une nouvelle forme du modèle Cooperative CSP (CoCSP) est ainsi mise au point afin de résoudre les conflits de conception en détectant le compromis entre les contraintes. Le système de résolution des conflits peut être adopté grâce à différentes stratégies proposées qui prennent en compte l'architecture de solidarité des agents. Les résultats des simulations montrent que l'intensité des conflits en conception distribuée est réduite par la promotion de la solidarité qui déclenche une aide aux agents en souffrance.In the product dimensioning phase of a distributed design, inconsistencies can emerge among design objectives as well as among working procedures of heterogeneous subsystems. In this phase, design actors which compose subsystems must collaborate concurrently, since their works are linked to each other through dimensioning couplings among their sub-problems. Inconsistencies through these couplings yield thus to design conflicts. The issue is how to obtain a collaborative convergence to satisfy the global and individual objectives of design actors when making design decisions under uncertainty. The objective of this dissertation is to propose a model for preventing and resolving design conflicts in order to obtain a collaborative convergence, while overcoming the design uncertainty through Set-based Design (SBD). Design attitudes are modeled with Belief-Desire-Intention paradigm to explore inconsistencies and manage conflicts in design processes. The conventional bottom-up approach is thus extended through agent-based attitude modeling techniques. In this approach, design agents can set requirements directly on their wellbeing values that represent how their design targets are likely to be met at a given moment of the design process. Monte Carlo simulations are performed to evaluate the performance of this approach, providing a variety of agent attitudes. Compared to conventional bottom-up and top-down design approaches, the results reveal a fewer number of design conflicts and a reduced aggregated conflict intensity. Constraint satisfaction problem (CSP) techniques and design attitudes are both applied to detect and justify design conflicts of heterogeneous design agents. A novel cooperative CSP (CoCSP) is developed in order to resolve design conflicts through compromising constraint restriction. The conflict resolution system can be adopted for different proposed strategies which take into account the solidarity architecture of design agents. The simulation results show that while promoting solidarity in distributed design by helping agents that suffer, the conflict intensity is reduced, and better design results are obtained.CHATENAY MALABRY-Ecole centrale (920192301) / SudocSudocFranceF

Decomposition Approaches for Building Design Optimization

Building performance simulation can be integrated with optimization to achieve high-performance building design objectives such as low carbon emission and cost-effectiveness by holistically considering design variables across different disciplines. However, the complexity of the design problem increases greatly with increasing dimensionality. In some cases, solving high-dimension problems is not technically feasible nor time-efficient. Decomposition is one way to reduce the complexity and dimensionality of optimization problems. However, the decomposed optimization might achieve local optimum. Therefore, deploying appropriate decomposition strategies to achieve global optimum is paramount. This study investigates the deployment of hierarchical and parallel decomposition for building design optimization problems to ensure identification of global optimum. The feasibility of combining sensitivity analysis and decomposition is also explored. At the end of this study, some recommendations are given to help select an appropriate approach in practice. First, this thesis proposes a hierarchical decomposition. Hierarchical decomposition divides an optimization problem into several interconnected subproblems solved sequentially. The proposed approach is applied to the multi-objective optimization problem that minimizes buildings' operating costs and carbon emissions. The results show that the hierarchical decomposition approach can reduce the number of simulations while achieving global optimums. Second, this thesis proposes a parallel decomposition. Parallel decomposition divides the original problem into several smaller subproblems to be solved separately, and potentially, concurrently. The proposed parallel decomposition approach is applied to solve the single-objective optimization problems of a benchmark function and a low-rise office building. The results show that the proposed approach finds the global optimum and takes less computation time than optimization without decomposition. Third, this thesis explores the feasibility of combining sensitivity analysis with decomposition for dimensionality reduction. The efficiency and accuracy of different methods are compared through three case studies. The proposed hierarchical and parallel decomposition approaches can be applied individually or combined into a hybrid decomposition approach. This thesis concludes with some recommendations to help choose a decomposition approach to solve building design optimization problems