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Stream: Mixed integer optimization

Chair: Dimitri Papadimitriou

1. Space-filling visualization maps by means of Mathematical Optimization
   Vanesa Guerrero, Emilio Carrizosa, Dolores Romero Morales
   
   
   

   In this talk, we propose the use of MINLP to build visualization maps for a set of individuals which have attached dissimilarities as well a statistical variable. Visualization maps are built in such a way that distances between portions resemble the dissimilarities between the individuals and the areas of the portions represent the statistical variable. To guide the location of the portions, a tailored Multidimensional Scaling is designed, which allows reducing the computational costs as well as using heuristics to handle large instances.
   
   

2. Global Mixed Integer Nonlinear Programming Solutions by The Generalized-GRASP Method
   João Lauro Faco', Ricardo Silva, Mauricio Resende
   
   
   

   Continuous-GRASP solves efficiently general constrained global continuous optimization problems (Facó, Resende and Silva 2011, 2012, 2013, 2014, 2015) by adapting the greedy randomized adaptive search procedure (GRASP) -metaheuristic for discrete optimization- to the case of constrained continuous variables. A new version that considers also discrete variables is presented including integer variables. Generalized-GRASP does not do any relaxation as usual branch and bound methods. GRASP random search and local improvement phases use independently a discrete and a continuous set simultaneously.
   
   

3. On Computing Minimum Route Duration for Traveling Salesman Problem with Complex Time Constraints
   Jarosław Hurkała
   
   
   

   Almost every kind of time-oriented vehicle routing, orienteering or generally traveling salesman problem has a common problem of finding the minimum route duration for a given sequence of locations. Most papers consider single time window, and constant travel and visit time. In this work we address the problem of computing minimum route duration in TSP with multiple time windows and time-dependent travel and visit time. We present a mixed-integer linear model, show results obtained from commercial optimization software, and favorably compare our novel exact algorithm against three other.
   
   

4. Congested Hub-Location Routing Problem
   Dimitri Papadimitriou
   
   
   

   We propose a mixed integer formulation of hub-facility location routing problem where the bottom level corresponds to the customer demand points, the middle one to hubs and the upper one to facilities. Our formulation includes nonlinear proportional to the hub and facility load in the objective function to account for non-linear congestion effects. We solve this problem by means of Generalized Benders Decomposition and compare its performance with linearization methods. Using representative scenarios, we identify various tradeoffs when fixing the number of hubs vs. facilities.