Willem-Jan van Hoeve We present column elimination as a general framework for solving (large-scale) integer programming problems. In this framework, solutions are represented compactly as paths in a directed acyclic graph. Column elimination starts with a relaxed representation, that may contain infeasible paths, and solves a constrained network flow over the graph to find a solution. It then … Read more
This tutorial provides an introduction to the use of decision diagrams for solving discrete optimization problems. A decision diagram is a graphical representation of the solution space, representing decisions sequentially as paths from a root node to a target node. By merging isomorphic subgraphs (or equivalent subproblems), decision diagrams can compactly represent an exponential solution … Read more
We introduce a column elimination procedure for the capacitated vehicle routing problem. Our procedure maintains a decision diagram to represent a relaxation of the set of feasible routes, over which we define a constrained network flow. The optimal solution corresponds to a collection of paths in the decision diagram and yields a dual bound. The … Read more
For vehicle routing problems, strong dual bounds on the optimal value are needed to develop scalable exact algorithms, as well as to evaluate the performance of heuristics. In this work, we propose an iterative algorithm to compute dual bounds motivated by connections between decision diagrams (DDs) and dynamic programming (DP) models used for pricing in … Read more
We introduce an iterative framework for solving graph coloring problems using decision diagrams. The decision diagram compactly represents all possible color classes, some of which may contain edge conflicts. In each iteration, we use a constrained minimum network flow model to compute a lower bound and identify conflicts. Infeasible color classes associated with these conflicts … Read more
This paper develops an exact solution algorithm for the Multiple Sequence Alignment (MSA) problem. In the first step, we design a dynamic programming model and use it to construct a novel Multi-valued Decision Diagrams (MDD) representation of all pairwise sequence alignments (PSA). PSA MDDs are then synchronized using side constraints to model the MSA problem … Read more
Many cities have to cope with annual snowfall, but are struggling to manage their snow plowing activities efficiently. Despite the fact that winter road maintenance has been the subject of many research papers over the last 3 decades, very few practical decision support systems have been developed to deal with the complex decision problems involved … Read more
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
As an alternative to traditional integer programming (IP), decision diagrams (DDs) provide a new solution technology for discrete problems based on their combinatorial structure and dynamic programming representation. While the literature mainly focuses on the competitive aspects of DDs as a stand-alone solver, we investigate their complementary role by studying IP techniques that can be … Read more
We propose a constraint programming approach for the optimization of inventory routing in the liquefied natural gas industry. We present two constraint programming models that rely on a disjunctive scheduling representation of the problem. We also propose an iterative search heuristic to generate good feasible solutions for these models. Computational results on a set of … Read more