This paper uses the L1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (WDSND) vectorsof a multi-objective mixed integer linear programming (MOMILP) problem.The proposed method generalizes the proposed approach by Tohidi and Razavyan[Tohidi G., S. Razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

Post-hoc explanation methods for machine learning models have been widely used to support decision-making. One of the popular is Counterfactual Explanation (CE), also known as Actionable Recourse, which provides a user with perturbation vector features that alters prediction result. Given vector, can interpret it an "action" obtaining one's desired decision In practice, however, showing only of...

In this paper, we propose an algorithm base on decomposition technique for solvingthe mixed integer linear multiplicative-linear bilevel problems. In actuality, this al-gorithm is an application of the algorithm given by G. K. Saharidis et al for casethat the rst level objective function is linear multiplicative. We use properties ofquasi-concave of bilevel programming problems and decompose th...

Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [4], [11]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we ar...

Virtual power plant (VPP) is an effective approach to aggregate distributed generation resources under a central control. This paper introduces a mixed-integer linear programming model for optimal scheduling of the internal resources of a large scale VPP in order to maximize its profit. The proposed model studies the effect of a demand response (DR) program on the scheduling of the VPP. The pro...