Given a connected and undirected graph G, the degree preserving spanning tree problem (DPSTP) asks for a spanning tree of G with the maximum number of vertices with the same degree in the tree and in G. These are called full degree vertices. We introduce integer programming formulations, valid inequalities and four exact solution approaches based on different formulations. Two branch-and-bound ...

In this paper we explore the possibility of applying the notions of Recoverable Robustness and Price of Recoverability (introduced by [5]) to railway rolling stock planning, being interested in recoverability measures that can be computed in practice, thereby evaluating the robustness of rolling stock schedules. In order to lower bound the Price of Recoverability for any set of recovery algorit...

We present an algorithmic framework for integrating solution methods that is based on search, inference, and relaxation and their interactions. We show that the following are special cases: branch and cut, CP domain splitting with propagation, popular global optimization methods, DPL methods for SAT with conflict clauses, Benders decomposition and other nogood-based methods, partial-order dynam...

is eventually found and the method terminates. As convergence may require a large amount of computing time for hard instances, the method unsatisfactory from a heuristic point of view. Proximity Search is a recently-proposed heuristic paradigm in which the problem at hand is modified and iteratively solved with the aim of producing a sequence of improving feasible solutions. As such, Proximity ...

Logic-based Benders decomposition (BD) extends classic BD by allowing more complex subproblems with integral variables. Metaheuristics like variable neighborhood search are becoming useful here for faster solving the subproblems’ inference duals in order to separate approximate Benders cuts. After performing such a purely heuristic BD approach, we continue by exactly verifying and possibly corr...

We study a class of two-stage stochastic integer programs with general integer vari4 ables in both stages and finitely many realizations of the uncertain parameters. Based on Benders’ 5 method, we propose a decomposition algorithm that utilizes Gomory cuts in both stages. The Go6 mory cuts for the second-stage scenario subproblems are parameterized by the first-stage decision 7 variables, i.e.,...

We adopt Benders’ decomposition algorithm to solve scenariobased Stochastic Constraint Programs (SCPs) with linear recourse. Rather than attempting to solve SCPs via a monolithic model, we show that one can iteratively solve a collection of smaller sub-problems and arrive at a solution to the entire problem. In this approach, decision variables corresponding to the initial stage and linear reco...

We present the mean value cross decomposition algorithm and its simple enhancement for the two-stage stochastic linear programming problem with complete recourse. The mean value cross decomposition algorithm employs the Benders (primal) subproblems as in the so-called “L-shaped” method but eliminates the Benders master problem for generating the next trial first-stage solution, relying instead ...

We formulate a two-stage stochastic integer program to determine an optimal schedule for jobs requiring multiple classes of resources under uncertain processing times, due dates, resource consumption and availabilities. We allow temporary resource capacity expansion for a penalty. Potential applications of this model include team scheduling problems that arise in service industries such as engi...

We adopt Benders’ decomposition algorithm to solve scenariobased Stochastic Constraint Programs (SCPs) with linear recourse. Rather than attempting to solve SCPs via a monolithic model, we show that one can iteratively solve a collection of smaller sub-problems and arrive at a solution to the entire problem. In this approach, decision variables corresponding to the initial stage and linear reco...