Journées de l'optimisation 2018
HEC Montréal, Québec, Canada, 7 — 9 mai 2018
TB11 Multiobjective optimization
8 mai 2018 15h30 – 17h10
Salle: Xerox Canada (48)
Présidée par Merve Bodur
4 présentations

15h30  15h55
An algorithm to find the Pareto frontier for convex pure Integer biobjective problems
In this talk we tackle biobjective convex nonlinear optimzation problems with integer variables. The algorithm allows to construct the full Pareto frontier and is based on the definition of a finite number of subproblems each of them returning a Pareto optimal solution. The construction of the subproblems is done by adding cuts in the space of the objectives that define a partition of the original space. As a tool to find a Pareto solution of each subproblem we can use any method for multiobjective optimzation (weights, goal programming etc). The approach works only for pure integer biobjective convex nonlinear problems. We report preliminary numerical experiments of a benchmark of integer quadratic programming problems and compare with existing stateoftheart methods.

15h55  16h20
How information theory based mutual information metrics serve optimization in active Mapping?
Information theory is a very well known to be the basis of the communication systems developed during the last fifty years and more with Shannon theory (Entropy definition) and its continuous improvement and investigation in Telecommunication as well as in other disciplines, Machine learning, Data compressing, ICA, and recently introduced to the robotics community. Starting from the entropy definition and its direct connection with uncertainty, new information quantities such as relative entropy, mutual information and the latest quadratic mutual information metrics have been developed and the latest quadratic mutual information metrics used as a novel cost functions in many applications in robotics. The most famous challenging ones are active Mapping and active SLAM where the goal is to optimize the exploration by maximizing the mutual information between the state and the measurement. This presentation is dedicated to carrying out the information theory based optimization in robotics with a review and proposal of a new metrics recently investigated and proposed. New divergences and distances based mutual information will be discussed.

16h20  16h45
Decomposition for loosely coupled mixedinteger programs: A multiobjective perspective
We consider loosely coupled mixedinteger programs (MIPs), that consist of (possibly a large number of) interrelated subsystems and a small number of constraints, which link blocks of variables that correspond to different subsystems. Motivated by recent developments in multiobjective programming (MOP), we develop a MOPbased decomposition algorithm to solve loosely coupled MIPs. The proposed algorithm iteratively generates columns for the master problem. However, unlike traditional column generation methods, the master problem is an IP and considers a differently structured (and usually smaller) set of columns. We provide computational results on instances with knapsack structure in the subsystems, demonstrating the potential benefits of our approach.

16h45  17h10
Optimisation des structures vectorielles floues pour les données cartographiques continues
Cette présentation traite de la représentation des phénomènes continus au sein des Systèmes D’Information Géographiques (SIG). Nous introduisons une représentation vecteur basée sur les concepts flous. Cette nouvelle structure nécessite de spécifier différents anneaux géographiques. Leur nombre et leur position sont définis par l’optimisation d’un algorithme de classification par recouvrement. Nous donnons des exemples d’application sur la classification de forêts.