Section: Overall Objectives
Overall Objectives
Quantitative modeling is routinely used in both industry and administration to design and operate transportation, distribution, or production systems. Optimization concerns every stage of the decision-making process: investment budgeting, long term planning, the management of scarce resources, or the planning of day-to-day operations. Many optimization problems that arise in decision support applications involve discrete decision variables. Such problems can be modeled as linear or non-linear programs with integer variables. The solution is essentially based on enumeration techniques and is notoriously difficult given the huge size of the solution space. Commercial solvers have made significant progress but remain quickly overwhelmed beyond a certain problem size. A key to further progress is the development of better problem formulations that provide strong continuous approximations and hence help to prune the enumerative solution scheme. Central to our field is the characterization of polyhedron defining or approximating the solution set, and combinatorial algorithms to identify “efficiently” a minimum cost solution or separate an infeasible point. One must also avoid the drawback of enumerating what are essentially symmetric solutions.
The team's overall goals are:
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To design tight formulations for specific problems and generic models, relying on delayed cut and column generation, extended formulations, and inputs from non-linear programming (in particular quadratic programming) and graph theory.
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To contribute to theoretical developments in exact optimization and combinatorial optimization, while extending the scope of their application.
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To demonstrate the strength of cooperation between complementary exact mathematical programming techniques, constraint programming and combinatorial algorithms.
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To develop algorithms for large-scale real-life applications that provide provably good approximate solutions by hybridation of heuristic and exact methods.
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To provide generic software tools that build on our research developments, writing proof-of-concept code, while making our research findings available to external users.
