The process of multi-objective optimization involves finding optimal solutions to several objective functions. However, these are typically in conflict with each other in many real-world problems, such as production system design. Advanced post-optimization analysis can be used to provide the decision maker with information about the underlying system. The analysis can be based on the combination of simulation-based multi-objective optimization and learning from the obtained solution set. The goal of the analysis is to gain a deeper understanding of the problem at hand, to systematically explore and evaluate different alternatives, and to generate essential information and knowledge to support the decision maker to make more informed decisions in order to optimize the performance of the production system as a whole. The aim of this work is to explore the possibilities on how post-optimization analysis can be used in order to provide the decision maker with essential information about an underlying system and in what way this information can be presented. The analysis is mainly done on production system development problems, but may also be transferred to other application areas. The research process of the thesis has been iterative, and the initial approach for post-optimization analysis has been refined several times. The distance-based approach developed in the thesis is used to allow the extraction of information about the characteristics close to a user-defined reference point. The extracted rules are presented to the decision maker both visually, by mapping the rules to the objective space, and textually. The method has been applied to several industrial cases for proof-by-demonstration as well as to an artificial case with information known beforehand to verify the distance-based approach, and the extracted rules have also been used to limit the search space in the optimization. The major finding in the thesis is that to learn from optimization solution sets of production system problems with stochastic behavior, a distance-based approach is advantageous compared with a binary classification of optimal vs. non-optimal solutions. / <p>At the time of the doctoral defence the following articles were unpublished and had a status as follows: Paper 5: Epubl ahead of print; Paper 6: Accepted.</p>

abstract: Finding the optimal solution to a problem with an enormous search space can be challenging. Unless a combinatorial construction technique is found that also guarantees the optimality of the resulting solution, this could be an infeasible task. If such a technique is unavailable, different heuristic methods are generally used to improve the upper bound on the size of the optimal solution. This dissertation presents an alternative method which can be used to improve a solution to a problem rather than construct a solution from scratch. Necessity analysis, which is the key to this approach, is the process of analyzing the necessity of each element in a solution. The post-optimization algorithm presented here utilizes the result of the necessity analysis to improve the quality of the solution by eliminating unnecessary objects from the solution. While this technique could potentially be applied to different domains, this dissertation focuses on k-restriction problems, where a solution to the problem can be presented as an array. A scalable post-optimization algorithm for covering arrays is described, which starts from a valid solution and performs necessity analysis to iteratively improve the quality of the solution. It is shown that not only can this technique improve upon the previously best known results, it can also be added as a refinement step to any construction technique and in most cases further improvements are expected. The post-optimization algorithm is then modified to accommodate every k-restriction problem; and this generic algorithm can be used as a starting point to create a reasonable sized solution for any such problem. This generic algorithm is then further refined for hash family problems, by adding a conflict graph analysis to the necessity analysis phase. By recoloring the conflict graphs a new degree of flexibility is explored, which can further improve the quality of the solution. / Dissertation/Thesis / Ph.D. Computer Science 2011

abstract: Exhaustive testing is generally infeasible except in the smallest of systems. Research has shown that testing the interactions among fewer (up to 6) components is generally sufficient while retaining the capability to detect up to 99% of defects. This leads to a substantial decrease in the number of tests. Covering arrays are combinatorial objects that guarantee that every interaction is tested at least once. In the absence of direct constructions, forming small covering arrays is generally an expensive computational task. Algorithms to generate covering arrays have been extensively studied yet no single algorithm provides the smallest solution. More recently research has been directed towards a new technique called post-optimization. These algorithms take an existing covering array and attempt to reduce its size. This thesis presents a new idea for post-optimization by representing covering arrays as graphs. Some properties of these graphs are established and the results are contrasted with existing post-optimization algorithms. The idea is then generalized to close variants of covering arrays with surprising results which in some cases reduce the size by 30%. Applications of the method to generation and test prioritization are studied and some interesting results are reported. / Dissertation/Thesis / Masters Thesis Computer Science 2015

Real-world systems usually contain some degree of natural uncertainty, their parameters are more or less variable. When seeking optimal solution, optimization models often disregard this variability and consider parameters of the model to be constant. This thesis focuses on methods of post-optimization analysis. Thorough post-optimization analysis should be a part of every optimization process of systems with variable parameters. Post-optimization analysis can identify parameters whose variability poses the greatest threat to the systems performance. This thesis describes some of the basic post-optimization methods and then a new method based on interval arithmetics is formulated.

The burdensome capital cost of urban water distribution systems demands the use of efficient optimization methods capable of finding a relatively inexpensive design that guarantees a minimum functionality under all conditions of operation. The combinatorial and nonlinear nature of the optimization problem involved accepts no definitive method of solution. Adaptive search methods are well fitted for this type of problem (to which more formal methods cannot be applied), but their computational requirements demand the development and implementation of additional heuristics to find a satisfactory solution. This work seeks to employ adaptive search methods to enhance the search process used to find the optimal design of any water distribution system. A first study presented here introduces post-optimization heuristics that analyze the best design obtained by a genetic algorithm--arguably the most popular adaptive search method--and perform an ordered local search to maximize further cost savings. When used to analyze the best design found by a genetic algorithm, the proposed post-optimization heuristics method successfully achieved additional cost savings that the genetic algorithm failed to detect after an exhaustive search. The second study herein explores various ways to improve artificial neural networks employed as fast estimators of computationally intensive constraints. The study presents a new methodology for generating any large set of water supply networks to be used for the training of artificial neural networks. This dataset incorporates several distribution networks in the vicinity of the search space in which the genetic algorithm is expected to focus its search. The incorporation of these networks improved the accuracy of artificial neural networks trained with such a dataset. These neural networks consistently showed a lower margin of error than their counterparts trained with conventional training datasets populated by randomly generated distribution networks.