We present an algorithm for finding the complete Pareto frontier of biobjective integer programming problems. The method is based on the solution of a finite number of integer programs. The feasible sets of the integer programs are built from the original feasible set, by adding cuts that separate efficient solutions. Providing the existence of an … Read more
This paper presents a new method for identifying critical nodes in planar networks. We propose an efficient method to evaluate the quality of solutions by using special properties of planar networks. It enables us to develop a computationally efficient heuristic algorithm for the problem. The proposed algorithm assisted on randomly generated planar networks. The experimental … Read more
We study a robust monopoly pricing problem with a minimax regret objective, where a seller endeavors to sell multiple goods to a single buyer, only knowing that the buyer’s values for the goods range over a rectangular uncertainty set. We interpret this pricing problem as a zero-sum game between the seller, who chooses a selling … Read more
The classic version of the Inventory Routing Problem considers a system with one supplier that manages the stock level of a set of customers. The supplier defines when and how much products to supply and how to combine customers in routes while minimizing storage and transportation costs. We present a new version of this problem … Read more
In the last decades, research on emergency traffic management has received high attention from the operations research community and many pioneer researchers have established it as one of the most fertile research areas. We consider the computationally hard flows over time problems from wider perspective including flow/time dependent attributes (dynamic flows), a possibility of flows … Read more
In the arXiv paper [arXiv:1712.07761] from December 2017 we presented a convergent direct transcription method for optimal control problems. In the present paper we present a significantly generalized convergence theory in succinct form. Therein, we replace strong assumptions that we had formerly made on local uniqueness of the solution, and on differentiability of a particular … Read more
Motivated by Chubanov’s projection-based method for linear feasibility problems [Chubanov2015], a projection and rescaling algorithm for the conic feasibility problem \[ find \; x\in L\bigcap \Omega \] is proposed in [Pena2016], where $L$ and $\Omega$ are respectively a linear subspace and the interior of a symmetric cone in a finitely dimensional vector space $V$. When … Read more
State-of-the-art solvers for mixed integer programs (MIP) govern a variety of algorithmic components. Ideally, the solver adaptively learns to concentrate its computational budget on those components that perform well on a particular problem, especially if they are time consuming. We focus on three such algorithms, namely the classes of large neighborhood search and diving heuristics … Read more
Chvatal (1980) has given a simple example of a knapsack problem for which a branch-and-bound algorithm using domination and linear relaxations to eliminate subproblems will use an exponential number of steps in the best case. In this short note it is shown that Chvatals result remains true when the LP relaxation is replaced with a … Read more
Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthormalization methods are derived, the necessary quantities occurring in the theoretical bounds estimated and new practical algorithms derived. Numerical experiments suggest that the new methods have significant … Read more