The models used by model predictive controllers (MPCs) to predict future outcomes are usually unconstrained forms like impulse or step responses and discrete state space models. Certain MPC algorithms allow constraints to be imposed on the inputs or outputs of a system; but they may be infeasible as they are not checked for consistency via the process model. Consistent constraint handling methods - which account for their interdependence and disambiguate the language used to specify constraints – would therefore be an attractive aid when using any MPC package. A rigorous and systematic approach to constraint management has been developed, building on the work of Vinson (2000), Lima (2007) and Georgakis et al. (2003) in interpreting constraint interactions. The method supports linear steady-state system models, and provides routines to obtain the following information: <ul> <li> effects of constraint changes on the corresponding input and output constraints, </li><li> feasibility checks for constraints, </li><li> specification of constraint-set size and</li><li> optimal fitting of constraints within the desirable input and output space.</li></ul> Mathematical rigour and unambiguous language for identifying constraint types were key design criteria. The outputs of the program provide guidance when handling constraints, as opposed to rules of thumb and experience, and promote understanding of the system and its constraints. The metrics presented are not specific to any commercial MPC and can be implemented in the user interfaces of such MPCs. The method was applied to laboratory-scale test rigs to illustrate the information obtained. / Dissertation (MEng)--University of Pretoria, 2011. / Chemical Engineering / unrestricted

<p> Constraint Handling Rules ( CHRs) are a high level language extension to introduce user-defined constraints into a host language. Application of CHRs to reformulate functional dependencies (FDs) in the Haskell type system gives us a more precise definition of this concept, and a better understanding of FD behavior. But to preserve the confluence and termination properties of CHRs generated from FDs, some restrictions on the syntax of FDs and type class definitions have been imposed which confines the expressiveness power of Haskell type system. </p> <p> In this thesis we use this problem as a motivation to find a solution for the confluence and non-termination problem in CHRs. We build a formal framework for CHRs and model their different aspects mathematically to study how non-confluence and non-termination happens. Based on this formalization we introduce prioritized CHRs as a solution for the confluence problem. To solve the non-termination problem, we propose a method to detect non-termination in the constraint solver. We define a repetition candidate as a special type of derivation and prove that a derivation having this property can cause non-terminating rule applications in the system. Finally we define a deduction tree structure for a set of rules that can be used to find all the possible repetition candidates for a set of constraint rules. </p> / Thesis / Master of Science (MSc)

While there are efforts to establish a single international accounting standard, there are strong current and future needs to handle heterogeneous accounting methods and systems. We advocate a context-based approach to dealing with multiple accounting standards and equational ontological conflicts. In this paper we first define what we mean by equational ontological conflicts and then describe a new approach, using Constraint Logic Programming and abductive reasoning, to reconcile such conflicts among disparate information systems. In particular, we focus on the use of Constraint Handling Rules as a simultaneous symbolic equation solver, which is a powerful way to combine, invert and simplify multiple conversion functions that translate between different contexts. Finally, we demonstrate a sample application using our prototype implementation that demonstrates the viability of our approach. / Singapore-MIT Alliance (SMA)

