Final Report Summary - EL MUNDO (Embedding Measurement UNcertainty in Decision-making and Optimization) The El-MUNDO project is a multi-disciplinary effort to bring together two complementary fields of Computer Science, namely fuzzy regression analysis and constraint-based reasoning, in order to develop decision support systems for optimization problems permeated with measurement uncertainty. Data uncertainty due to imprecise or incomplete measurements is ubiquitous in many real world applications. The Constraint Programming paradigm, successful in tackling real world planning and resource optimization problems, has been extended in the past 15 years to handle some forms of data imprecision, commonly specified as bounded interval data. Also, models derived from regression analysis have been extended to seek a relationship between fuzzy measurements. Dependencies do exist among uncertain data in these problems, e.g. the sum of uncertain production rates is bounded. However, for tractability reasons existing approaches in optimization assume independence of the data. This assumption is safe, but can lead to large solution spaces and a loss of problem structure. Thus it cannot be overlooked. Our intent was to bring together the strengths of both paradigms to account for dependency constraints in such complex constrained problems.During this project we derived a methodology that combines the strengths of both paradigms to tackle parameter dependency effectively. It is an iterative process. The core intuitive idea was to generate a set of constrained models such that each model uses uncertain data instances that satisfy the dependency constraints. We then solved each generated model, and applied a regression between the consistent data instances and the corresponding model solutions we found, to yield a possible relationship function. Our findings showed that this methodology provided a new valuable insight to the decision maker showing how the solutions evolve in relationship with the uncertain data. In cases, the generated constraint model had no solutions, showing that the information carried by dependency constraints was core to the problem structure. However when applying our methodology to other problems, it came out that the set of constrained problems generated could be quite large and thus the efficiency of the approach impaired. In the second year we identified the context of matrix models, ubiquitous in planning, economics and resource management problems. We showed that for such problems we can derive an efficient model to solve the dependency constraints relatively to the decision variables of the problems. Existing techniques from constraint programming or mathematical programming could be used very efficiently. Both novel approaches were recognized and published in international conferences respectively in the fields of information systems (IPMU’14), and optimization techniques (CP’AIOR’15), and presented at the European project space session of ICPRAM’15. Through El-MUNDO, a Europe-based multi-disciplinary experience was provided to the fellow. The project gave her the possibility to acquire knowledge in regression analysis (expertise of the host research group), attend conferences in a field complementary to her expertise, and be invited to the European Project Space panel to discuss the benefits of such multi-disciplinary projects.
