My Research
Areas of interest
constraint solving: symbolic-numeric algorithms aiming at enhancing the solving process,
flexible/soft constraints
interval computations: more accurate evaluation of interval functions, handling uncertainty
optimization: global and local algorithms
bio-engineering: an intelligent system for gait therapy
multi-criteria decision making, and decision under uncertainty, combination with interval
computations
non-square interval matrices
More details about my research
CONSTRAINT SOLVING
For an introduction to constraint solving, please visit one of the following website:
about constraint solving
intro to constraints
CR2G©'s website.
My work in the area of constraint solving consists in designing symbolic-numeric algorithms
to enhance constraint consistency and propagation techniques traditionally used to solve
constraints.
With Laurent Granvilliers (LINA), we proposed an algorithm that takes advantage of the
Gaussian algorithm for linear systems, and adapt it to non-linear systems. The main idea was to
cope with the classical problem of consistency, the so-called locality of reasoning, by
somehow triangularizing the non-linear system at hand.
BIO-ENGINEERING: in particular, INTELLIGENT GAIT THERAPY
This is a joint project with Dr. Thompson Sarkodie-Gyan (UTEP, ECE), conducted at LIMA,
Laboratory for Industrial Metrology and Automation.
The objective of this project is to make automated the therapy for gait rehabilitation. For this, we need to:
design a diagnosis decision system: such a system will rely on the new classification of gait pattern that we are working on
control the therapy by providing assessment tools to ensure the progress of the therapy and choose exercises that are most
appropriate to the patients pathology
These will be made possible by using (among others) constraint programming.
More information about this project can be found in the following presentations:
FLEXIBLE CONSTRAINT SOLVING
My interests in this area are wide and encompass several different specific research directions:
defining a common framework for implementation and resolution
considering dynamic systems
designing an intuitive, ergonomic interface
considering robustness of the models
etc.
Flexible constraints are expected to have many applications. In particular, they seem to suit
bio-informatics problem such as secondary 3d structure recognition of RNA. It is also
anticipated to find applications in the area of mobile networks.
INTERVAL COMPUTATIONS
For a complete overview of intervals, the visitor is referred to Vladik Kreinovich's
interval computations website.
I am mostly using intervals for constraint solving and optimization, as they come with guarantees:
the guarantee that the solution set contains all solutions of the problem at hand (even if the down side is
that the solution may also come along with noise) + the guarantee that when we have a guaranteed
interval solution (i.e., not noise), a solution actually lies within the bounds of the intervals
(which is better that the "no-guarantee" provided by floating-point computations).
The drawback of such guarantees (everything comes at a cost) is that interval solutions are not as
accurate as floating-point ones (an interval of possible values as opposed to a single value).
BUT they are guaranteed (which fp computations are not).
For more details about reasons why use intervals, I refer you to a presentation of mine (pdf
here).
As a result, part of my research is dedicated to
finding better ways to use intervals such that we reach accuracy at least cost. I mainly
explored symbolic approaches. I plan to consider analytic approaches soon.
My other interests include, but are not limited to:
Constraints for verification and validation of softwareX
Optimization
Multi-criteria decision making (MCDM)
Non-square interval matrices
Constraints and security