Abstract: Health and convenience are two indispensable indicators of the society promotion. Nowadays, to improve community health levels, the comfort of patients and those in need of health services has received much attention. Providing Home Health Care (HHC) services is one of the critical issues of health care to improve the patient convenience. However, manual nurse planning which is still performed in many HHC institutes results in a waste of time, cost, and ultimately lower efficiency. In this research, a multi-objective mixed-integer model is presented for home health care planning so that in addition to focusing on the financial goals of the institution, other objectives that can help increase productivity and quality of services are highlighted. Therefore, four different objectives of the total cost, environmental emission, workload balance, and service quality are addressed. Taking into account medical staff with different service levels, and the preferences of patients in selecting a service level, as well as different vehicle types, are other aspects discussed in this model. The epsilon-constraint method is implemented in CPLEX to solve small-size instances. Moreover, a Multi-Objective Variable Neighborhood Search (MOVNS) composed of nine local neighborhood moves is developed to solve the practical-size instances. The results of the MOVNS are compared with the epsilon-constraint method, and the strengths and weaknesses of the proposed algorithm are demonstrated by a comprehensive sensitivity analysis. To show the applicability of the algorithm, a real example is designed based on a case study, and the results of the algorithm over real data are evaluated.

Abstract: Abstract Bilevel problems are used to model the interaction between two decision makers in which the lower-level problem, the so-called follower’s problem, appears as a constraint in the upper-level problem of the so-called leader. One issue in many practical situations is that the follower’s problem is not explicitly known by the leader. For such bilevel problems with unknown lower-level model we propose the use of neural networks to learn the follower’s optimal response for given decisions of the leader based on available historical data of pairs of leader and follower decisions. Integrating the resulting neural network in a single-level reformulation of the bilevel problem leads to a challenging model with a black-box constraint. We exploit Lipschitz optimization techniques from the literature to solve this reformulation and illustrate the applicability of the proposed method with some preliminary case studies using academic and linear bilevel instances.

Abstract: Abstract The semiproximal Support Vector Machine technique is a recent approach for Multiple Instance Learning (MIL) problems. It exploits the benefits exhibited in the supervised learning by the Support Vector Machine technique, in terms of generalization capability, and by the Proximal Support Vector Machine approach in terms of efficiency. We investigate the possibility of embedding the kernel transformations into the semiproximal framework to further improve the testing accuracy. Numerical results on benchmark MIL data sets show the effectiveness of our proposal.

Abstract: Abstract In the recent past, annual CO $$_2$$ 2 emissions at the international level were examined from various perspectives, motivated by rising concerns about pollution and climate change. Nevertheless, to the best of the authors’ knowledge, the problem of dealing with the potential inaccuracy/missingness of such data at the country and economic sector levels has been overlooked. Thereby, in this article we apply a supervised machine learning technique called Matrix Completion (MC) to predict, for each country in the available database, annual CO $$_2$$ 2 emissions data at the sector level, based on past data related to all the sectors, and more recent data related to a subset of sectors. The core idea of MC consists in the formulation of a suitable optimization problem, namely the minimization of a proper trade-off between the approximation error over a set of observed elements of a matrix (training set) and a proxy of the rank of the reconstructed matrix, e.g., its nuclear norm. In the article, we apply MC to the imputation of (artificially) missing elements of country-specific matrices whose elements come from annual CO $$_2$$ 2 emission levels related to different sectors, after proper pre-processing at the sector level. Results highlight typically a better performance of the combination of MC with suitably-constructed baseline estimates with respect to the baselines alone. Potential applications of our analysis arise in the prediction of currently missing elements of matrices of annual CO $$_2$$ 2 emission levels and in the construction of counterfactuals, useful to estimate the effects of policy changes able to influence the annual CO $$_2$$ 2 emission levels of specific sectors in selected countries.

Abstract: We extend the concept of well-posedness to the split equilibrium problem and establish Furi–Vignoli-type characterizations for the well-posedness. We prove that the well-posedness of the split equilibrium problem is equivalent to the existence and uniqueness of its solution under certain assumptions on the bifunctions involved. We also characterize the generalized well-posedness of the split equilibrium problem via the Kuratowski measure of noncompactness. We illustrate our theoretical results by several examples.

Abstract: Abstract Constrained Bayesian optimization optimizes a black-box objective function subject to black-box constraints. For simplicity, most existing works assume that multiple constraints are independent. To ask, when and how does dependence between constraints help? , we remove this assumption and implement probability of feasibility with dependence (Dep-PoF) by applying multiple output Gaussian processes (MOGPs) as surrogate models and using expectation propagation to approximate the probabilities. We compare Dep-PoF and the independent version PoF. We propose two new acquisition functions incorporating Dep-PoF and test them on synthetic and practical benchmarks. Our results are largely negative: incorporating dependence between the constraints does not help much. Empirically, incorporating dependence between constraints may be useful if: (i) the solution is on the boundary of the feasible region(s) or (ii) the feasible set is very small. When these conditions are satisfied, the predictive covariance matrix from the MOGP may be poorly approximated by a diagonal matrix and the off-diagonal matrix elements may become important. Dep-PoF may apply to settings where (i) the constraints and their dependence are totally unknown and (ii) experiments are so expensive that any slightly better Bayesian optimization procedure is preferred. But, in most cases, Dep-PoF is indistinguishable from PoF.

Abstract: Abstract We consider a lot-sizing problem with set-ups where the demands are uncertain, and propose a novel approach to evaluate the inventory costs. An interval uncertainty is assumed for the demands. Between two consecutive production periods, the adversary chooses to set the demand either to its higher value or to its lower value in order to maximize the inventory (holding or backlog) costs. A mixed-integer model is devised and a column-and-row generation algorithm is proposed. Computational tests based on random generated instances are conducted to evaluate the model, the decomposition algorithm, and compare the structure of the solutions from the robust model with those from the deterministic model.

Abstract: Abstract The aim of this paper is to extend some notions of proper minimality from vector optimization to set optimization. In particular, we focus our attention on the concepts of Henig and Geoffrion proper minimality, which are well-known in vector optimization. We introduce a generalization of both of them in set optimization with finite dimensional spaces, by considering also a special class of polyhedral ordering cone. In this framework, we prove that these two notions are equivalent, as it happens in the vector optimization context, where this property is well-known. Then, we study a characterization of these proper minimal points through nonlinear scalarization, without considering convexity hypotheses.