It is well known that the standard (linear) knapsack problem can be solved exactly by dynamic programming in O(nc) time, where n is the number of items and c is the capacity of the knapsack. The quadratic knapsack problem, on the other hand, is NP-hard in the strong sense, which makes it unlikely that it … Read more
The Steiner Traveling Salesman Problem (STSP) is a variant of the Traveling Salesman Problem (TSP) that is particularly suitable when dealing with sparse networks, such as road networks. The standard integer programming formulation of the STSP has an exponential number of constraints, just like the standard formulation of the TSP. On the other hand, there … Read more
We are interested in methods to solve mixed-integer nonlinear optimal control problems (MIOCPs) constrained by ordinary di erential equations and combinatorial constraints on some of the control functions. To solve these problems we use a rst discretize, then opti- mize approach to get a specially structured mixed-integer nonlinear program (MINLP). We decompose this MINLP into an … Read more
We present integer programming models of the service network design problem faced by less-than-truckload (LTL) freight transportation carriers, and a solution approach for the large-scale instances that result in practical applications. To accurately represent freight consolidation opportunities, the models use a fine discretization of time. Furthermore, the models simultaneously route freight and empty trailers, and … Read more
The feasibility pump is a recent, highly successful heuristic for general mixed integer linear programming problems. We show that the feasibility pump heuristic can be interpreted as a discrete version of the proximal point algorithm. In doing so, we extend and generalize some of the fundamental results in this area to provide new supporting theory. … Read more
The Feasibility Pump (FP) has proved to be an effective method for finding feasible solutions to mixed integer programming problems. FP iterates between a rounding procedure and a projection procedure, which together provide a sequence of points alternating between LP feasible but fractional solutions, and integer but LP relaxed infeasible solutions. The process attempts to … Read more
In this paper we examine the impact of using the Sherali-Adams procedure on highly symmetric integer programming problems. Linear relaxations of the extended formulations generated by Sherali-Adams can be very large, containing on the order of n choose d many variables for the level-d closure. When large amounts of symmetry are present in the problem … Read more
The Capacitated Arc Routing Problem (CARP) stands among the hardest combinatorial problems to solve or to find high quality solutions. This becomes even more true when dealing with large instances. This paper investigates methods to improve on lower and upper bounds of instances on graphs with over two hundred vertices and three hundred edges, dimensions … Read more
This paper introduces interdiction branching, a new branching method for binary integer programs that is designed to overcome the difficulties encountered in solving problems for which branching on variables is inherently weak. Unlike traditional methods, selection of the disjunction in interdiction branching takes into account the best feasible solution found so far. In particular, the … Read more
We study solution approaches for the design of reliably connected networks. Speci fically, given a network with arcs that may fail at random, the goal is to select a minimum cost subset of arcs such the probability that a connectivity requirement is satis ed is at least 1-\epsilon, where \epsilon is a risk tolerance. We consider two … Read more