Evolutionary algorithms (EAs) are population based heuristic optimization methods used to solve single and multi-objective optimization problems. They can simultaneously search multiple regions to find global optimum solutions. As EAs do not require gradient information for the search, they can be applied to optimization problems involving functions of real, integer, or discrete variables. One of the drawbacks of EAs is that they require evaluations of numerous candidate solutions for convergence. Most real life engineering design optimization problems involve highly nonlinear objective and constraint functions arising out of computationally expensive simulations. For such problems, the computation cost of optimization using EAs can become quite prohibitive. This has stimulated the research into improving the efficiency of EAs reported herein. In this thesis, two major improvements are suggested for EAs. The first improvement is the use of spatial surrogate models to replace the expensive simulations for the evaluation of candidate solutions, and other is a novel constraint handling technique. These modifications to EAs are tested on a number of numerical benchmarks and engineering examples using a fixed number of evaluations and the results are compared with basic EA. addition, the spatial surrogates are used in the truss design application. A generic framework for using spatial surrogate modeling, is proposed. Multiple types of surrogate models are used for better approximation performance and a prediction accuracy based validation is used to ensure that the approximations do not misguide the evolutionary search. Two EAs are proposed using spatial surrogate models for evaluation and evolution. For numerical benchmarks, the spatial surrogate assisted EAs obtain significantly better (even orders of magnitude better) results than EA and on an average 5-20% improvements in the objective value are observed for engineering examples. Most EAs use constraint handling schemes that prefer feasible solutions over infeasible solutions. In the proposed infeasibility driven evolutionary algorithm (IDEA), a few infeasible solutions are maintained in the population to augment the evolutionary search through the infeasible regions along with the feasible regions to accelerate convergence. The studies on single and multi-objective test problems demonstrate the faster convergence of IDEA over EA. In addition, the infeasible solutions in the population can be used for trade-off studies. Finally, discrete structures optimization (DSO) algorithm is proposed for sizing and topology optimization of trusses. In DSO, topology optimization and sizing optimization are separated to speed up the search for the optimum design. The optimum topology is identified using strain energy based material removal procedure. The topology optimization process correctly identifies the optimum topology for 2-D and 3-D trusses using less than 200 function evaluations. The sizing optimization is performed later to find the optimum cross-sectional areas of structural elements. In surrogate assisted DSO (SDSO), spatial surrogates are used to accelerate the sizing optimization. The truss designs obtained using SDSO are very close (within 7% of the weight) to the best reported in the literature using only a fraction of the function evaluations (less than 7%).

Resumo: Este trabalho apresenta uma metodologia composta de duas fases para resolver problemas de otimização com restrições usando uma estratégia multiobjetivo. Na primeira fase, o esforço concentra-se em encontrar, pelo menos, uma solução factível, descartando completamente a função objetivo. Na segunda fase, aborda-se o problema como biobjetivo, onde se busca a otimização da função objetivo original e maximizar o cumprimento das restrições. Na fase um propõe-se uma estratégia baseada na diminuição progressiva da tolerância de aceitação das restrições complexas para encontrar soluções factíveis. O desempenho do algoritmo é validado através de 11 casos testes bastantes conhecidos na literatura especializada. / Abstract: This work presents a two-phase framework for solving constrained optimization problems using a multi-objective strategy. In the first phase, the objective function is completely disregarded and entire search effort is directed toward finding a single feasible solution. In the second phase, the problem is treated as a bi-objective optimization problem, where the technique converts constrained optimization to a two-objective optimization: one is the original objective function; the other is the degree function violating the constraints. In the first phase a methodology based on progressive decrease of the tolerance of acceptance of complex constrains is proposed in order to find feasible solutions. The approach is tested on 11 well-know benchmark functions. / Orientador: Rubén Augusto Romero Lázaro / Coorientador: José Roberto Sanches Mantovani / Banca: Antonio Padilha Feltrin / Banca: Marcos Julio Rider Flores / Mestre

This manuscrit is a compact presentation of my research done between 1993 and 2008 and which concerns the global optimization of mechanical systems. General and specialized global optimization algorithms are presented. With respect to previously published work, an updated presentation of my work on composite optimization is given.

In this thesis, the basic principles and concepts of single and multi-objective Genetic Algorithms (GA) are reviewed. Two algorithms, one for single objective and the other for multi-objective problems, which are believed to be more efficient are described in details. The algorithms are coded with MATLAB and applied on several test functions. The results are compared with the existing solutions in literatures and shows promising results. Obtained pareto-fronts are exactly similar to the true pareto-fronts with a good spread of solution throughout the optimal region. Constraint handling techniques are studied and applied in the two algorithms. Constrained benchmarks are optimized and the outcomes show the ability of algorithm in maintaining solutions in the entire pareto-optimal region. In the end, a hybrid method based on the combination of the two algorithms is introduced and the performance is discussed. It is concluded that no significant strength is observed within the approach and more research is required on this topic. For further investigation on the performance of the proposed techniques, implementation on real-world engineering applications are recommended.

