Recommender systems have become one of the main components of web technologies that help people to cope with information overload. Based on the analysis of past user behavior, these systems filter items according to users’ likes and interests. Two of the most important metrics used to analyze the performance of these systems are the accuracy and diversity of the recommendation lists. Whereas all the efforts exerted in the prediction of the user interests aim at maximizing the former, the latter emerges in various forms, such as diversity in the lists across all user recommendation lists, referred to as aggregate diversity, and diversity in the lists of individuals, known as individual diversity. In this paper, we tackle the combination of these three objectives and justify this approach by showing through experiments that handling these objectives in pairs does not yield satisfactory results in the third one. To that end, we develop a mathematical model that is formulated using multiobjective optimization approaches. To cope with the intractability of this nonlinear integer programming model, its special structure is exploited by a decomposition technique. For the solution of the resulting formulation, we propose an iterative framework that is composed of a clique-generating genetic algorithm, a constructive heuristic, and an improvement heuristic. The former is designed to incorporate all objective functions into the generated cliques and specifically impose a certain level of individual diversity, whereas the latter chooses one clique for each user such that the desired aggregate diversity level is fulfilled. We conduct experiments on three data sets and show that the proposed modeling approach successfully handles all objectives according to the needs of the system and that the proposed methodology is capable of yielding good upper bounds.

The success of a recommender system is generally evaluated with respect to the accuracy of recommendations. However, recently diversity of recommendations has also become an important aspect in evaluating recommender systems. One dimension of diversity is called aggregate diversity, which refers to the diversity of items in the recommendation lists of all users and can be defined with different metrics. The maximization of both accuracy and the aggregate diversity simultaneously renders a multiobjective optimization problem that can be handled by different approaches. In this paper, after providing a thorough analysis of the multiobjective optimization approaches for this problem, we propose a new model that takes into account both accuracy and aggregate diversity. Different from previous works, our model is specifically designed to incorporate distributional diversity metrics, which measure how evenly the items are distributed in the recommendation lists of users. To solve the large-scale instances, we propose a column generation algorithm and a Lagrangian relaxation approach based on the decomposition of the model. We present the results of the mathematical models and the performance of the proposed methodology that are obtained by computational experiments on real-world data sets. These results reveal that our model successfully captures the trade-off between the objectives and reaches very high levels of distributional diversity.

We propose a new generic framework for solving combinatorial optimization problems that can be modeled as a set covering problem. The proposed algorithmic framework combines metaheuristics with exact algorithms through a guiding mechanism based on diversification and intensification decisions. After presenting this generic framework, we extensively demonstrate its application to the vehicle routing problem with time windows. We then conduct a thorough computational study on a set of well-known test problems, where we show that the proposed approach not only finds solutions that are very close to the best-known solutions reported in the literature, but also improves them. We finally set up an experimental design to analyze the effects of different parameters used in the proposed algorithm.