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.

A learning-from-data approach with soft clustering and path relinking to the history-matching problem

History matching is an important reservoir engineering process whereby the values of uncertain attributes of a reservoir model are changed to find models that have a better chance of reproducing the performance of an actual reservoir. As a typical inverse and ill-posed problem, different combinations of reservoir uncertain attributes lead to equally well-matched models and the success of a history-matching approach is usually measured in terms of its ability to efficiently find multiple history-matched models inside the search space defined by the parameterization of the problem (multiple-matched models have a higher chance of better representing the reservoir performance forecast). While studies on history-matching approaches have produced remarkable progress over the last two decades, given the uniqueness of each reservoir’s history-matching problem, no strategy is proven effective for all cases, and finding alternative, efficient, and effective history-matching methodologies is still a research challenge. In this work, we introduce a learning-from-data approach with path relinking and soft clustering to the history-matching problem. The proposed algorithm is designed to learn the patterns of input attributes that are associated with good matching quality from the set of available solutions, and has two stages that handle different types of reservoir uncertain attributes. In each stage, the algorithm evaluates the data of all-available solutions continuously and, based on the acquired information, dynamically decides what needs to be changed, where the changes shall take place, and how such changes will occur in order to generate new (and hopefully better) solutions. We validate our approach using the UNISIM-I-H benchmark, a complex synthetic case constructed with real data from the Namorado Field, Campos Basin, Brazil. Experimental results indicate the potential of the proposed approach in finding models with significantly better history-matching quality. Considering a global misfit quality metric, the final best solutions found by our approach are up to 77% better than the corresponding initial best solutions in the datasets used in the experiments. Moreover, compared with previous work for the same benchmark, the proposed learning-from-data approach is competitive regarding the quality of solutions found and, above all, it offers a significant reduction (up to 30 × less) in the number of simulations.

A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k-Balanced Center Location Problem

This paper presents a hybridization of Strategic Oscillation with Path Relinking to provide a set of high-quality nondominated solutions for the Multiobjective k-Balanced Center Location problem. The considered location problem seeks to locate k out of m facilities in order to serve n demand points, minimizing the maximum distance between any demand point and its closest facility while balancing the workload among the facilities. An extensive computational experimentation is carried out to compare the performance of our proposal, including the best method found in the state-of-the-art as well as traditional multiobjective evolutionary algorithms.