Solving the Max-Diversity Orthogonal Regrouping Problem by an Integer Linear Programming Model and a GRASP/VND with Path-Relinking Approach

Students from Master of Business Administration (MBA) programs are usually split into teams. In light of the generalistic nature of MBA programs, diversity within every team is desirable in terms of gender, major, age and other criteria. Many schools rotate the teams at the beginning of every term so that each student works with a different set of peers during every term, thus training his or her adaptation skills and expanding the peer network. Achieving diverse teams while avoiding–or minimizing—the repetition of student pairs is a complex and time-consuming task for MBA Directors. We introduce the Max-Diversity Orthogonal Regrouping (MDOR) problem to manage the challenge of splitting a group of people into teams several times, pursuing the goals of high diversity and few repetitions. We propose a hybrid Greedy Randomized Adaptive Search Procedure/Variable Neighborhood Descent (GRASP/VND) heuristic combined with tabu search and path relinking for its resolution, as well as an Integer Linear Programming (ILP) formulation. We compare both approaches through a set of real MBA cohorts, and the results show that, in all cases, the heuristic approach significantly outperforms the ILP and manually formed teams in terms of both diversity and repetition levels.

Memetic Chains for Improving the Local Wireless Sensor Networks Localization in Urban Scenarios

Local Positioning Systems (LPS) have become an active field of research in the last few years. Their application in harsh environments for high-demanded accuracy applications is allowing the development of technological activities such as autonomous navigation, indoor localization, or low-level flights in restricted environments. LPS consists of ad-hoc deployments of sensors which meets the design requirements of each activity. Among LPS, those based on temporal measurements are attracting higher interest due to their trade-off among accuracy, robustness, availability, and costs. The Time Difference of Arrival (TDOA) is extended in the literature for LPS applications and consequently we perform, in this paper, an analysis of the optimal sensor deployment of this architecture for achieving practical results. This is known as the Node Location Problem (NLP) and has been categorized as NP-Hard. Therefore, heuristic solutions such as Genetic Algorithms (GA) or Memetic Algorithms (MA) have been applied in the literature for the NLP. In this paper, we introduce an adaptation of the so-called MA-Solis Wets-Chains (MA-SW-Chains) for its application in the large-scale discrete discontinuous optimization of the NLP in urban scenarios. Our proposed algorithm MA-Variable Neighborhood Descent-Chains (MA-VND-Chains) outperforms the GA and the MA of previous proposals for the NLP, improving the accuracy achieved by 17% and by 10% respectively for the TDOA architecture in the urban scenario introduced.