Symbolic-Numeric Constraint-Based Solutions for Real-World Scientific Problems PI:Martine Ceberio, University of Texas at El Paso ABSTRACT Numerical constraint solving (NCS) techniques have proven to be efficient to solve real problems ranging from electronic circuit to aircraft design. Yet they are under-utilized. The lack of user support of the solvers can partly explain this, but most importantly NCS techniques have isolated themselves into a jargon (constraints) and a schema (propagation/reduction) that disconnect them, respectively, from real problems and real needs (e.g., scalability, flexibility, and distributivity). The goal of this career plan is to make NCS better adapted to real-world needs while making it more accessible. In order to achieve the goal, this project will concentrate on theory and algorithms at the crux of the efficiency, reliability, and distributivity aspects of problemsolving techniques. In particular, the following research objectives will be pursued: RO1 To open NCS to novel techniques, improving scalability and reliability. The research will be oriented towards designing new algorithms that lie between local consistency techniques and global constraints: symbolic-numeric approaches will be studied from the theoretical point of view, and algorithms will be developed and embedded in a new solving toolbox; RO2 To assist users facing over-constrained problems. New methods based on the topology of the search space, in terms of satisfaction of the constraints, will be designed to provide users with alternative solutions; and RO3 To extend the distributed use of NCS to reflect the emerging networked social structure. The structures of social groups and their potential to support distributed systems will be studied, resulting in new and more complete algorithms for distributing constraints. The results of the research objectives will feed into the work carried out to pursue our education objectives: EO1: to enhance the problem-solving skills and interest in advanced studies for 8-16 students; and EO2: to enhance the participation ofwomen and Hispanics in computing. Intellectual Merit. The success of the Career project will contribute to the NCS and decisionmaking body of knowledge. The proposed work will advance knowledge about: i. NCS algorithms: Along with theoretical results about the quality of the solution, the proposed work will address the noise in solution sets, as well as continuums of solutions; ii. Soft constraints: By developing decision algorithms for over-constrained problems, it will be possible to (semi-)autonomously determine the most relevant soft constraints scheme to solve the original problem; iii. Constraints distribution over different social groups structures: the expected communication algorithms will combine theory from speculative constraints with frameworks of social structures to improve the time to solution of given constraints. Broader Impacts. The project will result in a new Matlab toolbox, expected to enhance the way users approach problem solving and appeal to more users, in particular the Matlab community. The progress and results of the project will be disseminated through the PIs constraintsolving.com website, widely accessed by various communities. Moreover, the PI holds a CoProD workshop that annually brings together NCS researchers and practitioners. The project will take place at UTEP, an institution with more than 75% Hispanic citizens and a leader in the education and advancement of Hispanics. With UTEPs infrastructure and the proposed educational activities, the project will train a new generation of diverse computer scientists with strong problem-solving skills. It will also result in new constraint-based courses, including material that can contribute to a textbook on NCS that will have impact beyond UTEP. Workshops and constraint-oriented hands-on activities will be offered at one middle-school and three high-schools, one of which is a women-only high-school, with potential to inspire students to engage in computing disciplines. It is expected that over 450 students will be involved in outreach activities over the course of the grant.