Made available in DSpace on 2014-06-11T19:22:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-20Bitstream added on 2014-06-13T19:28:05Z : No. of bitstreams: 1 zini_eoc_me_ilha.pdf: 1142984 bytes, checksum: 4ff93a7fe459a5a56e15da26b7a6dd45 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho apresenta uma metodologia composta de duas fases para resolver problemas de otimização com restrições usando uma estratégia multiobjetivo. Na primeira fase, o esforço concentra-se em encontrar, pelo menos, uma solução factível, descartando completamente a função objetivo. Na segunda fase, aborda-se o problema como biobjetivo, onde se busca a otimização da função objetivo original e maximizar o cumprimento das restrições. Na fase um propõe-se uma estratégia baseada na diminuição progressiva da tolerância de aceitação das restrições complexas para encontrar soluções factíveis. O desempenho do algoritmo é validado através de 11 casos testes bastantes conhecidos na literatura especializada. / This work presents a two-phase framework for solving constrained optimization problems using a multi-objective strategy. In the first phase, the objective function is completely disregarded and entire search effort is directed toward finding a single feasible solution. In the second phase, the problem is treated as a bi-objective optimization problem, where the technique converts constrained optimization to a two-objective optimization: one is the original objective function; the other is the degree function violating the constraints. In the first phase a methodology based on progressive decrease of the tolerance of acceptance of complex constrains is proposed in order to find feasible solutions. The approach is tested on 11 well-know benchmark functions.

Many real-world decision processes require solving optimization problems which may involve different types of constraints such as inequality and equality constraints. The hurdles in solving these Constrained Optimization Problems (COPs) arise from the challenge of searching a huge variable space in order to locate feasible points with acceptable solution quality. Over the last decades Evolutionary Algorithms (EAs) have brought a tremendous advancement in the area of computer science and optimization with their ability to solve various problems. However, EAs have inherent difficulty in dealing with constraints when solving COPs. This thesis presents a new Agent-based Memetic Algorithm (AMA) for solving COPs, where the agents have the ability to independently select a suitable Life Span Learning Process (LSLP) from a set of LSLPs. Each agent represents a candidate solution of the optimization problem and tries to improve its solution through cooperation with other agents. Evolutionary operators consist of only crossover and one of the self-adaptively selected LSLPs. The performance of the proposed algorithm is tested on benchmark problems, and the experimental results show convincing performance. The quality of individuals in the initial population influences the performance of evolutionary algorithms, especially when the feasible region of the constrained optimization problems is very tiny in comparison to the entire search space. This thesis proposes a method that improves the quality of randomly generated initial solutions by sacrificing very little in diversity of the population. The proposed Search Space Reduction Technique (SSRT) is tested using five different existing EAs, including AMA, by solving a number of state-of-the-art test problems and a real world case problem. The experimental results show SSRT improves the solution quality, and speeds up the performance of the algorithms. The handling of equality constraints has long been a difficult issue for evolutionary optimization methods, although several methods are available in the literature for handling functional constraints. In any optimization problems with equality constraints, to satisfy the condition of feasibility and optimality the solution points must lie on each and every equality constraint. This reduces the size of the feasible space and makes it difficult for EAs to locate feasible and optimal solutions. A new Equality Constraint Handling Technique (ECHT) is presented in this thesis, to enhance the performance of AMA in solving constrained optimization problems with equality constraints. The basic concept is to reach a point on the equality constraint from its current position by the selected individual solution and then explore on the constraint landscape. The technique is used as an agent learning process in AMA. The experimental results confirm the improved performance of the proposed algorithm. This thesis also proposes a Modified Genetic Algorithm (MGA) for solving COPs with equality constraints. After achieving inspiring performance in AMA when dealing with equality constraints, the new technique is used in the design of MGA. The experimental results show that the proposed algorithm overcomes the limitations of GA in solving COPs with equality constraints, and provides good quality solutions.

Made available in DSpace on 2014-06-12T15:51:39Z (GMT). No. of bitstreams: 2 arquivo2757_1.pdf: 5759741 bytes, checksum: 8075c58c36a6d409b242f2a7873fb02f (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Vitorino dos Santos Filho, Jairson; Pierre Louis Robin, Jacques. CHROME: a model-driven component-based rule engine. 2009. Tese (Doutorado). Programa de Pós-Graduação em Ciência da Computação, Universidade Federal de Pernambuco, Recife, 2009.