The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and … Read more
Mathematical programming formulation to identify the optimal value function of a negative Markov decision process (MDP) is non-convex, non-smooth, and computationally intractable. Also note that other well-known solution methods of MDP do not work properly for a negative MDP. More specifically, the policy iteration diverges, and the value iteration converges but does not provide an … Read more
Circle packing problems are a class of packing problems which attempt to pack a given set of circles into a container with no overlap. In this paper, we focus on the circle packing problem proposed by L{\’o}pez et.al. The problem is to pack circles of unequal size into a fixed size circular container, so as … Read more
Thanks to the rapidly advancing development of (commercial) MILP software and hardware components, pseudo-polynomial formulations have been established as a powerful tool for solving cutting and packing problems in recent years. In this paper, we focus on the one-dimensional skiving stock problem (SSP), where a given inventory of small items has to be recomposed to … Read more
Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid constraints. So far, these techniques have mostly been studied independently: primal heuristics under the aspect of finding high-quality feasible solutions early during the … Read more
The optimal restoration problem lies at the foundation of the evaluation and improvement of resilience in power systems. In this paper we present a scalable decomposition algorithm, based on the integer L-shaped method, for solving this problem for realistic power systems. The algorithm works by partitioning the problem into a master problem and a slave … Read more
In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ one of the most effective and recently developed criterion space search algorithms, the so-called KSA, during our study. This algorithm computes all nondominated points of … Read more
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an L0 constraint restricting the support of the estimators is a challenging non-convex optimization problem. In this paper, we derive new strong convex relaxations for sparse regression. These relaxations are based … Read more
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and … Read more
Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn … Read more