## Balanced Partition of a Graph for Football Team Realignment in Ecuador

Abstract: In the second category of the Ecuadorian football league, a set of football teams must be grouped in k geographical zones according to some regulations, where the total distance of the road trips that all teams must travel to play a Double Round Robin Tournament in each zone is minimized. This problem can be modeled as a k clique partitioing problem with constraints on the sizes and weights of the cliques. An integer programming formulation and a heuristic approach were developed to provide a solution to the problem which has been implemented in the 2015 edition of this football championship.

## VEHICLE AND DUTY SCHEDULING FOR A PUBLICTRANSPORTATION SYSTEM IN QUITO

Abstract: We address the vehicle and duty scheduling problems in the context of the Trolebus public transportation system of Quito. An integer programming model for the vehicle scheduling problem based on a multi-commodity flow formulation is presented. The model aims at minimizing both the size of the fleet and the total idle time of the vehicles at the terminals. A primal heuristic for solving this model is proposed. This heuristic is later extended to an algorithm for solving the integrated vehicle and duty scheduling problem under the particular circumstances of the studied system. The method is based on the idea of aggregating sequences of trips that minimize the idle time and at the same time conform to legal and administrative constraints which are inherent to the duty scheduling problem. Computational results for real-world data with up to 1,400 timetabled trips are reported.

## LEARNING OPTIMAL SPATIALLY-DEPENDENT REGULARIZATION PARAMETERS IN TOTAL VARIATION IMAGE RESTORATION

Abstract: We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image restoration models. First- and second-order optimality conditions for the bilevel problem are studied, when the spatially-dependent parameter belongs to the Sobolev space $H1( )$. A combined Schwarz domain decomposition semismooth Newton method is proposed for the solution of the full optimality system and local superlinear convergence of the semismooth Newton method is analyzed. Exhaustive numerical computations are finally carried out to show the suitability of the approach.