This paper presents a generic reformulation framework for binary integer programs (BIPs) that does not impose additional specifications on the objective function or constraints. To enable this generality, we introduce a set system approximation theory designed to identify the tightest inner and outer approximations for any binary solution space using special types of set systems. … Read more
\(\) We consider an \(n\)-variate monomial function that is restricted both in value by lower and upper bounds and in domain by two homogeneous linear inequalities. Such functions are building blocks of several problems found in practical applications, and that fall under the class of Mixed Integer Nonlinear Optimization. We show that the upper envelope … Read more
In this paper, we study Adjustable Robust Optimization (ARO) problems with discrete uncertainty. Under a very general modeling framework, we show that such two-stage robust problems can be exactly reformulated as ARO problems with objective uncertainty only. This reformulation is valid with and without the fixed recourse assumption and is not limited to continuous wait-and-see … Read more
In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and … Read more
Real-world problems are often nonconvex and involve integer variables, representing vexing challenges to be tackled using state-of-the-art solvers. We introduce a mathematical identity-based reformulation of a class of polynomial integer nonlinear optimization (PINLO) problems using a technique that linearizes polynomial functions of separable and bounded integer variables of any degree. We also introduce an alternative … Read more
Knowledge-based determination of the best-possible experimental setups for nanoparticle design is highly challenging. Additionally, such processes are accompanied by noticeable uncertainties. Therefore, protection against these uncertainties is needed. Robust optimization helps determining such best possible processes. The latter guarantees quality requirements regardless of how the uncertainties, e.g. with regard to variations in raw materials, heat … Read more
This paper studies a two-stage distributionally robust stochastic linear program under the type-∞ Wasserstein ball by providing sufficient conditions under which the program can be efficiently computed via a tractable convex program. By exploring the properties of binary variables, the developed reformulation techniques are extended to those with mixed binary random parameters. The main tractable … Read more
In this paper, a reformulation that was proposed for a knapsack problem has been extended to single and bi-objective linear integer programs. A further reformulation by adding an upper bound constraint for a knapsack problem is also proposed and extended to the bi-objective case. These reformulations significantly reduce the number of branch and bound iterations … Read more
Team as a Service (TaaS) is a new outsourcing service that enables on-demand creation and management of distributed teams for fast growing companies. The companies that use the TaaS model form a team according to the needs of a given project and provide managerial service throughout. Motivated by this new application, we study the Team … Read more
In this paper we consider a particular method of clustering for graphs, namely the modularity density maximization. We propose a hierarchical divisive heuristic which works by splitting recursively a cluster into two new clusters by maximizing the modularity density, and we derive four reformulations for the mathematical programming model used to obtain the optimal splitting. … Read more