We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials t...

In this paper, a special class of redundancy optimization problem with fuzzy random variables is presented. In this model, fuzzy random lifetimes are considered as basic parameters and the Er-expected of system lifetime is used as a major type of system performance. Then a redundancy optimization problem is formulated as a binary integer programming model. Furthermore, illustrative numerical ex...

A finite test set for an integer optimization problem enables us to verify whether a feasible point attains the global optimum. We establish in this paper several general results that apply to integer optimization problems with nonlinear objective functions.

Robust supplier selection problem, in a scenario-based approach has been proposed, when the demand and exchange rates are subject to uncertainties. First, a deterministic multi-objective mixed integer linear programming is developed; then, the robust counterpart of the proposed mixed integer linear programming is presented using the recent extension in robust optimization theory. We discuss dec...

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...

Endogenous, i.e. decision-dependent, uncertainty has received increased interest in the stochastic programming community. In robust optimization context, however, it rarely been considered. This work addresses multistage mixed-integer with decision-dependent sets. The proposed framework allows us to consider both continuous and integer recourse, including recourse decisions that affect set. We ...

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Abstract Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification nonlinear dynamics (SINDy) framework, powered by heuristic regression methods, has become dominant tool for learning parsimonious models. We propose an exact formulation SINDy using mixed-integer optimization (MI...

Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method produce solutions that are immunized against uncertainty. The main focus in discrete been on analysis and solution of one- or two-stage problems, where decision maker limited options reacting additional knowledge gained after parts have fixed. Due it...