ACHIEVEMENTS

The research conducted at GERAD has given rise to major achievements in recent years. For instance, the members and their students have carried out the following research programs over the years:

  • Column generation algorithms to solve very large mathematical programs. Methods for stabilizing such algorithms
  • The Analytical Center Cutting-plane Method (an interior point algorithm for convex programs): extensions and applications.
  • Application of discrete and continuous global optimization, jointly with column generation, in localization and automatic classification.
  • Validation/invalidation of graph theoretic conjectures by means of software package AutoGraphiX; the software has been developed at GERAD and is mainly based on a variable search neighborhood metaheuristic.
  • Using recent theoretical developments in non convex quadratic programming, resolution of a combinatorial optimization problem which had remained open since 1950, and concerning the minimization of the maximal diameter of an octagon with unit size sides.
  • Development of techno-climatic and economic-techno-climatic mathematical models based on the nucleus of MARKAL models, for help in decision making in North American states/provinces and European nations as to choices that would lead to the right compromises between the likelihood of economic prosperity and sustainable development.
  • Application of game theory and optimal stochastic control for the synthesis of decentralized control policies in large random systems, with applications to wireless communications, and the Internet.
  • Modeling and estimation of financial products.
  • Portfolio optimization and risk management.
  • Pricing of financial derivatives (exotic options, futures…)

In addition, and in accordance with the mission GERAD sees for itself of being an active partner in technology transfer towards industry, businesses and society, the study of numerous applications has been undertaken. Such activities often result in the design of high performance analysis/optimization software:

  • Study of changes in Quebec's refining industry using the MARKAL model, for Energy, Mines and Resources Canada.
  • Application of the MARKAL environmental/economic model to the evolution of the refining industry in Quebec on behalf of the Ministry of Energy, Mining and Resources of Canada.
  • Planning of telecommunications networks for Bell Northern Research.
  • Real time scheduling of mining trucks fleet for the Québec-Cartier company. The related software has been in use within six mines located on three different continents.
  • A study of the impact of targeted gas emissions and pollutant acids reduction on the abilities of the provinces of Quebec and Ontario to cope, given their existing energy systems.
  • Analysis of the benefits that can derive from electricity exchanges between the province of Quebec and its neighbors in Canada and the Northeastern United States.
  • Analysis of the long term evolution of high energy consumption industries in Quebec.
  • Automated construction of exam schedules for HEC Montreal and the London School of Economics.
  • Automated construction of personnel shifts for École Polytechnique de Montréal.
  • Automated elaboration of itineraries and show times for Le Cirque du Soleil.
  • Optimal mangement of water ressources in Hydro-Québec.
  • Automated elaboration of personnel shifts for CLSC’s in Montreal.
  • Elaboration of electoral cards for the Quebec General Director of Elections.
  • Planning of oil refinery operations (OPLAR).
  • Scheduling of bus driver shifts in urban transportation (CREWOPT) for the GIRO Inc. Company. The associated software has been in use in thirty cities around the world (New York, Tokyo, Singapour, Toulouse, Turin, Sydney, Helsinki, ...)
  • Development of a general purpose software (GENCOL) for itinerary synthesis with special versions respectively for school bussing (BUS-OPT) and the transportation of people with reduced mobility (DARSY).
  • Design of software (CREDO) for the optimization of dosages and helicopter routes in the fight against onchocercosis in Africa (Result of a collaboration between the World Health Organization and the Université du Québec à Trois-Rivières).
  • Design of software (OPTINEST) for the automated cutting of laminary materials.
  • Software based design of shifts for pilots and on board agents in air transport (ALTITUDE PAIRING). The software has been adopted by major companies including Air France, Northwest, Air Transat, UPS, Canada 3000, Fedex, Swissair and Sabena.
  • Design of software for monthly workload balancing whether for pilots or on board agents in air transport (ALTITUDE PBS). The software has been in use in multiple companies including Air France, Air Transat, Air Canada, UPS, Delta, Fedex.
  • Design of software for automated flight assignments to air planes in the airline industry (ALTITUDE FLEET); main user, Air Transat.
  • Optimal flight planning for combined training of pilots and freight transportation in the Canadian Air Force.
  • Yield management : Dynamic allocation of seats within the distinct cost categories according to the most recent market information, whether in the context of air transportation (e.g. Air Canada), or train transportation (e.g. SNCF), via game theory and bi level optimization theory, with the goal of profit maximization.